%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SWW293+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 18:06:41 EDT 2024 % Result : Theorem 19.23s 19.02s % Output : CNFRefutation 19.28s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SWW293+1 : TPTP v8.2.0. Released v5.2.0. % 0.03/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.12/0.34 % Computer : n015.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Wed Jun 19 04:24:54 EDT 2024 % 0.12/0.34 % CPUTime : % 0.43/0.62 start to proof:theBenchmark % 18.76/18.86 %------------------------------------------- % 18.76/18.86 % File :CSE---1.7 % 18.76/18.86 % Problem :theBenchmark % 18.76/18.86 % Transform :cnf % 18.76/18.86 % Format :tptp:raw % 18.76/18.86 % Command :java -jar mcs_scs.jar %d %s % 18.76/18.86 % 18.76/18.86 % Result :Theorem 1.690000s % 18.76/18.86 % Output :CNFRefutation 1.690000s % 18.76/18.86 %------------------------------------------- % 18.76/18.87 %------------------------------------------------------------------------------ % 18.76/18.87 % File : SWW293+1 : TPTP v8.2.0. Released v5.2.0. % 18.76/18.87 % Domain : Software Verification % 18.76/18.87 % Problem : Hoare's Logic with Procedures 434709, 5000 axioms selected % 18.76/18.87 % Version : Especial. % 18.76/18.87 % English : % 18.76/18.87 % 18.76/18.87 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day % 18.76/18.87 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe % 18.78/18.87 % Source : [Bla11] % 18.78/18.87 % Names : hoare_434709.5000.p [Bla11] % 18.78/18.87 % 18.78/18.87 % Status : ContradictoryAxioms % 18.78/18.87 % Rating : 0.67 v8.2.0, 0.64 v8.1.0, 0.72 v7.4.0, 0.77 v7.3.0, 0.76 v7.1.0, 0.70 v7.0.0, 0.80 v6.4.0, 0.77 v6.3.0, 0.75 v6.2.0, 0.84 v6.1.0, 0.87 v5.5.0, 0.85 v5.4.0, 0.89 v5.3.0, 0.93 v5.2.0 % 18.78/18.87 % Syntax : Number of formulae : 5205 (1710 unt; 0 def) % 18.78/18.87 % Number of atoms : 12582 (4543 equ) % 18.78/18.87 % Maximal formula atoms : 13 ( 2 avg) % 18.78/18.87 % Number of connectives : 8476 (1099 ~; 158 |; 712 &) % 18.78/18.87 % ( 880 <=>;5627 =>; 0 <=; 0 <~>) % 18.78/18.87 % Maximal formula depth : 22 ( 6 avg) % 18.78/18.87 % Maximal term depth : 19 ( 2 avg) % 18.78/18.87 % Number of predicates : 142 ( 141 usr; 1 prp; 0-7 aty) % 18.78/18.87 % Number of functors : 397 ( 397 usr; 63 con; 0-10 aty) % 18.78/18.87 % Number of variables : 16764 (16632 !; 132 ?) % 18.78/18.87 % SPC : FOF_CAX_RFO_SEQ % 18.78/18.87 % 18.78/18.87 % Comments : This file was generated by Isabelle (most likely Sledgehammer) % 18.78/18.87 % 2011-03-01 11:24:42 % 18.78/18.87 %------------------------------------------------------------------------------ % 18.78/18.87 %----Relevant facts (4983) % 18.78/18.87 fof(fact_ext,axiom, % 18.78/18.87 ! [V_g_2,V_f_2] : % 18.78/18.87 ( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) % 18.78/18.87 => V_f_2 = V_g_2 ) ). % 18.78/18.87 % 18.78/18.87 fof(fact_triple_Oinject,axiom, % 18.78/18.87 ! [V_fun2_H_2,V_com_H_2,V_fun1_H_2,V_fun2_2,V_com_2,V_fun1_2,T_b] : % 18.78/18.87 ( hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_fun1_2),V_com_2),V_fun2_2) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_fun1_H_2),V_com_H_2),V_fun2_H_2) % 18.78/18.87 <=> ( V_fun1_2 = V_fun1_H_2 % 18.78/18.87 & V_com_2 = V_com_H_2 % 18.78/18.87 & V_fun2_2 = V_fun2_H_2 ) ) ). % 18.78/18.87 % 18.78/18.87 fof(fact_triple_Osize_I1_J,axiom, % 18.78/18.87 ! [V_fun2_2,V_com_2,V_fun1_2,V_fa_2,T_b] : c_Hoare__Mirabelle_Otriple_Otriple__size(T_b,V_fa_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_fun1_2),V_com_2),V_fun2_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 18.78/18.87 % 18.78/18.87 fof(fact_triple_Osize_I2_J,axiom, % 18.78/18.87 ! [V_fun2_2,V_com_2,V_fun1_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_fun1_2),V_com_2),V_fun2_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 18.78/18.87 % 18.78/18.87 fof(fact_triple_Orecs,axiom, % 18.78/18.87 ! [V_fun2_2,V_com_2,V_fun1_2,V_f1_2,T_b,T_c] : c_Hoare__Mirabelle_Otriple_Otriple__rec(T_c,T_b,V_f1_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_fun1_2),V_com_2),V_fun2_2)) = hAPP(hAPP(hAPP(V_f1_2,V_fun1_2),V_com_2),V_fun2_2) ). % 18.78/18.87 % 18.78/18.87 fof(fact_triple_Osimps_I2_J,axiom, % 18.78/18.87 ! [V_fun2_2,V_com_2,V_fun1_2,V_f1_2,T_b,T_c] : c_Hoare__Mirabelle_Otriple_Otriple__case(T_c,T_b,V_f1_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_fun1_2),V_com_2),V_fun2_2)) = hAPP(hAPP(hAPP(V_f1_2,V_fun1_2),V_com_2),V_fun2_2) ). % 18.78/18.87 % 18.78/18.87 fof(fact_com_Osimps_I6_J,axiom, % 18.78/18.87 ! [V_pname_H_2,V_pname_2] : % 18.78/18.87 ( hAPP(c_Com_Ocom_OBODY,V_pname_2) = hAPP(c_Com_Ocom_OBODY,V_pname_H_2) % 18.78/18.87 <=> V_pname_2 = V_pname_H_2 ) ). % 18.78/18.87 % 18.78/18.87 fof(fact_zero__reorient,axiom, % 18.78/18.87 ! [V_x_2,T_b] : % 18.78/18.87 ( class_Groups_Ozero(T_b) % 18.78/18.87 => ( c_Groups_Ozero__class_Ozero(T_b) = V_x_2 % 18.78/18.87 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 18.78/18.87 % 18.78/18.87 fof(fact_triple__valid__def2,axiom, % 18.78/18.87 ! [V_Qa_2,V_c_2,V_Pa_2,V_n_2,T_b] : % 18.78/18.87 ( c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),V_c_2),V_Qa_2)) % 18.78/18.87 <=> ! [B_Z,B_s] : % 18.78/18.87 ( hBOOL(hAPP(hAPP(V_Pa_2,B_Z),B_s)) % 18.78/18.87 => ! [B_s_H] : % 18.78/18.87 ( c_Natural_Oevaln(V_c_2,B_s,V_n_2,B_s_H) % 18.78/18.87 => hBOOL(hAPP(hAPP(V_Qa_2,B_Z),B_s_H)) ) ) ) ). % 18.78/18.88 % 18.78/18.88 fof(fact_com_Osize_I7_J,axiom, % 18.78/18.88 ! [V_pname] : c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY,V_pname)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 18.78/18.88 % 18.78/18.88 fof(fact_com_Osize_I15_J,axiom, % 18.78/18.88 ! [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) ). % 18.78/18.88 % 18.78/18.88 fof(fact_triple_Oexhaust,axiom, % 18.78/18.88 ! [T_b,V_y_2] : % 18.78/18.88 ~ ! [B_fun1,B_com,B_fun2] : V_y_2 != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),B_fun1),B_com),B_fun2) ). % 18.78/18.88 % 18.78/18.88 fof(fact_bool_Osize_I1_J,axiom, % 18.78/18.88 c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 18.78/18.88 % 18.78/18.88 fof(fact_bool_Osize_I2_J,axiom, % 18.78/18.88 c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 18.78/18.88 % 18.78/18.88 fof(fact_bool_Osize_I4_J,axiom, % 18.78/18.88 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 18.78/18.88 % 18.78/18.88 fof(fact_bool_Osize_I3_J,axiom, % 18.78/18.88 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 18.78/18.88 % 18.78/18.88 fof(fact_nat_Osize_I1_J,axiom, % 18.78/18.88 c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 18.78/18.88 % 18.78/18.88 fof(fact_com_Osize_I9_J,axiom, % 18.78/18.88 hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 18.78/18.88 % 18.78/18.88 fof(fact_com_Osize_I1_J,axiom, % 18.78/18.88 c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 18.78/18.88 % 18.78/18.88 fof(fact_nat_Osize_I3_J,axiom, % 18.78/18.88 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) ). % 18.78/18.88 % 18.78/18.88 fof(fact_com_Osize_I8_J,axiom, % 18.78/18.88 ! [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) ). % 18.78/18.88 % 18.78/18.88 fof(fact_com_Osize_I16_J,axiom, % 18.78/18.88 ! [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) ). % 18.78/18.88 % 18.78/18.88 fof(fact_com_Osize_I2_J,axiom, % 18.78/18.88 ! [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) ). % 18.78/18.88 % 18.78/18.88 fof(fact_com_Osize_I10_J,axiom, % 18.78/18.88 ! [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) ). % 18.78/18.88 % 18.78/18.88 fof(fact_com_Osimps_I70_J,axiom, % 18.78/18.88 ! [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_b] : c_Com_Ocom_Ocom__case(T_b,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) ). % 18.78/18.88 % 18.78/18.88 fof(fact_semigroup_Oassoc,axiom, % 18.78/18.88 ! [V_c_2,V_b_2,V_a_2,V_f_2,T_b] : % 18.78/18.88 ( c_Groups_Osemigroup(T_b,V_f_2) % 18.78/18.88 => hAPP(hAPP(V_f_2,hAPP(hAPP(V_f_2,V_a_2),V_b_2)),V_c_2) = hAPP(hAPP(V_f_2,V_a_2),hAPP(hAPP(V_f_2,V_b_2),V_c_2)) ) ). % 18.78/18.88 % 18.78/18.88 fof(fact_com_Osimps_I8_J,axiom, % 18.78/18.88 ! [V_fun_H_2,V_vname_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OAss(V_vname_H_2,V_fun_H_2) ). % 18.78/18.88 % 18.78/18.88 fof(fact_com_Osimps_I20_J,axiom, % 18.78/18.88 ! [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) ). % 18.78/18.88 % 18.78/18.88 fof(fact_com_Osimps_I9_J,axiom, % 18.78/18.88 ! [V_fun_H_2,V_vname_H_2] : c_Com_Ocom_OAss(V_vname_H_2,V_fun_H_2) != c_Com_Ocom_OSKIP ). % 18.78/18.88 % 18.78/18.88 fof(fact_com_Osimps_I32_J,axiom, % 18.78/18.88 ! [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) ). % 18.78/18.88 % 18.78/18.88 fof(fact_com_Osimps_I21_J,axiom, % 18.78/18.88 ! [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 ). % 18.78/18.88 % 18.78/18.88 fof(fact_com_Osimps_I33_J,axiom, % 18.78/18.88 ! [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) ). % 18.78/18.88 % 18.78/18.88 fof(fact_com_Osimps_I1_J,axiom, % 18.78/18.88 ! [V_fun_H_2,V_vname_H_2,V_fun_2,V_vname_2] : % 18.78/18.88 ( c_Com_Ocom_OAss(V_vname_2,V_fun_2) = c_Com_Ocom_OAss(V_vname_H_2,V_fun_H_2) % 18.78/18.88 <=> ( V_vname_2 = V_vname_H_2 % 18.78/18.88 & V_fun_2 = V_fun_H_2 ) ) ). % 18.78/18.88 % 18.78/18.88 fof(fact_com_Osimps_I7_J,axiom, % 18.78/18.88 ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_fun_2,V_pname_2,V_vname_2] : % 18.78/18.88 ( 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) % 18.78/18.88 <=> ( V_vname_2 = V_vname_H_2 % 18.78/18.88 & V_pname_2 = V_pname_H_2 % 18.78/18.88 & V_fun_2 = V_fun_H_2 ) ) ). % 18.78/18.88 % 18.78/18.88 fof(fact_com_Osimps_I64_J,axiom, % 18.78/18.88 ! [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_b] : c_Com_Ocom_Ocom__case(T_b,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 ). % 18.78/18.88 % 18.78/18.88 fof(fact_com_Osimps_I65_J,axiom, % 18.78/18.88 ! [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_b] : c_Com_Ocom_Ocom__case(T_b,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) ). % 18.78/18.88 % 18.78/18.88 fof(fact_com_Osimps_I71_J,axiom, % 18.78/18.88 ! [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_b] : c_Com_Ocom_Ocom__case(T_b,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) ). % 18.78/18.88 % 18.78/18.88 fof(fact_nat__size,axiom, % 18.78/18.88 ! [V_n] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_n) = V_n ). % 18.78/18.88 % 18.78/18.88 fof(fact_com_Osimps_I31_J,axiom, % 18.78/18.88 ! [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) ). % 18.78/18.88 % 18.78/18.88 fof(fact_com_Osimps_I30_J,axiom, % 18.78/18.88 ! [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) ). % 18.78/18.88 % 18.78/18.88 fof(fact_com_Osimps_I62_J,axiom, % 18.78/18.88 ! [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) ). % 18.78/18.88 % 18.78/18.88 fof(fact_com_Osimps_I63_J,axiom, % 18.78/18.88 ! [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) ). % 18.78/18.88 % 18.78/18.88 fof(fact_com_Osimps_I18_J,axiom, % 18.78/18.88 ! [V_pname_H] : c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,V_pname_H) ). % 18.78/18.88 % 18.78/18.88 fof(fact_com_Osimps_I19_J,axiom, % 18.78/18.88 ! [V_pname_H] : hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OSKIP ). % 18.78/18.88 % 18.78/18.88 fof(fact_evaln__elim__cases_I1_J,axiom, % 18.78/18.88 ! [V_t,V_n,V_s] : % 18.78/18.88 ( c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_t) % 18.78/18.88 => V_t = V_s ) ). % 18.78/18.88 % 18.78/18.88 fof(fact_evaln_OSkip,axiom, % 18.78/18.88 ! [V_n,V_s] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_s) ). % 18.78/18.88 % 18.78/18.88 fof(fact_evaln_Oequations_I1_J,axiom, % 18.78/18.88 ! [V_a2,V_a1] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_a1,V_a2,V_a1) ). % 18.78/18.88 % 18.78/18.88 fof(fact_WTs__elim__cases_I8_J,axiom, % 18.78/18.88 ! [V_a_2,V_Pa_2,V_X_2] : % 18.78/18.88 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_X_2,V_Pa_2,V_a_2))) % 18.78/18.88 => hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_Pa_2))) ) ). % 18.78/18.88 % 18.78/18.88 fof(fact_WT_OCall,axiom, % 18.78/18.88 ! [V_a_2,V_X_2,V_pna_2] : % 18.78/18.88 ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pna_2))) % 18.78/18.88 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_X_2,V_pna_2,V_a_2))) ) ). % 18.78/18.88 % 18.78/18.88 fof(fact_WT_Oequations_I8_J,axiom, % 18.78/18.88 ! [V_a3_2,V_a1_2,V_a2_2] : % 18.78/18.88 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_a2_2,V_a1_2,V_a3_2))) % 18.78/18.88 <=> hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_a1_2))) ) ). % 18.78/18.88 % 18.78/18.88 fof(fact_evaln__elim__cases_I2_J,axiom, % 18.78/18.88 ! [V_t_2,V_n_2,V_s_2,V_a_2,V_X_2] : % 18.78/18.88 ( c_Natural_Oevaln(c_Com_Ocom_OAss(V_X_2,V_a_2),V_s_2,V_n_2,V_t_2) % 18.78/18.88 => V_t_2 = hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s_2),V_X_2),hAPP(V_a_2,V_s_2)) ) ). % 18.78/18.88 % 18.78/18.88 fof(fact_evaln_OAssign,axiom, % 18.78/18.88 ! [V_n_2,V_s_2,V_a_2,V_X_2] : 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))) ). % 18.78/18.88 % 18.78/18.88 fof(fact_com_Orecs_I1_J,axiom, % 18.78/18.88 ! [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_b] : c_Com_Ocom_Ocom__rec(T_b,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 ). % 18.78/18.88 % 18.78/18.88 fof(fact_com_Orecs_I8_J,axiom, % 18.78/18.88 ! [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_b] : c_Com_Ocom_Ocom__rec(T_b,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) ). % 18.78/18.88 % 18.78/18.88 fof(fact_com_Orecs_I2_J,axiom, % 18.78/18.88 ! [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_b] : c_Com_Ocom_Ocom__rec(T_b,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) ). % 18.78/18.88 % 18.78/18.88 fof(fact_com_Osimps_I67_J,axiom, % 18.78/18.88 ! [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_b] : c_Com_Ocom_Ocom__case(T_b,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) ). % 18.78/18.88 % 18.78/18.88 fof(fact_evaln_OSemi,axiom, % 18.78/18.88 ! [V_s2,V_c1,V_s1,V_n,V_s0,V_c0] : % 18.78/18.88 ( c_Natural_Oevaln(V_c0,V_s0,V_n,V_s1) % 18.78/18.88 => ( c_Natural_Oevaln(V_c1,V_s1,V_n,V_s2) % 18.78/18.88 => c_Natural_Oevaln(c_Com_Ocom_OSemi(V_c0,V_c1),V_s0,V_n,V_s2) ) ) ). % 18.78/18.88 % 18.78/18.88 fof(fact_WTs__elim__cases_I4_J,axiom, % 18.78/18.88 ! [V_c2,V_c1] : % 18.78/18.88 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_c1,V_c2))) % 18.78/18.88 => ~ ( hBOOL(hAPP(c_Com_OWT,V_c1)) % 18.78/18.88 => ~ hBOOL(hAPP(c_Com_OWT,V_c2)) ) ) ). % 18.78/18.88 % 18.78/18.88 fof(fact_WT_OSemi,axiom, % 18.78/18.88 ! [V_c1,V_c0] : % 18.78/18.88 ( hBOOL(hAPP(c_Com_OWT,V_c0)) % 18.78/18.88 => ( hBOOL(hAPP(c_Com_OWT,V_c1)) % 18.78/18.88 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_c0,V_c1))) ) ) ). % 18.78/18.88 % 18.78/18.88 fof(fact_com_Orecs_I4_J,axiom, % 18.78/18.88 ! [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_b] : c_Com_Ocom_Ocom__rec(T_b,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_b,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_b,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)) ). % 18.78/18.88 % 18.78/18.88 fof(fact_com_Osimps_I3_J,axiom, % 18.78/18.88 ! [V_com2_H_2,V_com1_H_2,V_com2_2,V_com1_2] : % 18.78/18.88 ( c_Com_Ocom_OSemi(V_com1_2,V_com2_2) = c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2) % 18.78/18.88 <=> ( V_com1_2 = V_com1_H_2 % 18.78/18.88 & V_com2_2 = V_com2_H_2 ) ) ). % 18.78/18.88 % 18.78/18.88 fof(fact_WT_Oequations_I4_J,axiom, % 18.78/18.88 ! [V_a2_2,V_a1_2] : % 18.78/18.88 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_a1_2,V_a2_2))) % 18.78/18.88 <=> ( hBOOL(hAPP(c_Com_OWT,V_a1_2)) % 18.78/18.88 & hBOOL(hAPP(c_Com_OWT,V_a2_2)) ) ) ). % 18.78/18.88 % 18.78/18.88 fof(fact_evaln_Oequations_I4_J,axiom, % 18.78/18.88 ! [V_a6_2,V_a3_2,V_a2_2,V_a5_2,V_a1_2] : % 18.78/18.88 ( c_Natural_Oevaln(c_Com_Ocom_OSemi(V_a1_2,V_a5_2),V_a2_2,V_a3_2,V_a6_2) % 18.78/18.88 <=> ? [B_s1] : % 18.78/18.88 ( c_Natural_Oevaln(V_a1_2,V_a2_2,V_a3_2,B_s1) % 18.78/18.88 & c_Natural_Oevaln(V_a5_2,B_s1,V_a3_2,V_a6_2) ) ) ). % 18.78/18.88 % 18.78/18.88 fof(fact_WT_Oequations_I2_J,axiom, % 18.78/18.88 ! [V_a2_2,V_a1_2] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(V_a1_2,V_a2_2))) ). % 18.78/18.88 % 18.78/18.88 fof(fact_WT_OAssign,axiom, % 18.78/18.88 ! [V_a_2,V_X_2] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(V_X_2,V_a_2))) ). % 18.78/18.88 % 18.78/18.88 fof(fact_WT_Oequations_I1_J,axiom, % 18.78/18.88 hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)) ). % 18.78/18.88 % 18.78/18.88 fof(fact_WT_OSkip,axiom, % 18.78/18.88 hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)) ). % 18.78/18.88 % 18.78/18.88 fof(fact_com_Osimps_I48_J,axiom, % 18.78/18.88 ! [V_pname_H,V_com2,V_com1] : c_Com_Ocom_OSemi(V_com1,V_com2) != hAPP(c_Com_Ocom_OBODY,V_pname_H) ). % 18.78/18.88 % 18.78/18.88 fof(fact_com_Osimps_I49_J,axiom, % 18.78/18.88 ! [V_com2,V_com1,V_pname_H] : hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OSemi(V_com1,V_com2) ). % 18.78/18.88 % 18.78/18.88 fof(fact_com_Osimps_I25_J,axiom, % 18.78/18.88 ! [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) ). % 18.78/18.88 % 18.78/18.88 fof(fact_com_Osimps_I24_J,axiom, % 18.78/18.88 ! [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) ). % 18.78/18.88 % 18.78/18.88 fof(fact_com_Osimps_I51_J,axiom, % 18.78/18.88 ! [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) ). % 18.78/18.88 % 18.78/18.88 fof(fact_com_Osimps_I50_J,axiom, % 18.78/18.88 ! [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) ). % 18.78/18.88 % 18.78/18.88 fof(fact_com_Osimps_I13_J,axiom, % 18.78/18.88 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSemi(V_com1_H,V_com2_H) != c_Com_Ocom_OSKIP ). % 18.78/18.88 % 18.78/18.88 fof(fact_com_Osimps_I12_J,axiom, % 18.78/18.88 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(V_com1_H,V_com2_H) ). % 18.78/18.88 % 18.78/18.88 fof(fact_evaln_Oequations_I2_J,axiom, % 18.78/18.88 ! [V_a4_2,V_a3_2,V_a2_2,V_a1_2] : 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))) ). % 18.78/18.88 % 18.78/18.88 fof(fact_com_Orecs_I7_J,axiom, % 18.78/18.88 ! [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_b] : c_Com_Ocom_Ocom__rec(T_b,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) ). % 18.78/18.89 % 18.78/18.89 fof(fact_evaln__elim__cases_I4_J,axiom, % 18.78/18.89 ! [V_t,V_n,V_s,V_c2,V_c1] : % 18.78/18.89 ( c_Natural_Oevaln(c_Com_Ocom_OSemi(V_c1,V_c2),V_s,V_n,V_t) % 18.78/18.89 => ~ ! [B_s1] : % 18.78/18.89 ( c_Natural_Oevaln(V_c1,V_s,V_n,B_s1) % 18.78/18.89 => ~ c_Natural_Oevaln(V_c2,B_s1,V_n,V_t) ) ) ). % 18.78/18.89 % 18.78/18.89 fof(fact_evalc_OAssign,axiom, % 18.78/18.89 ! [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)))) ). % 18.78/18.89 % 18.78/18.89 fof(fact_evalc__elim__cases_I2_J,axiom, % 18.78/18.89 ! [V_t_2,V_s_2,V_a_2,V_X_2] : % 18.78/18.89 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(V_X_2,V_a_2)),V_s_2),V_t_2)) % 18.78/18.89 => V_t_2 = hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s_2),V_X_2),hAPP(V_a_2,V_s_2)) ) ). % 18.78/18.89 % 18.78/18.89 fof(fact_evalc_Oequations_I2_J,axiom, % 18.78/18.89 ! [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)))) ). % 18.78/18.89 % 18.78/18.89 fof(fact_comm__monoid_Ocomm__neutral,axiom, % 18.78/18.89 ! [V_a_2,V_z_2,V_f_2,T_b] : % 18.78/18.89 ( c_Groups_Ocomm__monoid(T_b,V_f_2,V_z_2) % 18.78/18.89 => hAPP(hAPP(V_f_2,V_a_2),V_z_2) = V_a_2 ) ). % 18.78/18.89 % 18.78/18.89 fof(fact_WTs__elim__cases_I5_J,axiom, % 18.78/18.89 ! [V_c2_2,V_c1_2,V_b_2] : % 18.78/18.89 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_b_2,V_c1_2,V_c2_2))) % 18.78/18.89 => ~ ( hBOOL(hAPP(c_Com_OWT,V_c1_2)) % 18.78/18.89 => ~ hBOOL(hAPP(c_Com_OWT,V_c2_2)) ) ) ). % 18.78/18.89 % 18.78/18.89 fof(fact_evaln_OIfFalse,axiom, % 18.78/18.89 ! [V_c0_2,V_s1_2,V_n_2,V_c1_2,V_s_2,V_b_2] : % 18.78/18.89 ( ~ hBOOL(hAPP(V_b_2,V_s_2)) % 18.78/18.89 => ( c_Natural_Oevaln(V_c1_2,V_s_2,V_n_2,V_s1_2) % 18.78/18.89 => 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) ) ) ). % 18.78/18.89 % 18.78/18.89 fof(fact_evaln_OIfTrue,axiom, % 18.78/18.89 ! [V_c1_2,V_s1_2,V_n_2,V_c0_2,V_s_2,V_b_2] : % 18.78/18.89 ( hBOOL(hAPP(V_b_2,V_s_2)) % 18.78/18.89 => ( c_Natural_Oevaln(V_c0_2,V_s_2,V_n_2,V_s1_2) % 18.78/18.89 => 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) ) ) ). % 18.78/18.89 % 18.78/18.89 fof(fact_evaln__elim__cases_I5_J,axiom, % 18.78/18.89 ! [V_t_2,V_n_2,V_s_2,V_c2_2,V_c1_2,V_b_2] : % 18.78/18.89 ( 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) % 18.78/18.89 => ( ( hBOOL(hAPP(V_b_2,V_s_2)) % 18.78/18.89 => ~ c_Natural_Oevaln(V_c1_2,V_s_2,V_n_2,V_t_2) ) % 18.78/18.89 => ~ ( ~ hBOOL(hAPP(V_b_2,V_s_2)) % 18.78/18.89 => ~ c_Natural_Oevaln(V_c2_2,V_s_2,V_n_2,V_t_2) ) ) ) ). % 18.78/18.89 % 18.78/18.89 fof(fact_WTs__elim__cases_I3_J,axiom, % 18.78/18.89 ! [V_c_2,V_a_2,V_Y_2] : % 18.78/18.89 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_c_2))) % 18.78/18.89 => hBOOL(hAPP(c_Com_OWT,V_c_2)) ) ). % 18.78/18.89 % 18.78/18.89 fof(fact_com_Osimps_I68_J,axiom, % 18.78/18.89 ! [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_b] : c_Com_Ocom_Ocom__case(T_b,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) ). % 18.78/18.89 % 18.78/18.89 fof(fact_com_Osimps_I66_J,axiom, % 18.78/18.89 ! [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_b] : c_Com_Ocom_Ocom__case(T_b,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) ). % 18.78/18.89 % 18.78/18.89 fof(fact_evalc_OIfFalse,axiom, % 18.78/18.89 ! [V_c0_2,V_s1_2,V_c1_2,V_s_2,V_b_2] : % 18.78/18.89 ( ~ hBOOL(hAPP(V_b_2,V_s_2)) % 18.78/18.89 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1_2),V_s_2),V_s1_2)) % 18.78/18.89 => 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)) ) ) ). % 18.78/18.89 % 18.78/18.89 fof(fact_evalc_OIfTrue,axiom, % 18.78/18.89 ! [V_c1_2,V_s1_2,V_c0_2,V_s_2,V_b_2] : % 18.78/18.89 ( hBOOL(hAPP(V_b_2,V_s_2)) % 18.78/18.89 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c0_2),V_s_2),V_s1_2)) % 18.78/18.89 => 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)) ) ) ). % 18.78/18.89 % 18.78/18.89 fof(fact_evalc__elim__cases_I5_J,axiom, % 18.78/18.89 ! [V_t_2,V_s_2,V_c2_2,V_c1_2,V_b_2] : % 18.78/18.89 ( 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)) % 18.78/18.89 => ( ( hBOOL(hAPP(V_b_2,V_s_2)) % 18.78/18.89 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1_2),V_s_2),V_t_2)) ) % 18.78/18.89 => ~ ( ~ hBOOL(hAPP(V_b_2,V_s_2)) % 18.78/18.89 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c2_2),V_s_2),V_t_2)) ) ) ) ). % 18.78/18.89 % 18.78/18.89 fof(fact_evalc_OSemi,axiom, % 18.78/18.89 ! [V_s2,V_c1,V_s1,V_s0,V_c0] : % 18.78/18.89 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c0),V_s0),V_s1)) % 18.78/18.89 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1),V_s1),V_s2)) % 18.78/18.89 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c0,V_c1)),V_s0),V_s2)) ) ) ). % 18.78/18.89 % 18.78/18.89 fof(fact_evalc__elim__cases_I1_J,axiom, % 18.78/18.89 ! [V_t,V_s] : % 18.78/18.89 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_s),V_t)) % 18.78/18.89 => V_t = V_s ) ). % 18.78/18.89 % 18.78/18.89 fof(fact_evalc_OSkip,axiom, % 18.78/18.89 ! [V_s] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_s),V_s)) ). % 18.78/18.89 % 18.78/18.89 fof(fact_evalc_Oequations_I5_J,axiom, % 18.78/18.89 ! [V_a4_2,V_a2_2,V_a5_2,V_a3_2,V_a1_2] : % 18.78/18.89 ( 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)) % 18.78/18.89 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 18.78/18.89 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),V_a4_2)) ) % 18.78/18.89 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2)) % 18.78/18.89 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a5_2),V_a2_2),V_a4_2)) ) ) ) ). % 18.78/18.89 % 18.78/18.89 fof(fact_evalc_Oequations_I6_J,axiom, % 18.78/18.89 ! [V_a4_2,V_a2_2,V_a3_2,V_a5_2,V_a1_2] : % 18.78/18.89 ( 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)) % 18.78/18.89 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 18.78/18.89 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a5_2),V_a2_2),V_a4_2)) ) % 18.78/18.89 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2)) % 18.78/18.89 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),V_a4_2)) ) ) ) ). % 18.78/18.89 % 18.78/18.89 fof(fact_com__det,axiom, % 18.78/18.89 ! [V_u,V_t,V_s,V_c] : % 18.78/18.89 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_t)) % 18.78/18.89 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_u)) % 18.78/18.89 => V_u = V_t ) ) ). % 18.78/18.89 % 18.78/18.89 fof(fact_com_Osimps_I37_J,axiom, % 18.78/18.89 ! [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) ). % 18.78/18.89 % 18.78/18.89 fof(fact_com_Osimps_I36_J,axiom, % 18.78/18.89 ! [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) ). % 18.78/18.89 % 18.78/18.89 fof(fact_com_Osimps_I4_J,axiom, % 18.78/18.89 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com2_2,V_com1_2,V_fun_2] : % 18.78/18.89 ( 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) % 18.78/18.89 <=> ( V_fun_2 = V_fun_H_2 % 18.78/18.89 & V_com1_2 = V_com1_H_2 % 18.78/18.89 & V_com2_2 = V_com2_H_2 ) ) ). % 18.78/18.89 % 18.78/18.89 fof(fact_com_Osimps_I2_J,axiom, % 18.78/18.89 ! [V_com_H_2,V_fun_H_2,V_loc_H_2,V_com_2,V_fun_2,V_loc_2] : % 18.78/18.89 ( 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) % 18.78/18.89 <=> ( V_loc_2 = V_loc_H_2 % 18.78/18.89 & V_fun_2 = V_fun_H_2 % 18.78/18.89 & V_com_2 = V_com_H_2 ) ) ). % 18.78/18.89 % 18.78/18.89 fof(fact_evaln__evalc,axiom, % 18.78/18.89 ! [V_t,V_n,V_s,V_c] : % 18.78/18.89 ( c_Natural_Oevaln(V_c,V_s,V_n,V_t) % 18.78/18.89 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_t)) ) ). % 18.78/18.89 % 18.78/18.89 fof(fact_eval__eq,axiom, % 18.78/18.89 ! [V_t_2,V_s_2,V_c_2] : % 18.78/18.89 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c_2),V_s_2),V_t_2)) % 18.78/18.89 <=> ? [B_n] : c_Natural_Oevaln(V_c_2,V_s_2,B_n,V_t_2) ) ). % 18.78/18.89 % 18.78/18.89 fof(fact_evalc_Oequations_I4_J,axiom, % 18.78/18.89 ! [V_a5_2,V_a2_2,V_a4_2,V_a1_2] : % 18.78/18.89 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_a1_2,V_a4_2)),V_a2_2),V_a5_2)) % 18.78/18.89 <=> ? [B_s1] : % 18.78/18.89 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a1_2),V_a2_2),B_s1)) % 18.78/18.89 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a4_2),B_s1),V_a5_2)) ) ) ). % 18.78/18.89 % 18.78/18.89 fof(fact_evalc_Oequations_I1_J,axiom, % 18.78/18.89 ! [V_a] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_a),V_a)) ). % 18.78/18.89 % 18.78/18.89 fof(fact_WT_Oequations_I3_J,axiom, % 18.78/18.89 ! [V_a1_2,V_a3_2,V_a2_2] : % 18.78/18.89 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_a2_2,V_a3_2,V_a1_2))) % 18.78/18.89 <=> hBOOL(hAPP(c_Com_OWT,V_a1_2)) ) ). % 18.78/18.89 % 18.78/18.89 fof(fact_WT_OLocal,axiom, % 18.78/18.89 ! [V_a_2,V_Y_2,V_c_2] : % 18.78/18.89 ( hBOOL(hAPP(c_Com_OWT,V_c_2)) % 18.78/18.89 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_c_2))) ) ). % 18.78/18.89 % 18.78/18.89 fof(fact_evaln_Oequations_I6_J,axiom, % 18.78/18.89 ! [V_a5_2,V_a4_2,V_a2_2,V_a3_2,V_a6_2,V_a1_2] : % 18.78/18.89 ( 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) % 18.78/18.89 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 18.78/18.89 & c_Natural_Oevaln(V_a6_2,V_a2_2,V_a4_2,V_a5_2) ) % 18.78/18.89 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2)) % 18.78/18.89 & c_Natural_Oevaln(V_a3_2,V_a2_2,V_a4_2,V_a5_2) ) ) ) ). % 18.78/18.89 % 18.78/18.89 fof(fact_evaln_Oequations_I5_J,axiom, % 18.78/18.89 ! [V_a5_2,V_a4_2,V_a2_2,V_a6_2,V_a3_2,V_a1_2] : % 18.78/18.89 ( 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) % 18.78/18.89 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 18.78/18.89 & c_Natural_Oevaln(V_a3_2,V_a2_2,V_a4_2,V_a5_2) ) % 18.78/18.89 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2)) % 18.78/18.89 & c_Natural_Oevaln(V_a6_2,V_a2_2,V_a4_2,V_a5_2) ) ) ) ). % 18.78/18.89 % 18.78/18.89 fof(fact_com_Osimps_I41_J,axiom, % 18.78/18.89 ! [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) ). % 18.78/18.89 % 18.78/18.89 fof(fact_com_Osimps_I40_J,axiom, % 18.78/18.89 ! [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) ). % 18.78/18.89 % 18.78/18.89 fof(fact_WT_Oequations_I5_J,axiom, % 18.78/18.89 ! [V_a2_2,V_a1_2,V_a3_2] : % 18.78/18.89 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_a3_2,V_a1_2,V_a2_2))) % 18.78/18.89 <=> ( hBOOL(hAPP(c_Com_OWT,V_a1_2)) % 18.78/18.89 & hBOOL(hAPP(c_Com_OWT,V_a2_2)) ) ) ). % 18.78/18.89 % 18.78/18.89 fof(fact_WT_OIf,axiom, % 18.78/18.89 ! [V_b_2,V_c1_2,V_c0_2] : % 18.78/18.89 ( hBOOL(hAPP(c_Com_OWT,V_c0_2)) % 18.78/18.89 => ( hBOOL(hAPP(c_Com_OWT,V_c1_2)) % 18.78/18.89 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2))) ) ) ). % 18.78/18.89 % 18.78/18.89 fof(fact_com_Osimps_I55_J,axiom, % 18.78/18.89 ! [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) ). % 18.78/18.89 % 18.78/18.89 fof(fact_com_Osimps_I54_J,axiom, % 18.78/18.89 ! [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) ). % 18.78/18.89 % 18.78/18.89 fof(fact_com_Osimps_I22_J,axiom, % 18.78/18.89 ! [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) ). % 18.78/18.89 % 18.78/18.89 fof(fact_com_Osimps_I23_J,axiom, % 18.78/18.89 ! [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) ). % 18.78/18.89 % 18.78/18.89 fof(fact_com_Osimps_I43_J,axiom, % 18.78/18.89 ! [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) ). % 18.78/18.89 % 18.78/18.89 fof(fact_com_Osimps_I42_J,axiom, % 18.78/18.89 ! [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) ). % 18.78/18.89 % 18.78/18.89 fof(fact_com_Osimps_I35_J,axiom, % 18.78/18.89 ! [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) ). % 18.78/18.89 % 18.78/18.89 fof(fact_com_Osimps_I34_J,axiom, % 18.78/18.89 ! [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) ). % 18.78/18.89 % 18.78/18.89 fof(fact_com_Osimps_I10_J,axiom, % 18.78/18.89 ! [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) ). % 18.78/18.89 % 18.78/18.89 fof(fact_com_Osimps_I11_J,axiom, % 18.78/18.89 ! [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 ). % 18.78/18.89 % 18.78/18.89 fof(fact_com_Osimps_I26_J,axiom, % 18.78/18.89 ! [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) ). % 18.78/18.89 % 18.78/18.89 fof(fact_com_Osimps_I27_J,axiom, % 18.78/18.89 ! [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) ). % 18.78/18.89 % 18.78/18.89 fof(fact_com_Osimps_I57_J,axiom, % 18.78/18.89 ! [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) ). % 18.78/18.89 % 18.78/18.89 fof(fact_com_Osimps_I56_J,axiom, % 18.78/18.89 ! [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) ). % 18.78/18.89 % 18.78/18.89 fof(fact_com_Osimps_I44_J,axiom, % 18.78/18.89 ! [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) ). % 18.78/18.89 % 18.78/18.89 fof(fact_com_Osimps_I45_J,axiom, % 18.78/18.89 ! [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) ). % 18.78/18.89 % 18.78/18.89 fof(fact_com_Osimps_I14_J,axiom, % 18.78/18.89 ! [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) ). % 18.78/18.89 % 18.78/18.89 fof(fact_com_Osimps_I15_J,axiom, % 18.78/18.89 ! [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 ). % 18.78/18.89 % 18.78/18.89 fof(fact_com_Orecs_I3_J,axiom, % 18.78/18.89 ! [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_b] : c_Com_Ocom_Ocom__rec(T_b,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_b,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)) ). % 18.78/18.89 % 18.78/18.89 fof(fact_com_Orecs_I5_J,axiom, % 18.78/18.89 ! [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_b] : c_Com_Ocom_Ocom__rec(T_b,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_b,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_b,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)) ). % 18.78/18.89 % 18.78/18.89 fof(fact_evalc__elim__cases_I4_J,axiom, % 18.78/18.89 ! [V_t,V_s,V_c2,V_c1] : % 18.78/18.89 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c1,V_c2)),V_s),V_t)) % 18.78/18.89 => ~ ! [B_s1] : % 18.78/18.89 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1),V_s),B_s1)) % 18.78/18.89 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c2),B_s1),V_t)) ) ) ). % 18.78/18.89 % 18.78/18.89 fof(fact_evalc__evaln,axiom, % 18.78/18.89 ! [V_t,V_s,V_c] : % 18.78/18.89 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_t)) % 18.78/18.89 => ? [B_n] : c_Natural_Oevaln(V_c,V_s,B_n,V_t) ) ). % 18.78/18.89 % 18.78/18.89 fof(fact_evalc_OLocal,axiom, % 18.78/18.89 ! [V_s1_2,V_a_2,V_Y_2,V_s0_2,V_c_2] : % 18.78/18.89 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c_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)) % 18.78/18.89 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_c_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)))) ) ). % 18.78/18.89 % 18.78/18.89 fof(fact_evaln_OLocal,axiom, % 18.78/18.89 ! [V_s1_2,V_n_2,V_a_2,V_Y_2,V_s0_2,V_c_2] : % 18.78/18.89 ( c_Natural_Oevaln(V_c_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) % 18.78/18.89 => c_Natural_Oevaln(c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_c_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))) ) ). % 18.78/18.89 % 18.78/18.89 fof(fact_evalc_Oequations_I3_J,axiom, % 18.78/18.89 ! [V_a5_2,V_a2_2,V_a1_2,V_a4_2,V_a3_2] : % 18.78/18.89 ( 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)))) % 18.78/18.89 <=> ? [B_s1] : % 18.78/18.89 ( 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)) % 18.78/18.89 & 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)) ) ) ). % 18.78/18.89 % 18.78/18.89 fof(fact_evaln_Oequations_I3_J,axiom, % 18.78/18.89 ! [V_a6_2,V_a5_2,V_a2_2,V_a1_2,V_a4_2,V_a3_2] : % 18.78/18.89 ( 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))) % 18.78/18.89 <=> ? [B_s1] : % 18.78/18.89 ( 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)) % 18.78/18.89 & 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) ) ) ). % 18.78/18.89 % 18.78/18.89 fof(fact_evalc_OBody,axiom, % 18.78/18.89 ! [V_s1,V_s0,V_pn] : % 18.78/18.89 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn))),V_s0),V_s1)) % 18.78/18.89 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_pn)),V_s0),V_s1)) ) ). % 18.78/18.89 % 18.78/18.89 fof(fact_evalc__elim__cases_I6_J,axiom, % 18.78/18.89 ! [V_s1,V_s,V_P] : % 18.78/18.89 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_P)),V_s),V_s1)) % 18.78/18.89 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_P))),V_s),V_s1)) ) ). % 18.78/18.89 % 18.78/18.89 fof(fact_WTs__elim__cases_I6_J,axiom, % 18.78/18.89 ! [V_c_2,V_b_2] : % 18.78/18.89 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_b_2,V_c_2))) % 18.78/18.89 => hBOOL(hAPP(c_Com_OWT,V_c_2)) ) ). % 18.78/18.89 % 18.78/18.89 fof(fact_evalc_OWhileFalse,axiom, % 18.78/18.89 ! [V_c_2,V_s_2,V_b_2] : % 18.78/18.89 ( ~ hBOOL(hAPP(V_b_2,V_s_2)) % 18.78/18.89 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s_2),V_s_2)) ) ). % 18.78/18.89 % 18.78/18.89 fof(fact_evalc_OWhileTrue,axiom, % 18.78/18.89 ! [V_s2_2,V_s1_2,V_c_2,V_s0_2,V_b_2] : % 18.78/18.89 ( hBOOL(hAPP(V_b_2,V_s0_2)) % 18.78/18.89 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c_2),V_s0_2),V_s1_2)) % 18.78/18.89 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s1_2),V_s2_2)) % 18.78/18.89 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s0_2),V_s2_2)) ) ) ) ). % 18.78/18.89 % 18.78/18.89 fof(fact_com_Osimps_I69_J,axiom, % 18.78/18.89 ! [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_b] : c_Com_Ocom_Ocom__case(T_b,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) ). % 18.78/18.89 % 18.78/18.89 fof(fact_evaln_OWhileFalse,axiom, % 18.78/18.89 ! [V_n_2,V_c_2,V_s_2,V_b_2] : % 18.78/18.89 ( ~ hBOOL(hAPP(V_b_2,V_s_2)) % 18.78/18.89 => c_Natural_Oevaln(c_Com_Ocom_OWhile(V_b_2,V_c_2),V_s_2,V_n_2,V_s_2) ) ). % 18.78/18.89 % 18.78/18.89 fof(fact_evaln_OWhileTrue,axiom, % 18.78/18.89 ! [V_s2_2,V_s1_2,V_n_2,V_c_2,V_s0_2,V_b_2] : % 18.78/18.89 ( hBOOL(hAPP(V_b_2,V_s0_2)) % 18.78/18.89 => ( c_Natural_Oevaln(V_c_2,V_s0_2,V_n_2,V_s1_2) % 18.78/18.89 => ( c_Natural_Oevaln(c_Com_Ocom_OWhile(V_b_2,V_c_2),V_s1_2,V_n_2,V_s2_2) % 18.78/18.89 => c_Natural_Oevaln(c_Com_Ocom_OWhile(V_b_2,V_c_2),V_s0_2,V_n_2,V_s2_2) ) ) ) ). % 18.78/18.89 % 18.78/18.89 fof(fact_com_Osimps_I5_J,axiom, % 18.78/18.89 ! [V_com_H_2,V_fun_H_2,V_com_2,V_fun_2] : % 18.78/18.89 ( c_Com_Ocom_OWhile(V_fun_2,V_com_2) = c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) % 18.78/18.89 <=> ( V_fun_2 = V_fun_H_2 % 18.78/18.89 & V_com_2 = V_com_H_2 ) ) ). % 18.78/18.89 % 18.78/18.89 fof(fact_vname_Osimps_I2_J,axiom, % 18.78/18.89 ! [V_loc_H_2,V_loc_2] : % 18.78/18.89 ( c_Com_Ovname_OLoc(V_loc_2) = c_Com_Ovname_OLoc(V_loc_H_2) % 18.78/18.89 <=> V_loc_2 = V_loc_H_2 ) ). % 18.78/18.89 % 18.78/18.89 fof(fact_evaln_Oequations_I7_J,axiom, % 18.78/18.89 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2] : % 18.78/18.89 ( c_Natural_Oevaln(c_Com_Ocom_OWhile(V_a1_2,V_a3_2),V_a2_2,V_a4_2,V_a2_2) % 18.78/18.89 <=> ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 18.78/18.89 => ? [B_s1] : % 18.78/18.89 ( c_Natural_Oevaln(V_a3_2,V_a2_2,V_a4_2,B_s1) % 18.78/18.89 & c_Natural_Oevaln(c_Com_Ocom_OWhile(V_a1_2,V_a3_2),B_s1,V_a4_2,V_a2_2) ) ) ) ). % 18.78/18.89 % 18.78/18.89 fof(fact_evaln_Oequations_I8_J,axiom, % 18.78/18.89 ! [V_a6_2,V_a4_2,V_a2_2,V_a3_2,V_a1_2] : % 18.78/18.89 ( c_Natural_Oevaln(c_Com_Ocom_OWhile(V_a1_2,V_a3_2),V_a2_2,V_a4_2,V_a6_2) % 18.78/18.89 <=> ( ( V_a6_2 = V_a2_2 % 18.78/18.89 & ~ hBOOL(hAPP(V_a1_2,V_a2_2)) ) % 18.78/18.89 | ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 18.78/18.89 & ? [B_s1] : % 18.78/18.89 ( c_Natural_Oevaln(V_a3_2,V_a2_2,V_a4_2,B_s1) % 18.78/18.89 & c_Natural_Oevaln(c_Com_Ocom_OWhile(V_a1_2,V_a3_2),B_s1,V_a4_2,V_a6_2) ) ) ) ) ). % 18.78/18.89 % 18.78/18.89 fof(fact_evalc_Oequations_I8_J,axiom, % 18.78/18.89 ! [V_a5_2,V_a2_2,V_a3_2,V_a1_2] : % 18.78/18.89 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a5_2)) % 18.78/18.89 <=> ( ( V_a5_2 = V_a2_2 % 18.78/18.89 & ~ hBOOL(hAPP(V_a1_2,V_a2_2)) ) % 18.78/18.89 | ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 18.78/18.89 & ? [B_s1] : % 18.78/18.89 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),B_s1)) % 18.78/18.89 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a5_2)) ) ) ) ) ). % 18.78/18.89 % 18.78/18.89 fof(fact_evalc_Oequations_I7_J,axiom, % 18.78/18.89 ! [V_a2_2,V_a3_2,V_a1_2] : % 18.78/18.89 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a2_2)) % 18.78/18.89 <=> ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 18.78/18.89 => ? [B_s1] : % 18.78/18.89 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),B_s1)) % 18.78/18.89 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a2_2)) ) ) ) ). % 18.78/18.89 % 18.78/18.89 fof(fact_While,axiom, % 18.78/18.89 ! [V_b_2,V_c_2] : % 18.78/18.89 ( hBOOL(hAPP(c_Com_OWT,V_c_2)) % 18.78/18.89 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_b_2,V_c_2))) ) ). % 18.78/18.89 % 18.78/18.89 fof(fact_WT_Oequations_I6_J,axiom, % 18.78/18.89 ! [V_a1_2,V_a2_2] : % 18.78/18.89 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_a2_2,V_a1_2))) % 18.78/18.89 <=> hBOOL(hAPP(c_Com_OWT,V_a1_2)) ) ). % 18.78/18.89 % 18.78/18.89 fof(fact_com_Osimps_I58_J,axiom, % 18.78/18.89 ! [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) ). % 18.78/18.90 % 18.78/18.90 fof(fact_com_Osimps_I59_J,axiom, % 18.78/18.90 ! [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) ). % 18.78/18.90 % 18.78/18.90 fof(fact_com_Osimps_I52_J,axiom, % 18.78/18.90 ! [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) ). % 18.78/18.90 % 18.78/18.90 fof(fact_com_Osimps_I53_J,axiom, % 18.78/18.90 ! [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) ). % 18.78/18.90 % 18.78/18.90 fof(fact_com_Osimps_I29_J,axiom, % 18.78/18.90 ! [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) ). % 18.78/18.90 % 18.78/18.90 fof(fact_com_Osimps_I28_J,axiom, % 18.78/18.90 ! [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) ). % 18.78/18.90 % 18.78/18.90 fof(fact_com_Osimps_I47_J,axiom, % 18.78/18.90 ! [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) ). % 18.78/18.90 % 18.78/18.90 fof(fact_com_Osimps_I46_J,axiom, % 18.78/18.90 ! [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) ). % 18.78/18.90 % 18.78/18.90 fof(fact_com_Osimps_I61_J,axiom, % 18.78/18.90 ! [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) ). % 18.78/18.90 % 18.78/18.90 fof(fact_com_Osimps_I60_J,axiom, % 18.78/18.90 ! [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) ). % 18.78/18.90 % 18.78/18.90 fof(fact_com_Osimps_I38_J,axiom, % 18.78/18.90 ! [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) ). % 18.78/18.90 % 18.78/18.90 fof(fact_com_Osimps_I39_J,axiom, % 18.78/18.90 ! [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) ). % 18.78/18.90 % 18.78/18.90 fof(fact_com_Osimps_I17_J,axiom, % 18.78/18.90 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSKIP ). % 18.78/18.90 % 18.78/18.90 fof(fact_com_Osimps_I16_J,axiom, % 18.78/18.90 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ). % 18.78/18.90 % 18.78/18.90 fof(fact_com_Orecs_I6_J,axiom, % 18.78/18.90 ! [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_b] : c_Com_Ocom_Ocom__rec(T_b,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_b,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)) ). % 18.78/18.90 % 18.78/18.90 fof(fact_evalc_Oequations_I9_J,axiom, % 18.78/18.90 ! [V_a3_2,V_a2_2,V_a1_2] : % 18.78/18.90 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_a1_2)),V_a2_2),V_a3_2)) % 18.78/18.90 <=> 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)) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_vname_Osize_I2_J,axiom, % 18.78/18.90 ! [V_loc] : c_Com_Ovname_Ovname__size(c_Com_Ovname_OLoc(V_loc)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 18.78/18.90 % 18.78/18.90 fof(fact_evalc__elim__cases_I3_J,axiom, % 18.78/18.90 ! [V_t_2,V_s_2,V_c_2,V_a_2,V_Y_2] : % 18.78/18.90 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_c_2)),V_s_2),V_t_2)) % 18.78/18.90 => ~ ! [B_s1] : % 18.78/18.90 ( 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)) % 18.78/18.90 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c_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)) ) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_evaln__elim__cases_I3_J,axiom, % 18.78/18.90 ! [V_t_2,V_n_2,V_s_2,V_c_2,V_a_2,V_Y_2] : % 18.78/18.90 ( c_Natural_Oevaln(c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_c_2),V_s_2,V_n_2,V_t_2) % 18.78/18.90 => ~ ! [B_s1] : % 18.78/18.90 ( 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)) % 18.78/18.90 => ~ c_Natural_Oevaln(V_c_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) ) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_vname_Osize_I4_J,axiom, % 18.78/18.90 ! [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) ). % 18.78/18.90 % 18.78/18.90 fof(fact_evaln_OBody,axiom, % 18.78/18.90 ! [V_s1,V_n,V_s0,V_pn] : % 18.78/18.90 ( c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn)),V_s0,V_n,V_s1) % 18.78/18.90 => c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,V_pn),V_s0,hAPP(c_Nat_OSuc,V_n),V_s1) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_vname_Osimps_I6_J,axiom, % 18.78/18.90 ! [V_loc_2,V_f2_2,V_f1_2,T_b] : c_Com_Ovname_Ovname__case(T_b,V_f1_2,V_f2_2,c_Com_Ovname_OLoc(V_loc_2)) = hAPP(V_f2_2,V_loc_2) ). % 18.78/18.90 % 18.78/18.90 fof(fact_vname_Orecs_I2_J,axiom, % 18.78/18.90 ! [V_loc_2,V_f2_2,V_f1_2,T_b] : c_Com_Ovname_Ovname__rec(T_b,V_f1_2,V_f2_2,c_Com_Ovname_OLoc(V_loc_2)) = hAPP(V_f2_2,V_loc_2) ). % 18.78/18.90 % 18.78/18.90 fof(fact_evaln_Oequations_I9_J,axiom, % 18.78/18.90 ! [V_a4_2,V_a3_2,V_a2_2,V_a1_2] : % 18.78/18.90 ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,V_a1_2),V_a2_2,hAPP(c_Nat_OSuc,V_a3_2),V_a4_2) % 18.78/18.90 <=> 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) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_WT_OBody,axiom, % 18.78/18.90 ! [V_pn] : % 18.78/18.90 ( hAPP(c_Com_Obody,V_pn) != c_Option_Ooption_ONone(tc_Com_Ocom) % 18.78/18.90 => hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn))) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_WT_Oequations_I7_J,axiom, % 18.78/18.90 ! [V_a_2] : % 18.78/18.90 ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_a_2))) % 18.78/18.90 <=> ? [B_y] : hAPP(c_Com_Obody,V_a_2) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_evalc_OCall,axiom, % 18.78/18.90 ! [V_X_2,V_s1_2,V_a_2,V_s0_2,V_pna_2] : % 18.78/18.90 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_pna_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)) % 18.78/18.90 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(V_X_2,V_pna_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)))) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_evaln_OCall,axiom, % 18.78/18.90 ! [V_X_2,V_s1_2,V_n_2,V_a_2,V_s0_2,V_pna_2] : % 18.78/18.90 ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,V_pna_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) % 18.78/18.90 => c_Natural_Oevaln(c_Com_Ocom_OCall(V_X_2,V_pna_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))) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_evaln__Suc,axiom, % 18.78/18.90 ! [V_s_H,V_n,V_s,V_c] : % 18.78/18.90 ( c_Natural_Oevaln(V_c,V_s,V_n,V_s_H) % 18.78/18.90 => c_Natural_Oevaln(V_c,V_s,hAPP(c_Nat_OSuc,V_n),V_s_H) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_evaln_Oequations_I10_J,axiom, % 18.78/18.90 ! [V_a5_2,V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_a6_2] : % 18.78/18.90 ( 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))) % 18.78/18.90 <=> ? [B_s1] : % 18.78/18.90 ( 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)) % 18.78/18.90 & 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) ) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_evalc_Oequations_I10_J,axiom, % 18.78/18.90 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_a5_2] : % 18.78/18.90 ( 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)))) % 18.78/18.90 <=> ? [B_s1] : % 18.78/18.90 ( 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)) % 18.78/18.90 & 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)) ) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_evalc__elim__cases_I7_J,axiom, % 18.78/18.90 ! [V_s1_2,V_s_2,V_a_2,V_Pa_2,V_X_2] : % 18.78/18.90 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(V_X_2,V_Pa_2,V_a_2)),V_s_2),V_s1_2)) % 18.78/18.90 => ~ ! [B_s1] : % 18.78/18.90 ( 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)) % 18.78/18.90 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_Pa_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)) ) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_evaln__elim__cases_I7_J,axiom, % 18.78/18.90 ! [V_s1_2,V_n_2,V_s_2,V_a_2,V_Pa_2,V_X_2] : % 18.78/18.90 ( c_Natural_Oevaln(c_Com_Ocom_OCall(V_X_2,V_Pa_2,V_a_2),V_s_2,V_n_2,V_s1_2) % 18.78/18.90 => ~ ! [B_s1] : % 18.78/18.90 ( 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)) % 18.78/18.90 => ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,V_Pa_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) ) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_WT__bodiesD,axiom, % 18.78/18.90 ! [V_b,V_pn] : % 18.78/18.90 ( c_Com_OWT__bodies % 18.78/18.90 => ( hAPP(c_Com_Obody,V_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) % 18.78/18.90 => hBOOL(hAPP(c_Com_OWT,V_b)) ) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_evaln__elim__cases_I6_J,axiom, % 18.78/18.90 ! [V_s1,V_n,V_s,V_P] : % 18.78/18.90 ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,V_P),V_s,V_n,V_s1) % 18.78/18.90 => ~ ! [B_n] : % 18.78/18.90 ( V_n = hAPP(c_Nat_OSuc,B_n) % 18.78/18.90 => ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_P)),V_s,B_n,V_s1) ) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_option_Osize_I1_J,axiom, % 18.78/18.90 ! [V_fa_2,T_b] : c_Option_Ooption_Ooption__size(T_b,V_fa_2,c_Option_Ooption_ONone(T_b)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 18.78/18.90 % 18.78/18.90 fof(fact_WTs__elim__cases_I7_J,axiom, % 18.78/18.90 ! [V_P] : % 18.78/18.90 ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_P))) % 18.78/18.90 => ~ ! [B_y] : hAPP(c_Com_Obody,V_P) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_the_Osimps,axiom, % 18.78/18.90 ! [V_x,T_a] : hAPP(c_Option_Othe(T_a),hAPP(c_Option_Ooption_OSome(T_a),V_x)) = V_x ). % 18.78/18.90 % 18.78/18.90 fof(fact_not__None__eq,axiom, % 18.78/18.90 ! [T_b,V_x_2] : % 18.78/18.90 ( V_x_2 != c_Option_Ooption_ONone(T_b) % 18.78/18.90 <=> ? [B_y] : V_x_2 = hAPP(c_Option_Ooption_OSome(T_b),B_y) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_not__Some__eq,axiom, % 18.78/18.90 ! [T_b,V_x_2] : % 18.78/18.90 ( ! [B_y] : V_x_2 != hAPP(c_Option_Ooption_OSome(T_b),B_y) % 18.78/18.90 <=> V_x_2 = c_Option_Ooption_ONone(T_b) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_option_Osimps_I3_J,axiom, % 18.78/18.90 ! [V_a_H,T_a] : hAPP(c_Option_Ooption_OSome(T_a),V_a_H) != c_Option_Ooption_ONone(T_a) ). % 18.78/18.90 % 18.78/18.90 fof(fact_option_Oinject,axiom, % 18.78/18.90 ! [V_a_H_2,V_a_2,T_b] : % 18.78/18.90 ( hAPP(c_Option_Ooption_OSome(T_b),V_a_2) = hAPP(c_Option_Ooption_OSome(T_b),V_a_H_2) % 18.78/18.90 <=> V_a_2 = V_a_H_2 ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_option_Osimps_I2_J,axiom, % 18.78/18.90 ! [V_a_H,T_a] : c_Option_Ooption_ONone(T_a) != hAPP(c_Option_Ooption_OSome(T_a),V_a_H) ). % 18.78/18.90 % 18.78/18.90 fof(fact_option_Osize_I4_J,axiom, % 18.78/18.90 ! [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) ). % 18.78/18.90 % 18.78/18.90 fof(fact_option_Osize_I3_J,axiom, % 18.78/18.90 ! [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) ). % 18.78/18.90 % 18.78/18.90 fof(fact_Suc__neq__Zero,axiom, % 18.78/18.90 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 18.78/18.90 % 18.78/18.90 fof(fact_Zero__neq__Suc,axiom, % 18.78/18.90 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ). % 18.78/18.90 % 18.78/18.90 fof(fact_nat_Osimps_I3_J,axiom, % 18.78/18.90 ! [V_nat_H_1] : hAPP(c_Nat_OSuc,V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 18.78/18.90 % 18.78/18.90 fof(fact_Suc__not__Zero,axiom, % 18.78/18.90 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 18.78/18.90 % 18.78/18.90 fof(fact_nat_Osimps_I2_J,axiom, % 18.78/18.90 ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_nat_H) ). % 18.78/18.90 % 18.78/18.90 fof(fact_Zero__not__Suc,axiom, % 18.78/18.90 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ). % 18.78/18.90 % 18.78/18.90 fof(fact_vname_Osize_I1_J,axiom, % 18.78/18.90 ! [V_glb] : c_Com_Ovname_Ovname__size(c_Com_Ovname_OGlb(V_glb)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 18.78/18.90 % 18.78/18.90 fof(fact_vname_Osize_I3_J,axiom, % 18.78/18.90 ! [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) ). % 18.78/18.90 % 18.78/18.90 fof(fact_option_Osize_I2_J,axiom, % 18.78/18.90 ! [V_a_2,V_fa_2,T_b] : c_Option_Ooption_Ooption__size(T_b,V_fa_2,hAPP(c_Option_Ooption_OSome(T_b),V_a_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 18.78/18.90 % 18.78/18.90 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom, % 18.78/18.90 ! [V_c,V_b,V_a,T_a] : % 18.78/18.90 ( class_Groups_Oab__semigroup__add(T_a) % 18.78/18.90 => 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)) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_add__left__cancel,axiom, % 18.78/18.90 ! [V_c_2,V_b_2,V_a_2,T_b] : % 18.78/18.90 ( class_Groups_Ocancel__semigroup__add(T_b) % 18.78/18.90 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_c_2) % 18.78/18.90 <=> V_b_2 = V_c_2 ) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_add__right__cancel,axiom, % 18.78/18.90 ! [V_c_2,V_a_2,V_b_2,T_b] : % 18.78/18.90 ( class_Groups_Ocancel__semigroup__add(T_b) % 18.78/18.90 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_a_2) % 18.78/18.90 <=> V_b_2 = V_c_2 ) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_add__left__imp__eq,axiom, % 18.78/18.90 ! [V_c,V_b,V_a,T_a] : % 18.78/18.90 ( class_Groups_Ocancel__semigroup__add(T_a) % 18.78/18.90 => ( 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) % 18.78/18.90 => V_b = V_c ) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_add__imp__eq,axiom, % 18.78/18.90 ! [V_c,V_b,V_a,T_a] : % 18.78/18.90 ( class_Groups_Ocancel__ab__semigroup__add(T_a) % 18.78/18.90 => ( 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) % 18.78/18.90 => V_b = V_c ) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_add__right__imp__eq,axiom, % 18.78/18.90 ! [V_c,V_a,V_b,T_a] : % 18.78/18.90 ( class_Groups_Ocancel__semigroup__add(T_a) % 18.78/18.90 => ( 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) % 18.78/18.90 => V_b = V_c ) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_nat__add__right__cancel,axiom, % 18.78/18.90 ! [V_n_2,V_k_2,V_m_2] : % 18.78/18.90 ( 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) % 18.78/18.90 <=> V_m_2 = V_n_2 ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_nat__add__left__cancel,axiom, % 18.78/18.90 ! [V_n_2,V_m_2,V_k_2] : % 18.78/18.90 ( 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) % 18.78/18.90 <=> V_m_2 = V_n_2 ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_nat__add__assoc,axiom, % 18.78/18.90 ! [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)) ). % 18.78/18.90 % 18.78/18.90 fof(fact_nat__add__left__commute,axiom, % 18.78/18.90 ! [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)) ). % 18.78/18.90 % 18.78/18.90 fof(fact_nat__add__commute,axiom, % 18.78/18.90 ! [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) ). % 18.78/18.90 % 18.78/18.90 fof(fact_vname_Osimps_I1_J,axiom, % 18.78/18.90 ! [V_glb_H_2,V_glb_2] : % 18.78/18.90 ( c_Com_Ovname_OGlb(V_glb_2) = c_Com_Ovname_OGlb(V_glb_H_2) % 18.78/18.90 <=> V_glb_2 = V_glb_H_2 ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_plus__nat_Oadd__0,axiom, % 18.78/18.90 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ). % 18.78/18.90 % 18.78/18.90 fof(fact_Nat_Oadd__0__right,axiom, % 18.78/18.90 ! [V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ). % 18.78/18.90 % 18.78/18.90 fof(fact_add__is__0,axiom, % 18.78/18.90 ! [V_n_2,V_m_2] : % 18.78/18.90 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 18.78/18.90 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 18.78/18.90 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_add__eq__self__zero,axiom, % 18.78/18.90 ! [V_n,V_m] : % 18.78/18.90 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_m % 18.78/18.90 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_add__Suc__shift,axiom, % 18.78/18.90 ! [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)) ). % 18.78/18.90 % 18.78/18.90 fof(fact_add__Suc,axiom, % 18.78/18.90 ! [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)) ). % 18.78/18.90 % 18.78/18.90 fof(fact_add__Suc__right,axiom, % 18.78/18.90 ! [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)) ). % 18.78/18.90 % 18.78/18.90 fof(fact_add__0__left,axiom, % 18.78/18.90 ! [V_a,T_a] : % 18.78/18.90 ( class_Groups_Omonoid__add(T_a) % 18.78/18.90 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_add__0,axiom, % 18.78/18.90 ! [V_a,T_a] : % 18.78/18.90 ( class_Groups_Ocomm__monoid__add(T_a) % 18.78/18.90 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_double__zero__sym,axiom, % 18.78/18.90 ! [V_a_2,T_b] : % 18.78/18.90 ( class_Groups_Olinordered__ab__group__add(T_b) % 18.78/18.90 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) % 18.78/18.90 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_add__0__right,axiom, % 18.78/18.90 ! [V_a,T_a] : % 18.78/18.90 ( class_Groups_Omonoid__add(T_a) % 18.78/18.90 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_add_Ocomm__neutral,axiom, % 18.78/18.90 ! [V_a,T_a] : % 18.78/18.90 ( class_Groups_Ocomm__monoid__add(T_a) % 18.78/18.90 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_one__is__add,axiom, % 18.78/18.90 ! [V_n_2,V_m_2] : % 18.78/18.90 ( 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) % 18.78/18.90 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 18.78/18.90 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 18.78/18.90 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 18.78/18.90 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_add__is__1,axiom, % 18.78/18.90 ! [V_n_2,V_m_2] : % 18.78/18.90 ( 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)) % 18.78/18.90 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 18.78/18.90 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 18.78/18.90 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 18.78/18.90 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_vname_Osimps_I3_J,axiom, % 18.78/18.90 ! [V_loc_H,V_glb] : c_Com_Ovname_OGlb(V_glb) != c_Com_Ovname_OLoc(V_loc_H) ). % 18.78/18.90 % 18.78/18.90 fof(fact_vname_Osimps_I4_J,axiom, % 18.78/18.90 ! [V_glb,V_loc_H] : c_Com_Ovname_OLoc(V_loc_H) != c_Com_Ovname_OGlb(V_glb) ). % 18.78/18.90 % 18.78/18.90 fof(fact_Suc__inject,axiom, % 18.78/18.90 ! [V_y,V_x] : % 18.78/18.90 ( hAPP(c_Nat_OSuc,V_x) = hAPP(c_Nat_OSuc,V_y) % 18.78/18.90 => V_x = V_y ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_nat_Oinject,axiom, % 18.78/18.90 ! [V_nat_H_2,V_nat_2] : % 18.78/18.90 ( hAPP(c_Nat_OSuc,V_nat_2) = hAPP(c_Nat_OSuc,V_nat_H_2) % 18.78/18.90 <=> V_nat_2 = V_nat_H_2 ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_Suc__n__not__n,axiom, % 18.78/18.90 ! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n ). % 18.78/18.90 % 18.78/18.90 fof(fact_n__not__Suc__n,axiom, % 18.78/18.90 ! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n) ). % 18.78/18.90 % 18.78/18.90 fof(fact_nat_Osize_I4_J,axiom, % 18.78/18.90 ! [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))) ). % 18.78/18.90 % 18.78/18.90 fof(fact_nat_Osize_I2_J,axiom, % 18.78/18.90 ! [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))) ). % 18.78/18.90 % 18.78/18.90 fof(fact_vname_Orecs_I1_J,axiom, % 18.78/18.90 ! [V_glb_2,V_f2_2,V_f1_2,T_b] : c_Com_Ovname_Ovname__rec(T_b,V_f1_2,V_f2_2,c_Com_Ovname_OGlb(V_glb_2)) = hAPP(V_f1_2,V_glb_2) ). % 18.78/18.90 % 18.78/18.90 fof(fact_vname_Osimps_I5_J,axiom, % 18.78/18.90 ! [V_glb_2,V_f2_2,V_f1_2,T_b] : c_Com_Ovname_Ovname__case(T_b,V_f1_2,V_f2_2,c_Com_Ovname_OGlb(V_glb_2)) = hAPP(V_f1_2,V_glb_2) ). % 18.78/18.90 % 18.78/18.90 fof(fact_com_Osize_I14_J,axiom, % 18.78/18.90 ! [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))) ). % 18.78/18.90 % 18.78/18.90 fof(fact_com_Osize_I6_J,axiom, % 18.78/18.90 ! [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))) ). % 18.78/18.90 % 18.78/18.90 fof(fact_com_Osize_I13_J,axiom, % 18.78/18.90 ! [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))) ). % 18.78/18.90 % 18.78/18.90 fof(fact_com_Osize_I5_J,axiom, % 18.78/18.90 ! [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))) ). % 18.78/18.90 % 18.78/18.90 fof(fact_com_Osize_I11_J,axiom, % 18.78/18.90 ! [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))) ). % 18.78/18.90 % 18.78/18.90 fof(fact_com_Osize_I3_J,axiom, % 18.78/18.90 ! [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))) ). % 18.78/18.90 % 18.78/18.90 fof(fact_com_Osize_I12_J,axiom, % 18.78/18.90 ! [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))) ). % 18.78/18.90 % 18.78/18.90 fof(fact_com_Osize_I4_J,axiom, % 18.78/18.90 ! [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))) ). % 18.78/18.90 % 18.78/18.90 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom, % 18.78/18.90 ! [V_a,T_a] : % 18.78/18.90 ( class_Rings_Ocomm__semiring__1(T_a) % 18.78/18.90 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom, % 18.78/18.90 ! [V_a,T_a] : % 18.78/18.90 ( class_Rings_Ocomm__semiring__1(T_a) % 18.78/18.90 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_add__0__iff,axiom, % 18.78/18.90 ! [V_a_2,V_b_2,T_b] : % 18.78/18.90 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b) % 18.78/18.90 => ( V_b_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2) % 18.78/18.90 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_double__eq__0__iff,axiom, % 18.78/18.90 ! [V_a_2,T_b] : % 18.78/18.90 ( class_Groups_Olinordered__ab__group__add(T_b) % 18.78/18.90 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b) % 18.78/18.90 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_option_Osimps_I5_J,axiom, % 18.78/18.90 ! [V_a_2,V_f2_2,V_f1_2,T_c,T_b] : hAPP(c_Option_Ooption_Ooption__case(T_b,T_c,V_f1_2,V_f2_2),hAPP(c_Option_Ooption_OSome(T_c),V_a_2)) = hAPP(V_f2_2,V_a_2) ). % 18.78/18.90 % 18.78/18.90 fof(fact_option_Orecs_I2_J,axiom, % 18.78/18.90 ! [V_a_2,V_f2_2,V_f1_2,T_c,T_b] : c_Option_Ooption_Ooption__rec(T_b,T_c,V_f1_2,V_f2_2,hAPP(c_Option_Ooption_OSome(T_c),V_a_2)) = hAPP(V_f2_2,V_a_2) ). % 18.78/18.90 % 18.78/18.90 fof(fact_option_Osimps_I4_J,axiom, % 18.78/18.90 ! [V_f2_2,V_f1_2,T_c,T_b] : hAPP(c_Option_Ooption_Ooption__case(T_b,T_c,V_f1_2,V_f2_2),c_Option_Ooption_ONone(T_c)) = V_f1_2 ). % 18.78/18.90 % 18.78/18.90 fof(fact_option_Orecs_I1_J,axiom, % 18.78/18.90 ! [V_f2_2,V_f1_2,T_c,T_b] : c_Option_Ooption_Ooption__rec(T_b,T_c,V_f1_2,V_f2_2,c_Option_Ooption_ONone(T_c)) = V_f1_2 ). % 18.78/18.90 % 18.78/18.90 fof(fact_is__none__code_I2_J,axiom, % 18.78/18.90 ! [V_x,T_b] : ~ c_Option_Ois__none(T_b,hAPP(c_Option_Ooption_OSome(T_b),V_x)) ). % 18.78/18.90 % 18.78/18.90 fof(fact_is__none__def,axiom, % 18.78/18.90 ! [V_x_2,T_b] : % 18.78/18.90 ( c_Option_Ois__none(T_b,V_x_2) % 18.78/18.90 <=> V_x_2 = c_Option_Ooption_ONone(T_b) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_is__none__code_I1_J,axiom, % 18.78/18.90 ! [T_a] : c_Option_Ois__none(T_a,c_Option_Ooption_ONone(T_a)) ). % 18.78/18.90 % 18.78/18.90 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom, % 18.78/18.90 ! [V_c,V_a,T_a] : % 18.78/18.90 ( class_Rings_Ocomm__semiring__1(T_a) % 18.78/18.90 => 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) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom, % 18.78/18.90 ! [V_d,V_c,V_a,T_a] : % 18.78/18.90 ( class_Rings_Ocomm__semiring__1(T_a) % 18.78/18.90 => 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)) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom, % 18.78/18.90 ! [V_d,V_c,V_a,T_a] : % 18.78/18.90 ( class_Rings_Ocomm__semiring__1(T_a) % 18.78/18.90 => 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) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom, % 18.78/18.90 ! [V_c,V_b,V_a,T_a] : % 18.78/18.90 ( class_Rings_Ocomm__semiring__1(T_a) % 18.78/18.90 => 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)) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom, % 18.78/18.90 ! [V_c,V_b,V_a,T_a] : % 18.78/18.90 ( class_Rings_Ocomm__semiring__1(T_a) % 18.78/18.90 => 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) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom, % 18.78/18.90 ! [V_d,V_c,V_b,V_a,T_a] : % 18.78/18.90 ( class_Rings_Ocomm__semiring__1(T_a) % 18.78/18.90 => 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)) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_of__nat__aux_Osimps_I2_J,axiom, % 18.78/18.90 ! [V_i_2,V_n_2,V_inc_2,T_b] : % 18.78/18.90 ( class_Rings_Osemiring__1(T_b) % 18.78/18.90 => c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,V_inc_2,hAPP(c_Nat_OSuc,V_n_2),V_i_2) = c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,V_inc_2,V_n_2,hAPP(V_inc_2,V_i_2)) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_of__nat__aux_Osimps_I1_J,axiom, % 18.78/18.90 ! [V_i_2,V_inc_2,T_b] : % 18.78/18.90 ( class_Rings_Osemiring__1(T_b) % 18.78/18.90 => c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,V_inc_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i_2) = V_i_2 ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_evalc__WHILE__case,axiom, % 18.78/18.90 ! [V_t_2,V_s_2,V_c_2,V_b_2] : % 18.78/18.90 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s_2),V_t_2)) % 18.78/18.90 => ( ( V_t_2 = V_s_2 % 18.78/18.90 => hBOOL(hAPP(V_b_2,V_s_2)) ) % 18.78/18.90 => ~ ( hBOOL(hAPP(V_b_2,V_s_2)) % 18.78/18.90 => ! [B_s1] : % 18.78/18.90 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c_2),V_s_2),B_s1)) % 18.78/18.90 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_c_2)),B_s1),V_t_2)) ) ) ) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_evaln__WHILE__case,axiom, % 18.78/18.90 ! [V_t_2,V_n_2,V_s_2,V_c_2,V_b_2] : % 18.78/18.90 ( c_Natural_Oevaln(c_Com_Ocom_OWhile(V_b_2,V_c_2),V_s_2,V_n_2,V_t_2) % 18.78/18.90 => ( ( V_t_2 = V_s_2 % 18.78/18.90 => hBOOL(hAPP(V_b_2,V_s_2)) ) % 18.78/18.90 => ~ ( hBOOL(hAPP(V_b_2,V_s_2)) % 18.78/18.90 => ! [B_s1] : % 18.78/18.90 ( c_Natural_Oevaln(V_c_2,V_s_2,V_n_2,B_s1) % 18.78/18.90 => ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(V_b_2,V_c_2),B_s1,V_n_2,V_t_2) ) ) ) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_pair__box_Osize_I1_J,axiom, % 18.78/18.90 ! [V_b_2,V_a_2,V_fb_2,V_fa_2,T_c,T_b] : c_Nitpick_Opair__box_Opair__box__size(T_b,T_c,V_fa_2,V_fb_2,c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_2,V_b_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),hAPP(V_fb_2,V_b_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 18.78/18.90 % 18.78/18.90 fof(fact_sum_Osize_I2_J,axiom, % 18.78/18.90 ! [V_b_2,V_fb_2,V_fa_2,T_c,T_b] : c_Sum__Type_Osum_Osum__size(T_b,T_c,V_fa_2,V_fb_2,hAPP(c_Sum__Type_OInr(T_c,T_b),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))) ). % 18.78/18.90 % 18.78/18.90 fof(fact_sum_Osize_I1_J,axiom, % 18.78/18.90 ! [V_a_2,V_fb_2,V_fa_2,T_c,T_b] : c_Sum__Type_Osum_Osum__size(T_b,T_c,V_fa_2,V_fb_2,hAPP(c_Sum__Type_OInl(T_b,T_c),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))) ). % 18.78/18.90 % 18.78/18.90 fof(fact_option_Oexhaust,axiom, % 18.78/18.90 ! [T_a,V_y] : % 18.78/18.90 ( V_y != c_Option_Ooption_ONone(T_a) % 18.78/18.90 => ~ ! [B_a] : V_y != hAPP(c_Option_Ooption_OSome(T_a),B_a) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_zero__less__Suc,axiom, % 18.78/18.90 ! [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))) ). % 18.78/18.90 % 18.78/18.90 fof(fact_nat_Oexhaust,axiom, % 18.78/18.90 ! [V_y] : % 18.78/18.90 ( V_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 18.78/18.90 => ~ ! [B_nat] : V_y != hAPP(c_Nat_OSuc,B_nat) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_zero__induct,axiom, % 18.78/18.90 ! [V_k_2,V_Pa_2] : % 18.78/18.90 ( hBOOL(hAPP(V_Pa_2,V_k_2)) % 18.78/18.90 => ( ! [B_n] : % 18.78/18.90 ( hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_OSuc,B_n))) % 18.78/18.90 => hBOOL(hAPP(V_Pa_2,B_n)) ) % 18.78/18.90 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_less__zeroE,axiom, % 18.78/18.90 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 18.78/18.90 % 18.78/18.90 fof(fact_Suc__mono,axiom, % 18.78/18.90 ! [V_n,V_m] : % 18.78/18.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 18.78/18.90 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_lessI,axiom, % 18.78/18.90 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_n))) ). % 18.78/18.90 % 18.78/18.90 fof(fact_pair__box_Oinject,axiom, % 18.78/18.90 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] : % 18.78/18.90 ( c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_2,V_b_2) = c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_H_2,V_b_H_2) % 18.78/18.90 <=> ( V_a_2 = V_a_H_2 % 18.78/18.90 & V_b_2 = V_b_H_2 ) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_less__not__refl,axiom, % 18.78/18.90 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ). % 18.78/18.90 % 18.78/18.90 fof(fact_nat__neq__iff,axiom, % 18.78/18.90 ! [V_n_2,V_m_2] : % 18.78/18.90 ( V_m_2 != V_n_2 % 18.78/18.90 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 18.78/18.90 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_linorder__neqE__nat,axiom, % 18.78/18.90 ! [V_y,V_x] : % 18.78/18.90 ( V_x != V_y % 18.78/18.90 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 18.78/18.90 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y),V_x)) ) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_less__irrefl__nat,axiom, % 18.78/18.90 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ). % 18.78/18.90 % 18.78/18.90 fof(fact_less__not__refl2,axiom, % 18.78/18.90 ! [V_m,V_n] : % 18.78/18.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m)) % 18.78/18.90 => V_m != V_n ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_less__not__refl3,axiom, % 18.78/18.90 ! [V_t,V_s] : % 18.78/18.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s),V_t)) % 18.78/18.90 => V_s != V_t ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_nat__less__cases,axiom, % 18.78/18.90 ! [V_Pa_2,V_n_2,V_m_2] : % 18.78/18.90 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 18.78/18.90 => hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) ) % 18.78/18.90 => ( ( V_m_2 = V_n_2 % 18.78/18.90 => hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) ) % 18.78/18.90 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 18.78/18.90 => hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) ) % 18.78/18.90 => hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) ) ) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_add__less__cancel__right,axiom, % 18.78/18.90 ! [V_b_2,V_c_2,V_a_2,T_b] : % 18.78/18.90 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b) % 18.78/18.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_c_2))) % 18.78/18.90 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_add__less__cancel__left,axiom, % 18.78/18.90 ! [V_b_2,V_a_2,V_c_2,T_b] : % 18.78/18.90 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b) % 18.78/18.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_b_2))) % 18.78/18.90 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_add__strict__right__mono,axiom, % 18.78/18.90 ! [V_c,V_b,V_a,T_a] : % 18.78/18.90 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 18.78/18.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 18.78/18.90 => 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))) ) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_add__strict__left__mono,axiom, % 18.78/18.90 ! [V_c,V_b,V_a,T_a] : % 18.78/18.90 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 18.78/18.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 18.78/18.90 => 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))) ) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_add__strict__mono,axiom, % 18.78/18.90 ! [V_d,V_c,V_b,V_a,T_a] : % 18.78/18.90 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 18.78/18.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 18.78/18.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 18.78/18.90 => 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))) ) ) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_add__less__imp__less__right,axiom, % 18.78/18.90 ! [V_b,V_c,V_a,T_a] : % 18.78/18.90 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 18.78/18.90 => ( 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))) % 18.78/18.90 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_add__less__imp__less__left,axiom, % 18.78/18.90 ! [V_b,V_a,V_c,T_a] : % 18.78/18.90 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 18.78/18.90 => ( 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))) % 18.78/18.90 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_not__less0,axiom, % 18.78/18.90 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 18.78/18.90 % 18.78/18.90 fof(fact_neq0__conv,axiom, % 18.78/18.90 ! [V_n_2] : % 18.78/18.90 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 18.78/18.90 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_less__nat__zero__code,axiom, % 18.78/18.90 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 18.78/18.90 % 18.78/18.90 fof(fact_gr__implies__not0,axiom, % 18.78/18.90 ! [V_n,V_m] : % 18.78/18.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 18.78/18.90 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_gr0I,axiom, % 18.78/18.90 ! [V_n] : % 18.78/18.90 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 18.78/18.90 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_Suc__less__SucD,axiom, % 18.78/18.90 ! [V_n,V_m] : % 18.78/18.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) % 18.78/18.90 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_Suc__lessD,axiom, % 18.78/18.90 ! [V_n,V_m] : % 18.78/18.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) % 18.78/18.90 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_less__SucE,axiom, % 18.78/18.90 ! [V_n,V_m] : % 18.78/18.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) % 18.78/18.90 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 18.78/18.90 => V_m = V_n ) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_less__trans__Suc,axiom, % 18.78/18.90 ! [V_k,V_j,V_i] : % 18.78/18.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 18.78/18.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k)) % 18.78/18.90 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_i)),V_k)) ) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_Suc__lessI,axiom, % 18.78/18.90 ! [V_n,V_m] : % 18.78/18.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 18.78/18.90 => ( hAPP(c_Nat_OSuc,V_m) != V_n % 18.78/18.90 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_less__SucI,axiom, % 18.78/18.90 ! [V_n,V_m] : % 18.78/18.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 18.78/18.90 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_less__antisym,axiom, % 18.78/18.90 ! [V_m,V_n] : % 18.78/18.90 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m)) % 18.78/18.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_m))) % 18.78/18.90 => V_m = V_n ) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_not__less__less__Suc__eq,axiom, % 18.78/18.90 ! [V_m_2,V_n_2] : % 18.78/18.90 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 18.78/18.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) % 18.78/18.90 <=> V_n_2 = V_m_2 ) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_Suc__less__eq,axiom, % 18.78/18.90 ! [V_n_2,V_m_2] : % 18.78/18.90 ( 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))) % 18.78/18.90 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_less__Suc__eq,axiom, % 18.78/18.90 ! [V_n_2,V_m_2] : % 18.78/18.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 18.78/18.90 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 18.78/18.90 | V_m_2 = V_n_2 ) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_not__less__eq,axiom, % 18.78/18.90 ! [V_n_2,V_m_2] : % 18.78/18.90 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 18.78/18.90 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_add__lessD1,axiom, % 18.78/18.90 ! [V_k,V_j,V_i] : % 18.78/18.90 ( 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)) % 18.78/18.90 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_k)) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_less__add__eq__less,axiom, % 18.78/18.90 ! [V_n,V_m,V_l,V_k] : % 18.78/18.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l)) % 18.78/18.90 => ( 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) % 18.78/18.90 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_add__less__mono,axiom, % 18.78/18.90 ! [V_l,V_k,V_j,V_i] : % 18.78/18.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 18.78/18.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l)) % 18.78/18.90 => 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))) ) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_add__less__mono1,axiom, % 18.78/18.90 ! [V_k,V_j,V_i] : % 18.78/18.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 18.78/18.90 => 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))) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_trans__less__add2,axiom, % 18.78/18.90 ! [V_m,V_j,V_i] : % 18.78/18.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 18.78/18.90 => 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))) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_trans__less__add1,axiom, % 18.78/18.90 ! [V_m,V_j,V_i] : % 18.78/18.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 18.78/18.90 => 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))) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_nat__add__left__cancel__less,axiom, % 18.78/18.90 ! [V_n_2,V_m_2,V_k_2] : % 18.78/18.90 ( 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))) % 18.78/18.90 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_not__add__less2,axiom, % 18.78/18.90 ! [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)) ). % 18.78/18.90 % 18.78/18.90 fof(fact_not__add__less1,axiom, % 18.78/18.90 ! [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)) ). % 18.78/18.90 % 18.78/18.90 fof(fact_add__neg__neg,axiom, % 18.78/18.90 ! [V_b,V_a,T_a] : % 18.78/18.90 ( class_Groups_Oordered__comm__monoid__add(T_a) % 18.78/18.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 18.78/18.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 18.78/18.90 => 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))) ) ) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_add__pos__pos,axiom, % 18.78/18.90 ! [V_b,V_a,T_a] : % 18.78/18.90 ( class_Groups_Oordered__comm__monoid__add(T_a) % 18.78/18.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 18.78/18.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 18.78/18.90 => 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))) ) ) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom, % 18.78/18.90 ! [V_a_2,T_b] : % 18.78/18.90 ( class_Groups_Olinordered__ab__group__add(T_b) % 18.78/18.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b))) % 18.78/18.90 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom, % 18.78/18.90 ! [V_a_2,T_b] : % 18.78/18.90 ( class_Groups_Olinordered__ab__group__add(T_b) % 18.78/18.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2))) % 18.78/18.90 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_even__less__0__iff,axiom, % 18.78/18.90 ! [V_a_2,T_b] : % 18.78/18.90 ( class_Rings_Olinordered__idom(T_b) % 18.78/18.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b))) % 18.78/18.90 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_gr0__conv__Suc,axiom, % 18.78/18.90 ! [V_n_2] : % 18.78/18.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 18.78/18.90 <=> ? [B_m] : V_n_2 = hAPP(c_Nat_OSuc,B_m) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_less__Suc0,axiom, % 18.78/18.90 ! [V_n_2] : % 18.78/18.90 ( 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)))) % 18.78/18.90 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_less__Suc__eq__0__disj,axiom, % 18.78/18.90 ! [V_n_2,V_m_2] : % 18.78/18.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 18.78/18.90 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 18.78/18.90 | ? [B_j] : % 18.78/18.90 ( V_m_2 = hAPP(c_Nat_OSuc,B_j) % 18.78/18.90 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_n_2)) ) ) ) ). % 18.78/18.90 % 18.78/18.90 fof(fact_add__gr__0,axiom, % 18.78/18.90 ! [V_n_2,V_m_2] : % 18.78/18.90 ( 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))) % 18.78/18.90 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) % 18.78/18.91 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_less__add__Suc1,axiom, % 18.78/18.91 ! [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)))) ). % 18.78/18.91 % 18.78/18.91 fof(fact_less__add__Suc2,axiom, % 18.78/18.91 ! [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)))) ). % 18.78/18.91 % 18.78/18.91 fof(fact_less__iff__Suc__add,axiom, % 18.78/18.91 ! [V_n_2,V_m_2] : % 18.78/18.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 18.78/18.91 <=> ? [B_k] : V_n_2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_pair__box_Osize_I2_J,axiom, % 18.78/18.91 ! [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) ). % 18.78/18.91 % 18.78/18.91 fof(fact_pair__box_Osimps_I2_J,axiom, % 18.78/18.91 ! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : c_Nitpick_Opair__box_Opair__box__case(T_c,T_d,T_b,V_f1_2,c_Nitpick_Opair__box_OPairBox(T_c,T_d,V_a_2,V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2) ). % 18.78/18.91 % 18.78/18.91 fof(fact_pair__box_Orecs,axiom, % 18.78/18.91 ! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : c_Nitpick_Opair__box_Opair__box__rec(T_c,T_d,T_b,V_f1_2,c_Nitpick_Opair__box_OPairBox(T_c,T_d,V_a_2,V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2) ). % 18.78/18.91 % 18.78/18.91 fof(fact_pos__add__strict,axiom, % 18.78/18.91 ! [V_c,V_b,V_a,T_a] : % 18.78/18.91 ( class_Rings_Olinordered__semidom(T_a) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 18.78/18.91 => 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))) ) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_sum_Osimps_I4_J,axiom, % 18.78/18.91 ! [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) ). % 18.78/18.91 % 18.78/18.91 fof(fact_Inr__not__Inl,axiom, % 18.78/18.91 ! [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) ). % 18.78/18.91 % 18.78/18.91 fof(fact_sum_Osimps_I3_J,axiom, % 18.78/18.91 ! [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) ). % 18.78/18.91 % 18.78/18.91 fof(fact_Inl__not__Inr,axiom, % 18.78/18.91 ! [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) ). % 18.78/18.91 % 18.78/18.91 fof(fact_sum_Osize_I3_J,axiom, % 18.78/18.91 ! [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) ). % 18.78/18.91 % 18.78/18.91 fof(fact_sum_Osize_I4_J,axiom, % 18.78/18.91 ! [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) ). % 18.78/18.91 % 18.78/18.91 fof(fact_termination__basic__simps_I2_J,axiom, % 18.78/18.91 ! [V_y,V_z,V_x] : % 18.78/18.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_z)) % 18.78/18.91 => 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))) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_linorder__neqE__linordered__idom,axiom, % 18.78/18.91 ! [V_y,V_x,T_a] : % 18.78/18.91 ( class_Rings_Olinordered__idom(T_a) % 18.78/18.91 => ( V_x != V_y % 18.78/18.91 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 18.78/18.91 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_sum_Osimps_I2_J,axiom, % 18.78/18.91 ! [V_b_H_2,V_b_2,T_b,T_c] : % 18.78/18.91 ( hAPP(c_Sum__Type_OInr(T_c,T_b),V_b_2) = hAPP(c_Sum__Type_OInr(T_c,T_b),V_b_H_2) % 18.78/18.91 <=> V_b_2 = V_b_H_2 ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_Inr__inject,axiom, % 18.78/18.91 ! [V_y,V_x,T_a,T_b] : % 18.78/18.91 ( hAPP(c_Sum__Type_OInr(T_b,T_a),V_x) = hAPP(c_Sum__Type_OInr(T_b,T_a),V_y) % 18.78/18.91 => V_x = V_y ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_sum_Osimps_I1_J,axiom, % 18.78/18.91 ! [V_a_H_2,V_a_2,T_c,T_b] : % 18.78/18.91 ( hAPP(c_Sum__Type_OInl(T_b,T_c),V_a_2) = hAPP(c_Sum__Type_OInl(T_b,T_c),V_a_H_2) % 18.78/18.91 <=> V_a_2 = V_a_H_2 ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_Inl__inject,axiom, % 18.78/18.91 ! [V_y,V_x,T_b,T_a] : % 18.78/18.91 ( hAPP(c_Sum__Type_OInl(T_a,T_b),V_x) = hAPP(c_Sum__Type_OInl(T_a,T_b),V_y) % 18.78/18.91 => V_x = V_y ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_termination__basic__simps_I1_J,axiom, % 18.78/18.91 ! [V_z,V_y,V_x] : % 18.78/18.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 18.78/18.91 => 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))) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_Projl_Osimps,axiom, % 18.78/18.91 ! [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 ). % 18.78/18.91 % 18.78/18.91 fof(fact_Projr_Osimps,axiom, % 18.78/18.91 ! [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 ). % 18.78/18.91 % 18.78/18.91 fof(fact_sum_Orecs_I1_J,axiom, % 18.78/18.91 ! [V_a_2,V_f2_2,V_f1_2,T_d,T_b,T_c] : c_Sum__Type_Osum_Osum__rec(T_c,T_b,T_d,V_f1_2,V_f2_2,hAPP(c_Sum__Type_OInl(T_c,T_d),V_a_2)) = hAPP(V_f1_2,V_a_2) ). % 18.78/18.91 % 18.78/18.91 fof(fact_sum_Orecs_I2_J,axiom, % 18.78/18.91 ! [V_b_2,V_f2_2,V_f1_2,T_d,T_b,T_c] : c_Sum__Type_Osum_Osum__rec(T_c,T_b,T_d,V_f1_2,V_f2_2,hAPP(c_Sum__Type_OInr(T_d,T_c),V_b_2)) = hAPP(V_f2_2,V_b_2) ). % 18.78/18.91 % 18.78/18.91 fof(fact_Suml_Osimps,axiom, % 18.78/18.91 ! [V_x_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Sum__Type_OSuml(T_c,T_b,T_d,V_f_2),hAPP(c_Sum__Type_OInl(T_c,T_d),V_x_2)) = hAPP(V_f_2,V_x_2) ). % 18.78/18.91 % 18.78/18.91 fof(fact_Sumr_Osimps,axiom, % 18.78/18.91 ! [V_x_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Sum__Type_OSumr(T_c,T_b,T_d,V_f_2),hAPP(c_Sum__Type_OInr(T_c,T_d),V_x_2)) = hAPP(V_f_2,V_x_2) ). % 18.78/18.91 % 18.78/18.91 fof(fact_of__nat__0__less__iff,axiom, % 18.78/18.91 ! [V_n_2,T_b] : % 18.78/18.91 ( class_Rings_Olinordered__semidom(T_b) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2))) % 18.78/18.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_less__imp__Suc__add,axiom, % 18.78/18.91 ! [V_n,V_m] : % 18.78/18.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 18.78/18.91 => ? [B_k] : V_n = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),B_k)) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_less__imp__add__positive,axiom, % 18.78/18.91 ! [V_j,V_i] : % 18.78/18.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 18.78/18.91 => ? [B_k] : % 18.78/18.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_k)) % 18.78/18.91 & hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),B_k) = V_j ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_gr0__implies__Suc,axiom, % 18.78/18.91 ! [V_n] : % 18.78/18.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 18.78/18.91 => ? [B_m] : V_n = hAPP(c_Nat_OSuc,B_m) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_of__nat__eq__iff,axiom, % 18.78/18.91 ! [V_n_2,V_m_2,T_b] : % 18.78/18.91 ( class_Nat_Osemiring__char__0(T_b) % 18.78/18.91 => ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_m_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2) % 18.78/18.91 <=> V_m_2 = V_n_2 ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_Sumr__inject,axiom, % 18.78/18.91 ! [V_g_2,V_f_2,T_b,T_d,T_c] : % 18.78/18.91 ( c_Sum__Type_OSumr(T_c,T_d,T_b,V_f_2) = c_Sum__Type_OSumr(T_c,T_d,T_b,V_g_2) % 18.78/18.91 => V_f_2 = V_g_2 ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_Suml__inject,axiom, % 18.78/18.91 ! [V_g_2,V_f_2,T_c,T_d,T_b] : % 18.78/18.91 ( c_Sum__Type_OSuml(T_b,T_d,T_c,V_f_2) = c_Sum__Type_OSuml(T_b,T_d,T_c,V_g_2) % 18.78/18.91 => V_f_2 = V_g_2 ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_int__eq__0__conv,axiom, % 18.78/18.91 ! [V_n_2] : % 18.78/18.91 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 18.78/18.91 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_int__0,axiom, % 18.78/18.91 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) ). % 18.78/18.91 % 18.78/18.91 fof(fact_zless__iff__Suc__zadd,axiom, % 18.78/18.91 ! [V_z_2,V_w_2] : % 18.78/18.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) % 18.78/18.91 <=> ? [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))) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_zless__int,axiom, % 18.78/18.91 ! [V_n_2,V_m_2] : % 18.78/18.91 ( 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))) % 18.78/18.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_zadd__int,axiom, % 18.78/18.91 ! [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)) ). % 18.78/18.91 % 18.78/18.91 fof(fact_zadd__int__left,axiom, % 18.78/18.91 ! [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) ). % 18.78/18.91 % 18.78/18.91 fof(fact_zero__less__int__conv,axiom, % 18.78/18.91 ! [V_n_2] : % 18.78/18.91 ( 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))) % 18.78/18.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_of__nat__less__0__iff,axiom, % 18.78/18.91 ! [V_m,T_a] : % 18.78/18.91 ( class_Rings_Olinordered__semidom(T_a) % 18.78/18.91 => ~ 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))) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_of__nat__0,axiom, % 18.78/18.91 ! [T_a] : % 18.78/18.91 ( class_Rings_Osemiring__1(T_a) % 18.78/18.91 => 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) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_of__nat__less__iff,axiom, % 18.78/18.91 ! [V_n_2,V_m_2,T_b] : % 18.78/18.91 ( class_Rings_Olinordered__semidom(T_b) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2))) % 18.78/18.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_less__imp__of__nat__less,axiom, % 18.78/18.91 ! [V_n,V_m,T_a] : % 18.78/18.91 ( class_Rings_Olinordered__semidom(T_a) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 18.78/18.91 => 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))) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_of__nat__less__imp__less,axiom, % 18.78/18.91 ! [V_n,V_m,T_a] : % 18.78/18.91 ( class_Rings_Olinordered__semidom(T_a) % 18.78/18.91 => ( 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))) % 18.78/18.91 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_of__nat__add,axiom, % 18.78/18.91 ! [V_n,V_m,T_a] : % 18.78/18.91 ( class_Rings_Osemiring__1(T_a) % 18.78/18.91 => 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)) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_lift__Suc__mono__less,axiom, % 18.78/18.91 ! [V_n_H_2,V_n_2,V_f_2,T_b] : % 18.78/18.91 ( class_Orderings_Oorder(T_b) % 18.78/18.91 => ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_n)),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_n)))) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_n_H_2)) % 18.78/18.91 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,V_n_2)),hAPP(V_f_2,V_n_H_2))) ) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_lift__Suc__mono__less__iff,axiom, % 18.78/18.91 ! [V_m_2,V_n_2,V_f_2,T_b] : % 18.78/18.91 ( class_Orderings_Oorder(T_b) % 18.78/18.91 => ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_n)),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_n)))) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,V_n_2)),hAPP(V_f_2,V_m_2))) % 18.78/18.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom, % 18.78/18.91 ! [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)) ). % 18.78/18.91 % 18.78/18.91 fof(fact_transfer__int__nat__relations_I2_J,axiom, % 18.78/18.91 ! [V_y_2,V_x_2] : % 18.78/18.91 ( 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))) % 18.78/18.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_transfer__int__nat__numerals_I1_J,axiom, % 18.78/18.91 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)) ). % 18.78/18.91 % 18.78/18.91 fof(fact_linorder__cases,axiom, % 18.78/18.91 ! [V_y,V_x,T_a] : % 18.78/18.91 ( class_Orderings_Olinorder(T_a) % 18.78/18.91 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 18.78/18.91 => ( V_x != V_y % 18.78/18.91 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_order__less__asym,axiom, % 18.78/18.91 ! [V_y,V_x,T_a] : % 18.78/18.91 ( class_Orderings_Opreorder(T_a) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 18.78/18.91 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_xt1_I10_J,axiom, % 18.78/18.91 ! [V_z,V_x,V_y,T_a] : % 18.78/18.91 ( class_Orderings_Oorder(T_a) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y)) % 18.78/18.91 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_order__less__trans,axiom, % 18.78/18.91 ! [V_z,V_y,V_x,T_a] : % 18.78/18.91 ( class_Orderings_Opreorder(T_a) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z)) % 18.78/18.91 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_xt1_I2_J,axiom, % 18.78/18.91 ! [V_c,V_a,V_b,T_a] : % 18.78/18.91 ( class_Orderings_Oorder(T_a) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 18.78/18.91 => ( V_b = V_c % 18.78/18.91 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_int__less__0__conv,axiom, % 18.78/18.91 ! [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))) ). % 18.78/18.91 % 18.78/18.91 fof(fact_int__int__eq,axiom, % 18.78/18.91 ! [V_n_2,V_m_2] : % 18.78/18.91 ( 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) % 18.78/18.91 <=> V_m_2 = V_n_2 ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_transfer__int__nat__relations_I1_J,axiom, % 18.78/18.91 ! [V_y_2,V_x_2] : % 18.78/18.91 ( 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) % 18.78/18.91 <=> V_x_2 = V_y_2 ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_zadd__commute,axiom, % 18.78/18.91 ! [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) ). % 18.78/18.91 % 18.78/18.91 fof(fact_zadd__left__commute,axiom, % 18.78/18.91 ! [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)) ). % 18.78/18.91 % 18.78/18.91 fof(fact_zadd__assoc,axiom, % 18.78/18.91 ! [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)) ). % 18.78/18.91 % 18.78/18.91 fof(fact_zadd__0__right,axiom, % 18.78/18.91 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z ). % 18.78/18.91 % 18.78/18.91 fof(fact_zadd__0,axiom, % 18.78/18.91 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z) = V_z ). % 18.78/18.91 % 18.78/18.91 fof(fact_zless__linear,axiom, % 18.78/18.91 ! [V_y,V_x] : % 18.78/18.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),V_y)) % 18.78/18.91 | V_x = V_y % 18.78/18.91 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_x)) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_zadd__strict__right__mono,axiom, % 18.78/18.91 ! [V_k,V_j,V_i] : % 18.78/18.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) % 18.78/18.91 => 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))) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_order__less__irrefl,axiom, % 18.78/18.91 ! [V_x,T_a] : % 18.78/18.91 ( class_Orderings_Opreorder(T_a) % 18.78/18.91 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_x)) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_linorder__neq__iff,axiom, % 18.78/18.91 ! [V_y_2,V_x_2,T_b] : % 18.78/18.91 ( class_Orderings_Olinorder(T_b) % 18.78/18.91 => ( V_x_2 != V_y_2 % 18.78/18.91 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 18.78/18.91 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_not__less__iff__gr__or__eq,axiom, % 18.78/18.91 ! [V_y_2,V_x_2,T_b] : % 18.78/18.91 ( class_Orderings_Olinorder(T_b) % 18.78/18.91 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 18.78/18.91 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) % 18.78/18.91 | V_x_2 = V_y_2 ) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_linorder__less__linear,axiom, % 18.78/18.91 ! [V_y,V_x,T_a] : % 18.78/18.91 ( class_Orderings_Olinorder(T_a) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 18.78/18.91 | V_x = V_y % 18.78/18.91 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_linorder__antisym__conv3,axiom, % 18.78/18.91 ! [V_x_2,V_y_2,T_b] : % 18.78/18.91 ( class_Orderings_Olinorder(T_b) % 18.78/18.91 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) % 18.78/18.91 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 18.78/18.91 <=> V_x_2 = V_y_2 ) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_linorder__neqE,axiom, % 18.78/18.91 ! [V_y,V_x,T_a] : % 18.78/18.91 ( class_Orderings_Olinorder(T_a) % 18.78/18.91 => ( V_x != V_y % 18.78/18.91 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 18.78/18.91 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_less__imp__neq,axiom, % 18.78/18.91 ! [V_y,V_x,T_a] : % 18.78/18.91 ( class_Orderings_Oorder(T_a) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 18.78/18.91 => V_x != V_y ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_order__less__not__sym,axiom, % 18.78/18.91 ! [V_y,V_x,T_a] : % 18.78/18.91 ( class_Orderings_Opreorder(T_a) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 18.78/18.91 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_order__less__imp__not__less,axiom, % 18.78/18.91 ! [V_y,V_x,T_a] : % 18.78/18.91 ( class_Orderings_Opreorder(T_a) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 18.78/18.91 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_order__less__imp__not__eq,axiom, % 18.78/18.91 ! [V_y,V_x,T_a] : % 18.78/18.91 ( class_Orderings_Oorder(T_a) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 18.78/18.91 => V_x != V_y ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_order__less__imp__not__eq2,axiom, % 18.78/18.91 ! [V_y,V_x,T_a] : % 18.78/18.91 ( class_Orderings_Oorder(T_a) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 18.78/18.91 => V_y != V_x ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_order__less__asym_H,axiom, % 18.78/18.91 ! [V_b,V_a,T_a] : % 18.78/18.91 ( class_Orderings_Opreorder(T_a) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 18.78/18.91 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_xt1_I9_J,axiom, % 18.78/18.91 ! [V_a,V_b,T_a] : % 18.78/18.91 ( class_Orderings_Oorder(T_a) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 18.78/18.91 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_ord__eq__less__trans,axiom, % 18.78/18.91 ! [V_c,V_b,V_a,T_a] : % 18.78/18.91 ( class_Orderings_Oord(T_a) % 18.78/18.91 => ( V_a = V_b % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 18.78/18.91 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_xt1_I1_J,axiom, % 18.78/18.91 ! [V_c,V_b,V_a,T_a] : % 18.78/18.91 ( class_Orderings_Oorder(T_a) % 18.78/18.91 => ( V_a = V_b % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_b)) % 18.78/18.91 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_ord__less__eq__trans,axiom, % 18.78/18.91 ! [V_c,V_b,V_a,T_a] : % 18.78/18.91 ( class_Orderings_Oord(T_a) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 18.78/18.91 => ( V_b = V_c % 18.78/18.91 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_zero__less__imp__eq__int,axiom, % 18.78/18.91 ! [V_k] : % 18.78/18.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 18.78/18.91 => ? [B_n] : % 18.78/18.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)) % 18.78/18.91 & V_k = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_of__int__0__less__iff,axiom, % 18.78/18.91 ! [V_z_2,T_b] : % 18.78/18.91 ( class_Rings_Olinordered__idom(T_b) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2))) % 18.78/18.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_of__int__less__0__iff,axiom, % 18.78/18.91 ! [V_z_2,T_b] : % 18.78/18.91 ( class_Rings_Olinordered__idom(T_b) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)),c_Groups_Ozero__class_Ozero(T_b))) % 18.78/18.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_zmult__zless__mono2__lemma,axiom, % 18.78/18.91 ! [V_k,V_j,V_i] : % 18.78/18.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 18.78/18.91 => 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))) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_negative__zless__0,axiom, % 18.78/18.91 ! [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))) ). % 18.78/18.91 % 18.78/18.91 fof(fact_split__nat,axiom, % 18.78/18.91 ! [V_i_2,V_Pa_2] : % 18.78/18.91 ( hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,V_i_2))) % 18.78/18.91 <=> ( ! [B_n] : % 18.78/18.91 ( V_i_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) % 18.78/18.91 => hBOOL(hAPP(V_Pa_2,B_n)) ) % 18.78/18.91 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 18.78/18.91 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_zero__less__nat__eq,axiom, % 18.78/18.91 ! [V_z_2] : % 18.78/18.91 ( 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))) % 18.78/18.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_negative__zless,axiom, % 18.78/18.91 ! [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))) ). % 18.78/18.91 % 18.78/18.91 fof(fact_int__Suc,axiom, % 18.78/18.91 ! [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)) ). % 18.78/18.91 % 18.78/18.91 fof(fact_odd__less__0,axiom, % 18.78/18.91 ! [V_z_2] : % 18.78/18.91 ( 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))) % 18.78/18.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom, % 18.78/18.91 ! [V_m,T_a] : % 18.78/18.91 ( class_Rings_Ocomm__semiring__1(T_a) % 18.78/18.91 => 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) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom, % 18.78/18.91 ! [V_a,V_m,T_a] : % 18.78/18.91 ( class_Rings_Ocomm__semiring__1(T_a) % 18.78/18.91 => 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) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom, % 18.78/18.91 ! [V_m,V_a,T_a] : % 18.78/18.91 ( class_Rings_Ocomm__semiring__1(T_a) % 18.78/18.91 => 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) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_less__1__mult,axiom, % 18.78/18.91 ! [V_n,V_m,T_a] : % 18.78/18.91 ( class_Rings_Olinordered__semidom(T_a) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_m)) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_n)) % 18.78/18.91 => 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))) ) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_minus__mult__right,axiom, % 18.78/18.91 ! [V_b,V_a,T_a] : % 18.78/18.91 ( class_Rings_Oring(T_a) % 18.78/18.91 => 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)) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_minus__mult__left,axiom, % 18.78/18.91 ! [V_b,V_a,T_a] : % 18.78/18.91 ( class_Rings_Oring(T_a) % 18.78/18.91 => 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) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_minus__mult__commute,axiom, % 18.78/18.91 ! [V_b,V_a,T_a] : % 18.78/18.91 ( class_Rings_Oring(T_a) % 18.78/18.91 => 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)) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_minus__mult__minus,axiom, % 18.78/18.91 ! [V_b,V_a,T_a] : % 18.78/18.91 ( class_Rings_Oring(T_a) % 18.78/18.91 => 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) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_square__eq__1__iff,axiom, % 18.78/18.91 ! [V_x_2,T_b] : % 18.78/18.91 ( class_Rings_Oring__1__no__zero__divisors(T_b) % 18.78/18.91 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_b) % 18.78/18.91 <=> ( V_x_2 = c_Groups_Oone__class_Oone(T_b) % 18.78/18.91 | V_x_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b)) ) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_square__eq__iff,axiom, % 18.78/18.91 ! [V_b_2,V_a_2,T_b] : % 18.78/18.91 ( class_Rings_Oidom(T_b) % 18.78/18.91 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_a_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_b_2) % 18.78/18.91 <=> ( V_a_2 = V_b_2 % 18.78/18.91 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) ) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_of__int__1,axiom, % 18.78/18.91 ! [T_a] : % 18.78/18.91 ( class_Rings_Oring__1(T_a) % 18.78/18.91 => 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) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom, % 18.78/18.91 ! [V_x,T_a] : % 18.78/18.91 ( class_Rings_Ocomm__ring__1(T_a) % 18.78/18.91 => 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) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_zminus__zminus,axiom, % 18.78/18.91 ! [V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = V_z ). % 18.78/18.91 % 18.78/18.91 fof(fact_of__int__minus,axiom, % 18.78/18.91 ! [V_z,T_a] : % 18.78/18.91 ( class_Rings_Oring__1(T_a) % 18.78/18.91 => 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)) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_of__int__mult,axiom, % 18.78/18.91 ! [V_z,V_w,T_a] : % 18.78/18.91 ( class_Rings_Oring__1(T_a) % 18.78/18.91 => 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)) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom, % 18.78/18.91 ! [V_a,T_a] : % 18.78/18.91 ( class_Rings_Ocomm__semiring__1(T_a) % 18.78/18.91 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_zmult__1,axiom, % 18.78/18.91 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z ). % 18.78/18.91 % 18.78/18.91 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom, % 18.78/18.91 ! [V_a,T_a] : % 18.78/18.91 ( class_Rings_Ocomm__semiring__1(T_a) % 18.78/18.91 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_zmult__1__right,axiom, % 18.78/18.91 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z ). % 18.78/18.91 % 18.78/18.91 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom, % 18.78/18.91 ! [V_b,V_a,T_a] : % 18.78/18.91 ( class_Rings_Ocomm__semiring__1(T_a) % 18.78/18.91 => 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) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_zmult__commute,axiom, % 18.78/18.91 ! [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) ). % 18.78/18.91 % 18.78/18.91 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom, % 18.78/18.91 ! [V_ry,V_rx,V_lx,T_a] : % 18.78/18.91 ( class_Rings_Ocomm__semiring__1(T_a) % 18.78/18.91 => 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)) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom, % 18.78/18.91 ! [V_ry,V_rx,V_lx,T_a] : % 18.78/18.91 ( class_Rings_Ocomm__semiring__1(T_a) % 18.78/18.91 => 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) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_zmult__zminus,axiom, % 18.78/18.91 ! [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)) ). % 18.78/18.91 % 18.78/18.91 fof(fact_of__int__eq__iff,axiom, % 18.78/18.91 ! [V_z_2,V_w_2,T_b] : % 18.78/18.91 ( class_Int_Oring__char__0(T_b) % 18.78/18.91 => ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_w_2) = hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2) % 18.78/18.91 <=> V_w_2 = V_z_2 ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom, % 18.78/18.91 ! [V_rx,V_ly,V_lx,T_a] : % 18.78/18.91 ( class_Rings_Ocomm__semiring__1(T_a) % 18.78/18.91 => 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)) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_zmult__assoc,axiom, % 18.78/18.91 ! [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)) ). % 18.78/18.91 % 18.78/18.91 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom, % 18.78/18.91 ! [V_rx,V_ly,V_lx,T_a] : % 18.78/18.91 ( class_Rings_Ocomm__semiring__1(T_a) % 18.78/18.91 => 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) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom, % 18.78/18.91 ! [V_ry,V_rx,V_ly,V_lx,T_a] : % 18.78/18.91 ( class_Rings_Ocomm__semiring__1(T_a) % 18.78/18.91 => 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))) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom, % 18.78/18.91 ! [V_ry,V_rx,V_ly,V_lx,T_a] : % 18.78/18.91 ( class_Rings_Ocomm__semiring__1(T_a) % 18.78/18.91 => 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)) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom, % 18.78/18.91 ! [V_ry,V_rx,V_ly,V_lx,T_a] : % 18.78/18.91 ( class_Rings_Ocomm__semiring__1(T_a) % 18.78/18.91 => 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)) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_minus__minus,axiom, % 18.78/18.91 ! [V_a,T_a] : % 18.78/18.91 ( class_Groups_Ogroup__add(T_a) % 18.78/18.91 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = V_a ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_mult__1__left,axiom, % 18.78/18.91 ! [V_a,T_a] : % 18.78/18.91 ( class_Groups_Omonoid__mult(T_a) % 18.78/18.91 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_mult__1,axiom, % 18.78/18.91 ! [V_a,T_a] : % 18.78/18.91 ( class_Groups_Ocomm__monoid__mult(T_a) % 18.78/18.91 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_one__reorient,axiom, % 18.78/18.91 ! [V_x_2,T_b] : % 18.78/18.91 ( class_Groups_Oone(T_b) % 18.78/18.91 => ( c_Groups_Oone__class_Oone(T_b) = V_x_2 % 18.78/18.91 <=> V_x_2 = c_Groups_Oone__class_Oone(T_b) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_mult__1__right,axiom, % 18.78/18.91 ! [V_a,T_a] : % 18.78/18.91 ( class_Groups_Omonoid__mult(T_a) % 18.78/18.91 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_mult_Ocomm__neutral,axiom, % 18.78/18.91 ! [V_a,T_a] : % 18.78/18.91 ( class_Groups_Ocomm__monoid__mult(T_a) % 18.78/18.91 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_equation__minus__iff,axiom, % 18.78/18.91 ! [V_b_2,V_a_2,T_b] : % 18.78/18.91 ( class_Groups_Ogroup__add(T_b) % 18.78/18.91 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) % 18.78/18.91 <=> V_b_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_minus__equation__iff,axiom, % 18.78/18.91 ! [V_b_2,V_a_2,T_b] : % 18.78/18.91 ( class_Groups_Ogroup__add(T_b) % 18.78/18.91 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_b_2 % 18.78/18.91 <=> hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) = V_a_2 ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_neg__equal__iff__equal,axiom, % 18.78/18.91 ! [V_b_2,V_a_2,T_b] : % 18.78/18.91 ( class_Groups_Ogroup__add(T_b) % 18.78/18.91 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) % 18.78/18.91 <=> V_a_2 = V_b_2 ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom, % 18.78/18.91 ! [V_c,V_b,V_a,T_a] : % 18.78/18.91 ( class_Groups_Oab__semigroup__mult(T_a) % 18.78/18.91 => 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)) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_of__nat__mult,axiom, % 18.78/18.91 ! [V_n,V_m,T_a] : % 18.78/18.91 ( class_Rings_Osemiring__1(T_a) % 18.78/18.91 => 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)) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_of__nat__1,axiom, % 18.78/18.91 ! [T_a] : % 18.78/18.91 ( class_Rings_Osemiring__1(T_a) % 18.78/18.91 => 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) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_of__int__of__nat,axiom, % 18.78/18.91 ! [V_k,T_a] : % 18.78/18.91 ( class_Rings_Oring__1(T_a) % 18.78/18.91 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 18.78/18.91 => 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)))) ) % 18.78/18.91 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 18.78/18.91 => 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)) ) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_nat__zminus__int,axiom, % 18.78/18.91 ! [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) ). % 18.78/18.91 % 18.78/18.91 fof(fact_nat__1,axiom, % 18.78/18.91 hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 18.78/18.91 % 18.78/18.91 fof(fact_pos__zmult__eq__1__iff,axiom, % 18.78/18.91 ! [V_n_2,V_m_2] : % 18.78/18.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m_2)) % 18.78/18.91 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 18.78/18.91 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) % 18.78/18.91 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_minus__zero,axiom, % 18.78/18.91 ! [T_a] : % 18.78/18.91 ( class_Groups_Ogroup__add(T_a) % 18.78/18.91 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_neg__0__equal__iff__equal,axiom, % 18.78/18.91 ! [V_a_2,T_b] : % 18.78/18.91 ( class_Groups_Ogroup__add(T_b) % 18.78/18.91 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) % 18.78/18.91 <=> c_Groups_Ozero__class_Ozero(T_b) = V_a_2 ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_equal__neg__zero,axiom, % 18.78/18.91 ! [V_a_2,T_b] : % 18.78/18.91 ( class_Groups_Olinordered__ab__group__add(T_b) % 18.78/18.91 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) % 18.78/18.91 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_neg__equal__0__iff__equal,axiom, % 18.78/18.91 ! [V_a_2,T_b] : % 18.78/18.91 ( class_Groups_Ogroup__add(T_b) % 18.78/18.91 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b) % 18.78/18.91 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_neg__equal__zero,axiom, % 18.78/18.91 ! [V_a_2,T_b] : % 18.78/18.91 ( class_Groups_Olinordered__ab__group__add(T_b) % 18.78/18.91 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_a_2 % 18.78/18.91 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_less__minus__iff,axiom, % 18.78/18.91 ! [V_b_2,V_a_2,T_b] : % 18.78/18.91 ( class_Groups_Oordered__ab__group__add(T_b) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2))) % 18.78/18.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_minus__less__iff,axiom, % 18.78/18.91 ! [V_b_2,V_a_2,T_b] : % 18.78/18.91 ( class_Groups_Oordered__ab__group__add(T_b) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2)) % 18.78/18.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),V_a_2)) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_neg__less__iff__less,axiom, % 18.78/18.91 ! [V_a_2,V_b_2,T_b] : % 18.78/18.91 ( class_Groups_Oordered__ab__group__add(T_b) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) % 18.78/18.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_minus__add__distrib,axiom, % 18.78/18.91 ! [V_b,V_a,T_a] : % 18.78/18.91 ( class_Groups_Oab__group__add(T_a) % 18.78/18.91 => 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)) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_minus__add,axiom, % 18.78/18.91 ! [V_b,V_a,T_a] : % 18.78/18.91 ( class_Groups_Ogroup__add(T_a) % 18.78/18.91 => 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)) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_add__minus__cancel,axiom, % 18.78/18.91 ! [V_b,V_a,T_a] : % 18.78/18.91 ( class_Groups_Ogroup__add(T_a) % 18.78/18.91 => 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 ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_minus__add__cancel,axiom, % 18.78/18.91 ! [V_b,V_a,T_a] : % 18.78/18.91 ( class_Groups_Ogroup__add(T_a) % 18.78/18.91 => 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 ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom, % 18.78/18.91 ! [V_a,T_a] : % 18.78/18.91 ( class_Rings_Ocomm__semiring__1(T_a) % 18.78/18.91 => 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) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom, % 18.78/18.91 ! [V_a,T_a] : % 18.78/18.91 ( class_Rings_Ocomm__semiring__1(T_a) % 18.78/18.91 => 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) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_mult__zero__left,axiom, % 18.78/18.91 ! [V_a,T_a] : % 18.78/18.91 ( class_Rings_Omult__zero(T_a) % 18.78/18.91 => 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) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_mult__zero__right,axiom, % 18.78/18.91 ! [V_a,T_a] : % 18.78/18.91 ( class_Rings_Omult__zero(T_a) % 18.78/18.91 => 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) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_mult__eq__0__iff,axiom, % 18.78/18.91 ! [V_b_2,V_a_2,T_b] : % 18.78/18.91 ( class_Rings_Oring__no__zero__divisors(T_b) % 18.78/18.91 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b) % 18.78/18.91 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b) % 18.78/18.91 | V_b_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_no__zero__divisors,axiom, % 18.78/18.91 ! [V_b,V_a,T_a] : % 18.78/18.91 ( class_Rings_Ono__zero__divisors(T_a) % 18.78/18.91 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 18.78/18.91 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 18.78/18.91 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_divisors__zero,axiom, % 18.78/18.91 ! [V_b,V_a,T_a] : % 18.78/18.91 ( class_Rings_Ono__zero__divisors(T_a) % 18.78/18.91 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) % 18.78/18.91 => ( V_a = c_Groups_Ozero__class_Ozero(T_a) % 18.78/18.91 | V_b = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_one__neq__zero,axiom, % 18.78/18.91 ! [T_a] : % 18.78/18.91 ( class_Rings_Ozero__neq__one(T_a) % 18.78/18.91 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_zero__neq__one,axiom, % 18.78/18.91 ! [T_a] : % 18.78/18.91 ( class_Rings_Ozero__neq__one(T_a) % 18.78/18.91 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_zminus__0,axiom, % 18.78/18.91 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) ). % 18.78/18.91 % 18.78/18.91 fof(fact_nat__int,axiom, % 18.78/18.91 ! [V_n] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = V_n ). % 18.78/18.91 % 18.78/18.91 fof(fact_crossproduct__eq,axiom, % 18.78/18.91 ! [V_z_2,V_x_2,V_y_2,V_w_2,T_b] : % 18.78/18.91 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b) % 18.78/18.91 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_y_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_z_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_y_2)) % 18.78/18.91 <=> ( V_w_2 = V_x_2 % 18.78/18.91 | V_y_2 = V_z_2 ) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom, % 18.78/18.91 ! [V_b,V_m,V_a,T_a] : % 18.78/18.91 ( class_Rings_Ocomm__semiring__1(T_a) % 18.78/18.91 => 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) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom, % 18.78/18.91 ! [V_c,V_b,V_a,T_a] : % 18.78/18.91 ( class_Rings_Ocomm__semiring__1(T_a) % 18.78/18.91 => 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)) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_crossproduct__noteq,axiom, % 18.78/18.91 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] : % 18.78/18.91 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b) % 18.78/18.91 => ( ( V_a_2 != V_b_2 % 18.78/18.91 & V_c_2 != V_d_2 ) % 18.78/18.91 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_d_2)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2)) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom, % 18.78/18.91 ! [V_z,V_y,V_x,T_a] : % 18.78/18.91 ( class_Rings_Ocomm__semiring__1(T_a) % 18.78/18.91 => 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)) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_combine__common__factor,axiom, % 18.78/18.91 ! [V_c,V_b,V_e,V_a,T_a] : % 18.78/18.91 ( class_Rings_Osemiring(T_a) % 18.78/18.91 => 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) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_comm__semiring__class_Odistrib,axiom, % 18.78/18.91 ! [V_c,V_b,V_a,T_a] : % 18.78/18.91 ( class_Rings_Ocomm__semiring(T_a) % 18.78/18.91 => 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)) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_zminus__zadd__distrib,axiom, % 18.78/18.91 ! [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)) ). % 18.78/18.91 % 18.78/18.91 fof(fact_zadd__zmult__distrib,axiom, % 18.78/18.91 ! [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)) ). % 18.78/18.91 % 18.78/18.91 fof(fact_zadd__zmult__distrib2,axiom, % 18.78/18.91 ! [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)) ). % 18.78/18.91 % 18.78/18.91 fof(fact_int__0__neq__1,axiom, % 18.78/18.91 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint) ). % 18.78/18.91 % 18.78/18.91 fof(fact_of__int__int__eq,axiom, % 18.78/18.91 ! [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) ). % 18.78/18.91 % 18.78/18.91 fof(fact_one__less__nat__eq,axiom, % 18.78/18.91 ! [V_z_2] : % 18.78/18.91 ( 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))) % 18.78/18.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_neg__0__less__iff__less,axiom, % 18.78/18.91 ! [V_a_2,T_b] : % 18.78/18.91 ( class_Groups_Oordered__ab__group__add(T_b) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) % 18.78/18.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_neg__less__0__iff__less,axiom, % 18.78/18.91 ! [V_a_2,T_b] : % 18.78/18.91 ( class_Groups_Oordered__ab__group__add(T_b) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),c_Groups_Ozero__class_Ozero(T_b))) % 18.78/18.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_neg__less__nonneg,axiom, % 18.78/18.91 ! [V_a_2,T_b] : % 18.78/18.91 ( class_Groups_Olinordered__ab__group__add(T_b) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_a_2)) % 18.78/18.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_less__minus__self__iff,axiom, % 18.78/18.91 ! [V_a_2,T_b] : % 18.78/18.91 ( class_Rings_Olinordered__idom(T_b) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) % 18.78/18.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_minus__unique,axiom, % 18.78/18.91 ! [V_b,V_a,T_a] : % 18.78/18.91 ( class_Groups_Ogroup__add(T_a) % 18.78/18.91 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) % 18.78/18.91 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) = V_b ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_ab__left__minus,axiom, % 18.78/18.91 ! [V_a,T_a] : % 18.78/18.91 ( class_Groups_Oab__group__add(T_a) % 18.78/18.91 => 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) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_left__minus,axiom, % 18.78/18.91 ! [V_a,T_a] : % 18.78/18.91 ( class_Groups_Ogroup__add(T_a) % 18.78/18.91 => 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) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_eq__neg__iff__add__eq__0,axiom, % 18.78/18.91 ! [V_b_2,V_a_2,T_b] : % 18.78/18.91 ( class_Groups_Ogroup__add(T_b) % 18.78/18.91 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) % 18.78/18.91 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_right__minus,axiom, % 18.78/18.91 ! [V_a,T_a] : % 18.78/18.91 ( class_Groups_Ogroup__add(T_a) % 18.78/18.91 => 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) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_nat__0,axiom, % 18.78/18.91 hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 18.78/18.91 % 18.78/18.91 fof(fact_transfer__nat__int__numerals_I1_J,axiom, % 18.78/18.91 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ). % 18.78/18.91 % 18.78/18.91 fof(fact_not__square__less__zero,axiom, % 18.78/18.91 ! [V_a,T_a] : % 18.78/18.91 ( class_Rings_Olinordered__ring(T_a) % 18.78/18.91 => ~ 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))) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_mult__less__cancel__right__disj,axiom, % 18.78/18.91 ! [V_b_2,V_c_2,V_a_2,T_b] : % 18.78/18.91 ( class_Rings_Olinordered__ring__strict(T_b) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2))) % 18.78/18.91 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 18.78/18.91 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) % 18.78/18.91 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 18.78/18.91 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_mult__less__cancel__left__disj,axiom, % 18.78/18.91 ! [V_b_2,V_a_2,V_c_2,T_b] : % 18.78/18.91 ( class_Rings_Olinordered__ring__strict(T_b) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2))) % 18.78/18.91 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 18.78/18.91 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) % 18.78/18.91 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 18.78/18.91 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_mult__less__cancel__left__pos,axiom, % 18.78/18.91 ! [V_b_2,V_a_2,V_c_2,T_b] : % 18.78/18.91 ( class_Rings_Olinordered__ring__strict(T_b) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2))) % 18.78/18.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_mult__pos__pos,axiom, % 18.78/18.91 ! [V_b,V_a,T_a] : % 18.78/18.91 ( class_Rings_Olinordered__semiring__strict(T_a) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 18.78/18.91 => 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))) ) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_mult__pos__neg,axiom, % 18.78/18.91 ! [V_b,V_a,T_a] : % 18.78/18.91 ( class_Rings_Olinordered__semiring__strict(T_a) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 18.78/18.91 => 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))) ) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_mult__pos__neg2,axiom, % 18.78/18.91 ! [V_b,V_a,T_a] : % 18.78/18.91 ( class_Rings_Olinordered__semiring__strict(T_a) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 18.78/18.91 => 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))) ) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_zero__less__mult__pos,axiom, % 18.78/18.91 ! [V_b,V_a,T_a] : % 18.78/18.91 ( class_Rings_Olinordered__semiring__strict(T_a) % 18.78/18.91 => ( 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))) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 18.78/18.91 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_zero__less__mult__pos2,axiom, % 18.78/18.91 ! [V_a,V_b,T_a] : % 18.78/18.91 ( class_Rings_Olinordered__semiring__strict(T_a) % 18.78/18.91 => ( 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))) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 18.78/18.91 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_mult__less__cancel__left__neg,axiom, % 18.78/18.91 ! [V_b_2,V_a_2,V_c_2,T_b] : % 18.78/18.91 ( class_Rings_Olinordered__ring__strict(T_b) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2))) % 18.78/18.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_mult__neg__pos,axiom, % 18.78/18.91 ! [V_b,V_a,T_a] : % 18.78/18.91 ( class_Rings_Olinordered__semiring__strict(T_a) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 18.78/18.91 => 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))) ) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_mult__neg__neg,axiom, % 18.78/18.91 ! [V_b,V_a,T_a] : % 18.78/18.91 ( class_Rings_Olinordered__ring__strict(T_a) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 18.78/18.91 => 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))) ) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_mult__strict__right__mono,axiom, % 18.78/18.91 ! [V_c,V_b,V_a,T_a] : % 18.78/18.91 ( class_Rings_Olinordered__semiring__strict(T_a) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 18.78/18.91 => 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))) ) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_mult__strict__left__mono,axiom, % 18.78/18.91 ! [V_c,V_b,V_a,T_a] : % 18.78/18.91 ( class_Rings_Olinordered__semiring__strict(T_a) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 18.78/18.91 => 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))) ) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_comm__mult__strict__left__mono,axiom, % 18.78/18.91 ! [V_c,V_b,V_a,T_a] : % 18.78/18.91 ( class_Rings_Olinordered__comm__semiring__strict(T_a) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 18.78/18.91 => 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))) ) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_mult__strict__right__mono__neg,axiom, % 18.78/18.91 ! [V_c,V_a,V_b,T_a] : % 18.78/18.91 ( class_Rings_Olinordered__ring__strict(T_a) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 18.78/18.91 => 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))) ) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_mult__strict__left__mono__neg,axiom, % 18.78/18.91 ! [V_c,V_a,V_b,T_a] : % 18.78/18.91 ( class_Rings_Olinordered__ring__strict(T_a) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 18.78/18.91 => 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))) ) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_not__one__less__zero,axiom, % 18.78/18.91 ! [T_a] : % 18.78/18.91 ( class_Rings_Olinordered__semidom(T_a) % 18.78/18.91 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_zero__less__one,axiom, % 18.78/18.91 ! [T_a] : % 18.78/18.91 ( class_Rings_Olinordered__semidom(T_a) % 18.78/18.91 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_sum__squares__eq__zero__iff,axiom, % 18.78/18.91 ! [V_y_2,V_x_2,T_b] : % 18.78/18.91 ( class_Rings_Olinordered__ring__strict(T_b) % 18.78/18.91 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2)) = c_Groups_Ozero__class_Ozero(T_b) % 18.78/18.91 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b) % 18.78/18.91 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_add__scale__eq__noteq,axiom, % 18.78/18.91 ! [V_d,V_c,V_b,V_a,V_r,T_a] : % 18.78/18.91 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) % 18.78/18.91 => ( V_r != c_Groups_Ozero__class_Ozero(T_a) % 18.78/18.91 => ( ( V_a = V_b % 18.78/18.91 & V_c != V_d ) % 18.78/18.91 => 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)) ) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_less__add__one,axiom, % 18.78/18.91 ! [V_a,T_a] : % 18.78/18.91 ( class_Rings_Olinordered__semidom(T_a) % 18.78/18.91 => 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)))) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_zadd__zminus__inverse2,axiom, % 18.78/18.91 ! [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) ). % 18.78/18.91 % 18.78/18.91 fof(fact_negative__eq__positive,axiom, % 18.78/18.91 ! [V_m_2,V_n_2] : % 18.78/18.91 ( 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) % 18.78/18.91 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 18.78/18.91 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_not__int__zless__negative,axiom, % 18.78/18.91 ! [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)))) ). % 18.78/18.91 % 18.78/18.91 fof(fact_zmult__zless__mono2,axiom, % 18.78/18.91 ! [V_k,V_j,V_i] : % 18.78/18.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 18.78/18.91 => 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))) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_int__0__less__1,axiom, % 18.78/18.91 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))) ). % 18.78/18.91 % 18.78/18.91 fof(fact_odd__nonzero,axiom, % 18.78/18.91 ! [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) ). % 18.78/18.91 % 18.78/18.91 fof(fact_zless__add1__eq,axiom, % 18.78/18.91 ! [V_z_2,V_w_2] : % 18.78/18.91 ( 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)))) % 18.78/18.91 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) % 18.78/18.91 | V_w_2 = V_z_2 ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_of__int__0,axiom, % 18.78/18.91 ! [T_a] : % 18.78/18.91 ( class_Rings_Oring__1(T_a) % 18.78/18.91 => 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) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_of__int__0__eq__iff,axiom, % 18.78/18.91 ! [V_z_2,T_b] : % 18.78/18.91 ( class_Int_Oring__char__0(T_b) % 18.78/18.91 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2) % 18.78/18.91 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_of__int__eq__0__iff,axiom, % 18.78/18.91 ! [V_z_2,T_b] : % 18.78/18.91 ( class_Int_Oring__char__0(T_b) % 18.78/18.91 => ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2) = c_Groups_Ozero__class_Ozero(T_b) % 18.78/18.91 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_of__int__less__iff,axiom, % 18.78/18.91 ! [V_z_2,V_w_2,T_b] : % 18.78/18.91 ( class_Rings_Olinordered__idom(T_b) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_w_2)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2))) % 18.78/18.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_of__int__add,axiom, % 18.78/18.91 ! [V_z,V_w,T_a] : % 18.78/18.91 ( class_Rings_Oring__1(T_a) % 18.78/18.91 => 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)) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_of__int__of__nat__eq,axiom, % 18.78/18.91 ! [V_n,T_a] : % 18.78/18.91 ( class_Rings_Oring__1(T_a) % 18.78/18.91 => 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) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_nat__mono__iff,axiom, % 18.78/18.91 ! [V_w_2,V_z_2] : % 18.78/18.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 18.78/18.91 => ( 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))) % 18.78/18.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_zless__nat__conj,axiom, % 18.78/18.91 ! [V_z_2,V_w_2] : % 18.78/18.91 ( 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))) % 18.78/18.91 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 18.78/18.91 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_zless__nat__eq__int__zless,axiom, % 18.78/18.91 ! [V_z_2,V_m_2] : % 18.78/18.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,V_z_2))) % 18.78/18.91 <=> 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)) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_sum__squares__gt__zero__iff,axiom, % 18.78/18.91 ! [V_y_2,V_x_2,T_b] : % 18.78/18.91 ( class_Rings_Olinordered__ring__strict(T_b) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2)))) % 18.78/18.91 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_b) % 18.78/18.91 | V_y_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_not__sum__squares__lt__zero,axiom, % 18.78/18.91 ! [V_y,V_x,T_a] : % 18.78/18.91 ( class_Rings_Olinordered__ring(T_a) % 18.78/18.91 => ~ 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))) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_zero__less__two,axiom, % 18.78/18.91 ! [T_a] : % 18.78/18.91 ( class_Rings_Olinordered__semidom(T_a) % 18.78/18.91 => 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)))) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_of__nat__Suc,axiom, % 18.78/18.91 ! [V_m,T_a] : % 18.78/18.91 ( class_Rings_Osemiring__1(T_a) % 18.78/18.91 => 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)) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_int__Suc0__eq__1,axiom, % 18.78/18.91 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) ). % 18.78/18.91 % 18.78/18.91 fof(fact_nat__aux__def,axiom, % 18.78/18.91 ! [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) ). % 18.78/18.91 % 18.78/18.91 fof(fact_negD,axiom, % 18.78/18.91 ! [V_x] : % 18.78/18.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 18.78/18.91 => ? [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))) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_sgn__if,axiom, % 18.78/18.91 ! [V_x,T_a] : % 18.78/18.91 ( class_Groups_Osgn__if(T_a) % 18.78/18.91 => ( ( V_x = c_Groups_Ozero__class_Ozero(T_a) % 18.78/18.91 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a) ) % 18.78/18.91 & ( V_x != c_Groups_Ozero__class_Ozero(T_a) % 18.78/18.91 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 18.78/18.91 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a) ) % 18.78/18.91 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 18.78/18.91 => c_Groups_Osgn__class_Osgn(T_a,V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_sgn__neg,axiom, % 18.78/18.91 ! [V_a,T_a] : % 18.78/18.91 ( class_Rings_Olinordered__idom(T_a) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 18.78/18.91 => c_Groups_Osgn__class_Osgn(T_a,V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_sgn__1__neg,axiom, % 18.78/18.91 ! [V_a_2,T_b] : % 18.78/18.91 ( class_Rings_Olinordered__idom(T_b) % 18.78/18.91 => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b)) % 18.78/18.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_zsgn__def,axiom, % 18.78/18.91 ! [V_i] : % 18.78/18.91 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 18.78/18.91 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 18.78/18.91 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 18.78/18.91 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i)) % 18.78/18.91 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) % 18.78/18.91 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i)) % 18.78/18.91 => 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)) ) ) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_Suc__nat__eq__nat__zadd1,axiom, % 18.78/18.91 ! [V_z] : % 18.78/18.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 18.78/18.91 => 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)) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_nat__less__iff,axiom, % 18.78/18.91 ! [V_m_2,V_w_2] : % 18.78/18.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),V_m_2)) % 18.78/18.91 <=> 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))) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_convex__bound__lt,axiom, % 18.78/18.91 ! [V_v,V_u,V_y,V_a,V_x,T_a] : % 18.78/18.91 ( class_Rings_Olinordered__semiring__1__strict(T_a) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a)) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_a)) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u)) % 18.78/18.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v)) % 18.78/18.91 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a) % 18.78/18.91 => 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)) ) ) ) ) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_sgn__1__pos,axiom, % 18.78/18.91 ! [V_a_2,T_b] : % 18.78/18.91 ( class_Rings_Olinordered__idom(T_b) % 18.78/18.91 => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Oone__class_Oone(T_b) % 18.78/18.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_order__refl,axiom, % 18.78/18.91 ! [V_x,T_a] : % 18.78/18.91 ( class_Orderings_Opreorder(T_a) % 18.78/18.91 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_x)) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_le0,axiom, % 18.78/18.91 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ). % 18.78/18.91 % 18.78/18.91 fof(fact_negative__zle,axiom, % 18.78/18.91 ! [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))) ). % 18.78/18.91 % 18.78/18.91 fof(fact_mult__eq__self__implies__10,axiom, % 18.78/18.91 ! [V_n,V_m] : % 18.78/18.91 ( V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) % 18.78/18.91 => ( V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 18.78/18.91 | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_Suc__mult__le__cancel1,axiom, % 18.78/18.91 ! [V_n_2,V_m_2,V_k_2] : % 18.78/18.91 ( 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))) % 18.78/18.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 18.78/18.91 % 18.78/18.91 fof(fact_le__square,axiom, % 18.78/18.91 ! [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))) ). % 18.78/18.91 % 18.78/18.91 fof(fact_le__cube,axiom, % 18.78/18.92 ! [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)))) ). % 18.78/18.92 % 18.78/18.92 fof(fact_nat__mult__1,axiom, % 18.78/18.92 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n ). % 18.78/18.92 % 18.78/18.92 fof(fact_nat__1__eq__mult__iff,axiom, % 18.78/18.92 ! [V_n_2,V_m_2] : % 18.78/18.92 ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) % 18.78/18.92 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 18.78/18.92 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_nat__mult__1__right,axiom, % 18.78/18.92 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ). % 18.78/18.92 % 18.78/18.92 fof(fact_nat__mult__commute,axiom, % 18.78/18.92 ! [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) ). % 18.78/18.92 % 18.78/18.92 fof(fact_nat__mult__eq__1__iff,axiom, % 18.78/18.92 ! [V_n_2,V_m_2] : % 18.78/18.92 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 18.78/18.92 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 18.78/18.92 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_nat__mult__assoc,axiom, % 18.78/18.92 ! [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)) ). % 18.78/18.92 % 18.78/18.92 fof(fact_mult__le__mono1,axiom, % 18.78/18.92 ! [V_k,V_j,V_i] : % 18.78/18.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 18.78/18.92 => 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))) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_mult__le__mono2,axiom, % 18.78/18.92 ! [V_k,V_j,V_i] : % 18.78/18.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 18.78/18.92 => 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))) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_mult__le__mono,axiom, % 18.78/18.92 ! [V_l,V_k,V_j,V_i] : % 18.78/18.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l)) % 18.78/18.92 => 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))) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_zle__antisym,axiom, % 18.78/18.92 ! [V_w,V_z] : % 18.78/18.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) % 18.78/18.92 => V_z = V_w ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_zle__trans,axiom, % 18.78/18.92 ! [V_k,V_j,V_i] : % 18.78/18.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_j),V_k)) % 18.78/18.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_k)) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_zle__linear,axiom, % 18.78/18.92 ! [V_w,V_z] : % 18.78/18.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w)) % 18.78/18.92 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_zle__refl,axiom, % 18.78/18.92 ! [V_w] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_w)) ). % 18.78/18.92 % 18.78/18.92 fof(fact_sgn__sgn,axiom, % 18.78/18.92 ! [V_a,T_a] : % 18.78/18.92 ( class_Rings_Olinordered__idom(T_a) % 18.78/18.92 => 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) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_linorder__le__cases,axiom, % 18.78/18.92 ! [V_y,V_x,T_a] : % 18.78/18.92 ( class_Orderings_Olinorder(T_a) % 18.78/18.92 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 18.78/18.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_le__funE,axiom, % 18.78/18.92 ! [V_x_2,V_g_2,V_f_2,T_b,T_c] : % 18.78/18.92 ( class_Orderings_Oord(T_c) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) % 18.78/18.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_xt1_I6_J,axiom, % 18.78/18.92 ! [V_z,V_x,V_y,T_a] : % 18.78/18.92 ( class_Orderings_Oorder(T_a) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y)) % 18.78/18.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_xt1_I5_J,axiom, % 18.78/18.92 ! [V_x,V_y,T_a] : % 18.78/18.92 ( class_Orderings_Oorder(T_a) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 18.78/18.92 => V_x = V_y ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_order__trans,axiom, % 18.78/18.92 ! [V_z,V_y,V_x,T_a] : % 18.78/18.92 ( class_Orderings_Opreorder(T_a) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z)) % 18.78/18.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_order__antisym,axiom, % 18.78/18.92 ! [V_y,V_x,T_a] : % 18.78/18.92 ( class_Orderings_Oorder(T_a) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 18.78/18.92 => V_x = V_y ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_xt1_I4_J,axiom, % 18.78/18.92 ! [V_c,V_a,V_b,T_a] : % 18.78/18.92 ( class_Orderings_Oorder(T_a) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 18.78/18.92 => ( V_b = V_c % 18.78/18.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_ord__le__eq__trans,axiom, % 18.78/18.92 ! [V_c,V_b,V_a,T_a] : % 18.78/18.92 ( class_Orderings_Oord(T_a) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 18.78/18.92 => ( V_b = V_c % 18.78/18.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_xt1_I3_J,axiom, % 18.78/18.92 ! [V_c,V_b,V_a,T_a] : % 18.78/18.92 ( class_Orderings_Oorder(T_a) % 18.78/18.92 => ( V_a = V_b % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_b)) % 18.78/18.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_ord__eq__le__trans,axiom, % 18.78/18.92 ! [V_c,V_b,V_a,T_a] : % 18.78/18.92 ( class_Orderings_Oord(T_a) % 18.78/18.92 => ( V_a = V_b % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c)) % 18.78/18.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_order__antisym__conv,axiom, % 18.78/18.92 ! [V_x_2,V_y_2,T_b] : % 18.78/18.92 ( class_Orderings_Oorder(T_b) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 18.78/18.92 <=> V_x_2 = V_y_2 ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_le__funD,axiom, % 18.78/18.92 ! [V_x_2,V_g_2,V_f_2,T_b,T_c] : % 18.78/18.92 ( class_Orderings_Oord(T_c) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) % 18.78/18.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_order__eq__refl,axiom, % 18.78/18.92 ! [V_y,V_x,T_a] : % 18.78/18.92 ( class_Orderings_Opreorder(T_a) % 18.78/18.92 => ( V_x = V_y % 18.78/18.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_order__eq__iff,axiom, % 18.78/18.92 ! [V_y_2,V_x_2,T_b] : % 18.78/18.92 ( class_Orderings_Oorder(T_b) % 18.78/18.92 => ( V_x_2 = V_y_2 % 18.78/18.92 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 18.78/18.92 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_linorder__linear,axiom, % 18.78/18.92 ! [V_y,V_x,T_a] : % 18.78/18.92 ( class_Orderings_Olinorder(T_a) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 18.78/18.92 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_le__fun__def,axiom, % 18.78/18.92 ! [V_g_2,V_f_2,T_b,T_c] : % 18.78/18.92 ( class_Orderings_Oord(T_c) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) % 18.78/18.92 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_of__nat__le__iff,axiom, % 18.78/18.92 ! [V_n_2,V_m_2,T_b] : % 18.78/18.92 ( class_Rings_Olinordered__semidom(T_b) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2))) % 18.78/18.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_zle__int,axiom, % 18.78/18.92 ! [V_n_2,V_m_2] : % 18.78/18.92 ( 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))) % 18.78/18.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_transfer__int__nat__relations_I3_J,axiom, % 18.78/18.92 ! [V_y_2,V_x_2] : % 18.78/18.92 ( 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))) % 18.78/18.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_of__int__le__iff,axiom, % 18.78/18.92 ! [V_z_2,V_w_2,T_b] : % 18.78/18.92 ( class_Rings_Olinordered__idom(T_b) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_w_2)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2))) % 18.78/18.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_one__le__mult__iff,axiom, % 18.78/18.92 ! [V_n_2,V_m_2] : % 18.78/18.92 ( 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))) % 18.78/18.92 <=> ( 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)) % 18.78/18.92 & 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)) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_mult__le__cancel1,axiom, % 18.78/18.92 ! [V_n_2,V_m_2,V_k_2] : % 18.78/18.92 ( 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))) % 18.78/18.92 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 18.78/18.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_mult__le__cancel2,axiom, % 18.78/18.92 ! [V_n_2,V_k_2,V_m_2] : % 18.78/18.92 ( 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))) % 18.78/18.92 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 18.78/18.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_transfer__nat__int__relations_I3_J,axiom, % 18.78/18.92 ! [V_y_2,V_x_2] : % 18.78/18.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) % 18.78/18.92 => ( 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))) % 18.78/18.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_linorder__not__less,axiom, % 18.78/18.92 ! [V_y_2,V_x_2,T_b] : % 18.78/18.92 ( class_Orderings_Olinorder(T_b) % 18.78/18.92 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 18.78/18.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_linorder__not__le,axiom, % 18.78/18.92 ! [V_y_2,V_x_2,T_b] : % 18.78/18.92 ( class_Orderings_Olinorder(T_b) % 18.78/18.92 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 18.78/18.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_linorder__le__less__linear,axiom, % 18.78/18.92 ! [V_y,V_x,T_a] : % 18.78/18.92 ( class_Orderings_Olinorder(T_a) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 18.78/18.92 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_order__less__le,axiom, % 18.78/18.92 ! [V_y_2,V_x_2,T_b] : % 18.78/18.92 ( class_Orderings_Oorder(T_b) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 18.78/18.92 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 18.78/18.92 & V_x_2 != V_y_2 ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_less__le__not__le,axiom, % 18.78/18.92 ! [V_y_2,V_x_2,T_b] : % 18.78/18.92 ( class_Orderings_Opreorder(T_b) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 18.78/18.92 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 18.78/18.92 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_order__le__less,axiom, % 18.78/18.92 ! [V_y_2,V_x_2,T_b] : % 18.78/18.92 ( class_Orderings_Oorder(T_b) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 18.78/18.92 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 18.78/18.92 | V_x_2 = V_y_2 ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_leI,axiom, % 18.78/18.92 ! [V_y,V_x,T_a] : % 18.78/18.92 ( class_Orderings_Olinorder(T_a) % 18.78/18.92 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 18.78/18.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_not__leE,axiom, % 18.78/18.92 ! [V_x,V_y,T_a] : % 18.78/18.92 ( class_Orderings_Olinorder(T_a) % 18.78/18.92 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 18.78/18.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_linorder__antisym__conv1,axiom, % 18.78/18.92 ! [V_y_2,V_x_2,T_b] : % 18.78/18.92 ( class_Orderings_Olinorder(T_b) % 18.78/18.92 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 18.78/18.92 <=> V_x_2 = V_y_2 ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_order__neq__le__trans,axiom, % 18.78/18.92 ! [V_b,V_a,T_a] : % 18.78/18.92 ( class_Orderings_Oorder(T_a) % 18.78/18.92 => ( V_a != V_b % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 18.78/18.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_xt1_I12_J,axiom, % 18.78/18.92 ! [V_b,V_a,T_a] : % 18.78/18.92 ( class_Orderings_Oorder(T_a) % 18.78/18.92 => ( V_a != V_b % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 18.78/18.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_leD,axiom, % 18.78/18.92 ! [V_x,V_y,T_a] : % 18.78/18.92 ( class_Orderings_Olinorder(T_a) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 18.78/18.92 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_order__less__imp__le,axiom, % 18.78/18.92 ! [V_y,V_x,T_a] : % 18.78/18.92 ( class_Orderings_Opreorder(T_a) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 18.78/18.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_linorder__antisym__conv2,axiom, % 18.78/18.92 ! [V_y_2,V_x_2,T_b] : % 18.78/18.92 ( class_Orderings_Olinorder(T_b) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 18.78/18.92 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 18.78/18.92 <=> V_x_2 = V_y_2 ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_order__le__imp__less__or__eq,axiom, % 18.78/18.92 ! [V_y,V_x,T_a] : % 18.78/18.92 ( class_Orderings_Oorder(T_a) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 18.78/18.92 | V_x = V_y ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_order__le__neq__trans,axiom, % 18.78/18.92 ! [V_b,V_a,T_a] : % 18.78/18.92 ( class_Orderings_Oorder(T_a) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 18.78/18.92 => ( V_a != V_b % 18.78/18.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_xt1_I11_J,axiom, % 18.78/18.92 ! [V_a,V_b,T_a] : % 18.78/18.92 ( class_Orderings_Oorder(T_a) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 18.78/18.92 => ( V_a != V_b % 18.78/18.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_order__less__le__trans,axiom, % 18.78/18.92 ! [V_z,V_y,V_x,T_a] : % 18.78/18.92 ( class_Orderings_Opreorder(T_a) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z)) % 18.78/18.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_xt1_I7_J,axiom, % 18.78/18.92 ! [V_z,V_x,V_y,T_a] : % 18.78/18.92 ( class_Orderings_Oorder(T_a) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y)) % 18.78/18.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_order__le__less__trans,axiom, % 18.78/18.92 ! [V_z,V_y,V_x,T_a] : % 18.78/18.92 ( class_Orderings_Opreorder(T_a) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z)) % 18.78/18.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_xt1_I8_J,axiom, % 18.78/18.92 ! [V_z,V_x,V_y,T_a] : % 18.78/18.92 ( class_Orderings_Oorder(T_a) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y)) % 18.78/18.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_add__le__imp__le__left,axiom, % 18.78/18.92 ! [V_b,V_a,V_c,T_a] : % 18.78/18.92 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 18.78/18.92 => ( 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))) % 18.78/18.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_add__le__imp__le__right,axiom, % 18.78/18.92 ! [V_b,V_c,V_a,T_a] : % 18.78/18.92 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 18.78/18.92 => ( 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))) % 18.78/18.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_add__mono,axiom, % 18.78/18.92 ! [V_d,V_c,V_b,V_a,T_a] : % 18.78/18.92 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 18.78/18.92 => 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))) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_add__left__mono,axiom, % 18.78/18.92 ! [V_c,V_b,V_a,T_a] : % 18.78/18.92 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 18.78/18.92 => 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))) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_add__right__mono,axiom, % 18.78/18.92 ! [V_c,V_b,V_a,T_a] : % 18.78/18.92 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 18.78/18.92 => 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))) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_add__le__cancel__left,axiom, % 18.78/18.92 ! [V_b_2,V_a_2,V_c_2,T_b] : % 18.78/18.92 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_b_2))) % 18.78/18.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_add__le__cancel__right,axiom, % 18.78/18.92 ! [V_b_2,V_c_2,V_a_2,T_b] : % 18.78/18.92 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_c_2))) % 18.78/18.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_mult__cancel2,axiom, % 18.78/18.92 ! [V_n_2,V_k_2,V_m_2] : % 18.78/18.92 ( 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) % 18.78/18.92 <=> ( V_m_2 = V_n_2 % 18.78/18.92 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_mult__cancel1,axiom, % 18.78/18.92 ! [V_n_2,V_m_2,V_k_2] : % 18.78/18.92 ( 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) % 18.78/18.92 <=> ( V_m_2 = V_n_2 % 18.78/18.92 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_mult__is__0,axiom, % 18.78/18.92 ! [V_n_2,V_m_2] : % 18.78/18.92 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 18.78/18.92 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 18.78/18.92 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_mult__0__right,axiom, % 18.78/18.92 ! [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) ). % 18.78/18.92 % 18.78/18.92 fof(fact_mult__0,axiom, % 18.78/18.92 ! [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) ). % 18.78/18.92 % 18.78/18.92 fof(fact_Suc__mult__cancel1,axiom, % 18.78/18.92 ! [V_n_2,V_m_2,V_k_2] : % 18.78/18.92 ( 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) % 18.78/18.92 <=> V_m_2 = V_n_2 ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_le__0__eq,axiom, % 18.78/18.92 ! [V_n_2] : % 18.78/18.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) % 18.78/18.92 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_less__eq__nat_Osimps_I1_J,axiom, % 18.78/18.92 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ). % 18.78/18.92 % 18.78/18.92 fof(fact_le__imp__neg__le,axiom, % 18.78/18.92 ! [V_b,V_a,T_a] : % 18.78/18.92 ( class_Groups_Oordered__ab__group__add(T_a) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 18.78/18.92 => 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))) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_neg__le__iff__le,axiom, % 18.78/18.92 ! [V_a_2,V_b_2,T_b] : % 18.78/18.92 ( class_Groups_Oordered__ab__group__add(T_b) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) % 18.78/18.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_minus__le__iff,axiom, % 18.78/18.92 ! [V_b_2,V_a_2,T_b] : % 18.78/18.92 ( class_Groups_Oordered__ab__group__add(T_b) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2)) % 18.78/18.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),V_a_2)) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_le__minus__iff,axiom, % 18.78/18.92 ! [V_b_2,V_a_2,T_b] : % 18.78/18.92 ( class_Groups_Oordered__ab__group__add(T_b) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2))) % 18.78/18.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_add__mult__distrib2,axiom, % 18.78/18.92 ! [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)) ). % 18.78/18.92 % 18.78/18.92 fof(fact_add__mult__distrib,axiom, % 18.78/18.92 ! [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)) ). % 18.78/18.92 % 18.78/18.92 fof(fact_Suc__n__not__le__n,axiom, % 18.78/18.92 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),V_n)) ). % 18.78/18.92 % 18.78/18.92 fof(fact_not__less__eq__eq,axiom, % 18.78/18.92 ! [V_n_2,V_m_2] : % 18.78/18.92 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 18.78/18.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_le__Suc__eq,axiom, % 18.78/18.92 ! [V_n_2,V_m_2] : % 18.78/18.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 18.78/18.92 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 18.78/18.92 | V_m_2 = hAPP(c_Nat_OSuc,V_n_2) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_Suc__le__mono,axiom, % 18.78/18.92 ! [V_m_2,V_n_2] : % 18.78/18.92 ( 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))) % 18.78/18.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_le__SucI,axiom, % 18.78/18.92 ! [V_n,V_m] : % 18.78/18.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 18.78/18.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_le__SucE,axiom, % 18.78/18.92 ! [V_n,V_m] : % 18.78/18.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) % 18.78/18.92 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 18.78/18.92 => V_m = hAPP(c_Nat_OSuc,V_n) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_Suc__leD,axiom, % 18.78/18.92 ! [V_n,V_m] : % 18.78/18.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) % 18.78/18.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom, % 18.78/18.92 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))) ). % 18.78/18.92 % 18.78/18.92 fof(fact_termination__basic__simps_I5_J,axiom, % 18.78/18.92 ! [V_y,V_x] : % 18.78/18.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 18.78/18.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_less__or__eq__imp__le,axiom, % 18.78/18.92 ! [V_n,V_m] : % 18.78/18.92 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 18.78/18.92 | V_m = V_n ) % 18.78/18.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_le__neq__implies__less,axiom, % 18.78/18.92 ! [V_n,V_m] : % 18.78/18.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 18.78/18.92 => ( V_m != V_n % 18.78/18.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_less__imp__le__nat,axiom, % 18.78/18.92 ! [V_n,V_m] : % 18.78/18.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 18.78/18.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_le__eq__less__or__eq,axiom, % 18.78/18.92 ! [V_n_2,V_m_2] : % 18.78/18.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 18.78/18.92 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 18.78/18.92 | V_m_2 = V_n_2 ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_nat__less__le,axiom, % 18.78/18.92 ! [V_n_2,V_m_2] : % 18.78/18.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 18.78/18.92 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 18.78/18.92 & V_m_2 != V_n_2 ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_termination__basic__simps_I3_J,axiom, % 18.78/18.92 ! [V_z,V_y,V_x] : % 18.78/18.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) % 18.78/18.92 => 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))) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_termination__basic__simps_I4_J,axiom, % 18.78/18.92 ! [V_y,V_z,V_x] : % 18.78/18.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_z)) % 18.78/18.92 => 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))) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_le__add2,axiom, % 18.78/18.92 ! [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))) ). % 18.78/18.92 % 18.78/18.92 fof(fact_le__add1,axiom, % 18.78/18.92 ! [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))) ). % 18.78/18.92 % 18.78/18.92 fof(fact_le__iff__add,axiom, % 18.78/18.92 ! [V_n_2,V_m_2] : % 18.78/18.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 18.78/18.92 <=> ? [B_k] : V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_nat__add__left__cancel__le,axiom, % 18.78/18.92 ! [V_n_2,V_m_2,V_k_2] : % 18.78/18.92 ( 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))) % 18.78/18.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_trans__le__add1,axiom, % 18.78/18.92 ! [V_m,V_j,V_i] : % 18.78/18.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 18.78/18.92 => 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))) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_trans__le__add2,axiom, % 18.78/18.92 ! [V_m,V_j,V_i] : % 18.78/18.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 18.78/18.92 => 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))) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_add__le__mono1,axiom, % 18.78/18.92 ! [V_k,V_j,V_i] : % 18.78/18.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 18.78/18.92 => 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))) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_add__le__mono,axiom, % 18.78/18.92 ! [V_l,V_k,V_j,V_i] : % 18.78/18.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l)) % 18.78/18.92 => 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))) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_add__leD2,axiom, % 18.78/18.92 ! [V_n,V_k,V_m] : % 18.78/18.92 ( 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)) % 18.78/18.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_add__leD1,axiom, % 18.78/18.92 ! [V_n,V_k,V_m] : % 18.78/18.92 ( 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)) % 18.78/18.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_add__leE,axiom, % 18.78/18.92 ! [V_n,V_k,V_m] : % 18.78/18.92 ( 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)) % 18.78/18.92 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 18.78/18.92 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_zless__le,axiom, % 18.78/18.92 ! [V_w_2,V_z_2] : % 18.78/18.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),V_w_2)) % 18.78/18.92 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),V_w_2)) % 18.78/18.92 & V_z_2 != V_w_2 ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_zadd__left__mono,axiom, % 18.78/18.92 ! [V_k,V_j,V_i] : % 18.78/18.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 18.78/18.92 => 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))) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_evaln__nonstrict,axiom, % 18.78/18.92 ! [V_m,V_t,V_n,V_s,V_c] : % 18.78/18.92 ( c_Natural_Oevaln(V_c,V_s,V_n,V_t) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 18.78/18.92 => c_Natural_Oevaln(V_c,V_s,V_m,V_t) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_nat__le__eq__zle,axiom, % 18.78/18.92 ! [V_z_2,V_w_2] : % 18.78/18.92 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 18.78/18.92 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) % 18.78/18.92 => ( 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))) % 18.78/18.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_nat__mult__distrib,axiom, % 18.78/18.92 ! [V_z_H,V_z] : % 18.78/18.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 18.78/18.92 => 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)) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J,axiom, % 18.78/18.92 ! [V_y,V_x] : % 18.78/18.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 18.78/18.92 => 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)) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_of__int__0__le__iff,axiom, % 18.78/18.92 ! [V_z_2,T_b] : % 18.78/18.92 ( class_Rings_Olinordered__idom(T_b) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2))) % 18.78/18.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_of__int__le__0__iff,axiom, % 18.78/18.92 ! [V_z_2,T_b] : % 18.78/18.92 ( class_Rings_Olinordered__idom(T_b) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)),c_Groups_Ozero__class_Ozero(T_b))) % 18.78/18.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_sgn__0__0,axiom, % 18.78/18.92 ! [V_a_2,T_b] : % 18.78/18.92 ( class_Rings_Olinordered__idom(T_b) % 18.78/18.92 => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Ozero__class_Ozero(T_b) % 18.78/18.92 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_sgn0,axiom, % 18.78/18.92 ! [T_a] : % 18.78/18.92 ( class_Groups_Osgn__if(T_a) % 18.78/18.92 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_sgn__times,axiom, % 18.78/18.92 ! [V_b,V_a,T_a] : % 18.78/18.92 ( class_Rings_Olinordered__idom(T_a) % 18.78/18.92 => 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)) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_nat__mult__distrib__neg,axiom, % 18.78/18.92 ! [V_z_H,V_z] : % 18.78/18.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 18.78/18.92 => 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))) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom, % 18.78/18.92 ! [V_a_2,T_b] : % 18.78/18.92 ( class_Groups_Olinordered__ab__group__add(T_b) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2))) % 18.78/18.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom, % 18.78/18.92 ! [V_a_2,T_b] : % 18.78/18.92 ( class_Groups_Olinordered__ab__group__add(T_b) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b))) % 18.78/18.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_add__nonneg__nonneg,axiom, % 18.78/18.92 ! [V_b,V_a,T_a] : % 18.78/18.92 ( class_Groups_Oordered__comm__monoid__add(T_a) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 18.78/18.92 => 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))) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_add__nonneg__eq__0__iff,axiom, % 18.78/18.92 ! [V_y_2,V_x_2,T_b] : % 18.78/18.92 ( class_Groups_Oordered__comm__monoid__add(T_b) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_x_2)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_y_2)) % 18.78/18.92 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_b) % 18.78/18.92 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b) % 18.78/18.92 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_add__increasing,axiom, % 18.78/18.92 ! [V_c,V_b,V_a,T_a] : % 18.78/18.92 ( class_Groups_Oordered__comm__monoid__add(T_a) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c)) % 18.78/18.92 => 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))) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_add__increasing2,axiom, % 18.78/18.92 ! [V_a,V_b,V_c,T_a] : % 18.78/18.92 ( class_Groups_Oordered__comm__monoid__add(T_a) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 18.78/18.92 => 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))) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_add__nonpos__nonpos,axiom, % 18.78/18.92 ! [V_b,V_a,T_a] : % 18.78/18.92 ( class_Groups_Oordered__comm__monoid__add(T_a) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 18.78/18.92 => 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))) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_split__mult__neg__le,axiom, % 18.78/18.92 ! [V_b,V_a,T_a] : % 18.78/18.92 ( class_Rings_Oordered__cancel__semiring(T_a) % 18.78/18.92 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 18.78/18.92 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) % 18.78/18.92 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 18.78/18.92 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) % 18.78/18.92 => 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))) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_split__mult__pos__le,axiom, % 18.78/18.92 ! [V_b,V_a,T_a] : % 18.78/18.92 ( class_Rings_Oordered__ring(T_a) % 18.78/18.92 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 18.78/18.92 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) % 18.78/18.92 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 18.78/18.92 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) ) % 18.78/18.92 => 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))) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_mult__mono,axiom, % 18.78/18.92 ! [V_d,V_c,V_b,V_a,T_a] : % 18.78/18.92 ( class_Rings_Oordered__semiring(T_a) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 18.78/18.92 => 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))) ) ) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_mult__mono_H,axiom, % 18.78/18.92 ! [V_d,V_c,V_b,V_a,T_a] : % 18.78/18.92 ( class_Rings_Oordered__semiring(T_a) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 18.78/18.92 => 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))) ) ) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_mult__left__mono__neg,axiom, % 18.78/18.92 ! [V_c,V_a,V_b,T_a] : % 18.78/18.92 ( class_Rings_Oordered__ring(T_a) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 18.78/18.92 => 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))) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_mult__right__mono__neg,axiom, % 18.78/18.92 ! [V_c,V_a,V_b,T_a] : % 18.78/18.92 ( class_Rings_Oordered__ring(T_a) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 18.78/18.92 => 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))) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_comm__mult__left__mono,axiom, % 18.78/18.92 ! [V_c,V_b,V_a,T_a] : % 18.78/18.92 ( class_Rings_Oordered__comm__semiring(T_a) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 18.78/18.92 => 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))) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_mult__left__mono,axiom, % 18.78/18.92 ! [V_c,V_b,V_a,T_a] : % 18.78/18.92 ( class_Rings_Oordered__semiring(T_a) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 18.78/18.92 => 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))) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_mult__right__mono,axiom, % 18.78/18.92 ! [V_c,V_b,V_a,T_a] : % 18.78/18.92 ( class_Rings_Oordered__semiring(T_a) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 18.78/18.92 => 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))) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_mult__nonpos__nonpos,axiom, % 18.78/18.92 ! [V_b,V_a,T_a] : % 18.78/18.92 ( class_Rings_Oordered__ring(T_a) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 18.78/18.92 => 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))) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_mult__nonpos__nonneg,axiom, % 18.78/18.92 ! [V_b,V_a,T_a] : % 18.78/18.92 ( class_Rings_Oordered__cancel__semiring(T_a) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 18.78/18.92 => 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))) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_mult__nonneg__nonpos2,axiom, % 18.78/18.92 ! [V_b,V_a,T_a] : % 18.78/18.92 ( class_Rings_Oordered__cancel__semiring(T_a) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 18.78/18.92 => 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))) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_mult__nonneg__nonpos,axiom, % 18.78/18.92 ! [V_b,V_a,T_a] : % 18.78/18.92 ( class_Rings_Oordered__cancel__semiring(T_a) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 18.78/18.92 => 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))) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_mult__nonneg__nonneg,axiom, % 18.78/18.92 ! [V_b,V_a,T_a] : % 18.78/18.92 ( class_Rings_Oordered__cancel__semiring(T_a) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 18.78/18.92 => 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))) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_mult__le__0__iff,axiom, % 18.78/18.92 ! [V_b_2,V_a_2,T_b] : % 18.78/18.92 ( class_Rings_Olinordered__ring__strict(T_b) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))) % 18.78/18.92 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) % 18.78/18.92 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) % 18.78/18.92 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) % 18.78/18.92 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_zero__le__mult__iff,axiom, % 18.78/18.92 ! [V_b_2,V_a_2,T_b] : % 18.78/18.92 ( class_Rings_Olinordered__ring__strict(T_b) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2))) % 18.78/18.92 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) % 18.78/18.92 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) % 18.78/18.92 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) % 18.78/18.92 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_zero__le__square,axiom, % 18.78/18.92 ! [V_a,T_a] : % 18.78/18.92 ( class_Rings_Olinordered__ring(T_a) % 18.78/18.92 => 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))) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_add__le__less__mono,axiom, % 18.78/18.92 ! [V_d,V_c,V_b,V_a,T_a] : % 18.78/18.92 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 18.78/18.92 => 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))) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_add__less__le__mono,axiom, % 18.78/18.92 ! [V_d,V_c,V_b,V_a,T_a] : % 18.78/18.92 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 18.78/18.92 => 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))) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_zero__le__one,axiom, % 18.78/18.92 ! [T_a] : % 18.78/18.92 ( class_Rings_Olinordered__semidom(T_a) % 18.78/18.92 => 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))) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_not__one__le__zero,axiom, % 18.78/18.92 ! [T_a] : % 18.78/18.92 ( class_Rings_Olinordered__semidom(T_a) % 18.78/18.92 => ~ 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))) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_neg__0__le__iff__le,axiom, % 18.78/18.92 ! [V_a_2,T_b] : % 18.78/18.92 ( class_Groups_Oordered__ab__group__add(T_b) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) % 18.78/18.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_le__minus__self__iff,axiom, % 18.78/18.92 ! [V_a_2,T_b] : % 18.78/18.92 ( class_Groups_Olinordered__ab__group__add(T_b) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) % 18.78/18.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_neg__le__0__iff__le,axiom, % 18.78/18.92 ! [V_a_2,T_b] : % 18.78/18.92 ( class_Groups_Oordered__ab__group__add(T_b) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),c_Groups_Ozero__class_Ozero(T_b))) % 18.78/18.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_minus__le__self__iff,axiom, % 18.78/18.92 ! [V_a_2,T_b] : % 18.78/18.92 ( class_Groups_Olinordered__ab__group__add(T_b) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_a_2)) % 18.78/18.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_mult__eq__1__iff,axiom, % 18.78/18.92 ! [V_n_2,V_m_2] : % 18.78/18.92 ( 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)) % 18.78/18.92 <=> ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 18.78/18.92 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_zero__le__imp__of__nat,axiom, % 18.78/18.92 ! [V_m,T_a] : % 18.78/18.92 ( class_Rings_Olinordered__semidom(T_a) % 18.78/18.92 => 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))) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_of__nat__0__le__iff,axiom, % 18.78/18.92 ! [V_n,T_a] : % 18.78/18.92 ( class_Rings_Olinordered__semidom(T_a) % 18.78/18.92 => 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))) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_mult__less__mono2,axiom, % 18.78/18.92 ! [V_k,V_j,V_i] : % 18.78/18.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 18.78/18.92 => 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))) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_mult__less__mono1,axiom, % 18.78/18.92 ! [V_k,V_j,V_i] : % 18.78/18.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 18.78/18.92 => 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))) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_mult__less__cancel2,axiom, % 18.78/18.92 ! [V_n_2,V_k_2,V_m_2] : % 18.78/18.92 ( 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))) % 18.78/18.92 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 18.78/18.92 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_mult__less__cancel1,axiom, % 18.78/18.92 ! [V_n_2,V_m_2,V_k_2] : % 18.78/18.92 ( 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))) % 18.78/18.92 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 18.78/18.92 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_nat__0__less__mult__iff,axiom, % 18.78/18.92 ! [V_n_2,V_m_2] : % 18.78/18.92 ( 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))) % 18.78/18.92 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) % 18.78/18.92 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_Suc__mult__less__cancel1,axiom, % 18.78/18.92 ! [V_n_2,V_m_2,V_k_2] : % 18.78/18.92 ( 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))) % 18.78/18.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_mult__Suc,axiom, % 18.78/18.92 ! [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)) ). % 18.78/18.92 % 18.78/18.92 fof(fact_mult__Suc__right,axiom, % 18.78/18.92 ! [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)) ). % 18.78/18.92 % 18.78/18.92 fof(fact_One__nat__def,axiom, % 18.78/18.92 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 18.78/18.92 % 18.78/18.92 fof(fact_Suc__le__lessD,axiom, % 18.78/18.92 ! [V_n,V_m] : % 18.78/18.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) % 18.78/18.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_le__less__Suc__eq,axiom, % 18.78/18.92 ! [V_n_2,V_m_2] : % 18.78/18.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) % 18.78/18.92 <=> V_n_2 = V_m_2 ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_Suc__leI,axiom, % 18.78/18.92 ! [V_n,V_m] : % 18.78/18.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 18.78/18.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_le__imp__less__Suc,axiom, % 18.78/18.92 ! [V_n,V_m] : % 18.78/18.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 18.78/18.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_Suc__le__eq,axiom, % 18.78/18.92 ! [V_n_2,V_m_2] : % 18.78/18.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2)) % 18.78/18.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_less__Suc__eq__le,axiom, % 18.78/18.92 ! [V_n_2,V_m_2] : % 18.78/18.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 18.78/18.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_less__eq__Suc__le,axiom, % 18.78/18.92 ! [V_m_2,V_n_2] : % 18.78/18.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 18.78/18.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_Suc__eq__plus1,axiom, % 18.78/18.92 ! [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)) ). % 18.78/18.92 % 18.78/18.92 fof(fact_Suc__eq__plus1__left,axiom, % 18.78/18.92 ! [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) ). % 18.78/18.92 % 18.78/18.92 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom, % 18.78/18.92 ! [V_y,V_x] : % 18.78/18.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 18.78/18.92 => 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))) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_zero__zle__int,axiom, % 18.78/18.92 ! [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))) ). % 18.78/18.92 % 18.78/18.92 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom, % 18.78/18.92 ! [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))) ). % 18.78/18.92 % 18.78/18.92 fof(fact_transfer__int__nat__quantifiers_I2_J,axiom, % 18.78/18.92 ! [V_Pa_2] : % 18.78/18.92 ( ? [B_x] : % 18.78/18.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 18.78/18.92 & hBOOL(hAPP(V_Pa_2,B_x)) ) % 18.78/18.92 <=> ? [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_transfer__int__nat__quantifiers_I1_J,axiom, % 18.78/18.92 ! [V_Pa_2] : % 18.78/18.92 ( ! [B_x] : % 18.78/18.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 18.78/18.92 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 18.78/18.92 <=> ! [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom, % 18.78/18.92 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))) ). % 18.78/18.92 % 18.78/18.92 fof(fact_eq__nat__nat__iff,axiom, % 18.78/18.92 ! [V_z_H_2,V_z_2] : % 18.78/18.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H_2)) % 18.78/18.92 => ( hAPP(c_Int_Onat,V_z_2) = hAPP(c_Int_Onat,V_z_H_2) % 18.78/18.92 <=> V_z_2 = V_z_H_2 ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_ex__nat,axiom, % 18.78/18.92 ! [V_Pa_2] : % 18.78/18.92 ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 18.78/18.92 <=> ? [B_x] : % 18.78/18.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 18.78/18.92 & hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,B_x))) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_all__nat,axiom, % 18.78/18.92 ! [V_Pa_2] : % 18.78/18.92 ( ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 18.78/18.92 <=> ! [B_x] : % 18.78/18.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 18.78/18.92 => hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,B_x))) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_transfer__nat__int__relations_I1_J,axiom, % 18.78/18.92 ! [V_y_2,V_x_2] : % 18.78/18.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) % 18.78/18.92 => ( hAPP(c_Int_Onat,V_x_2) = hAPP(c_Int_Onat,V_y_2) % 18.78/18.92 <=> V_x_2 = V_y_2 ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_zadd__zless__mono,axiom, % 18.78/18.92 ! [V_z,V_z_H,V_w,V_w_H] : % 18.78/18.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_H),V_w)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z)) % 18.78/18.92 => 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))) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom, % 18.78/18.92 ! [V_y,V_x] : % 18.78/18.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 18.78/18.92 => 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))) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_int__mult,axiom, % 18.78/18.92 ! [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)) ). % 18.78/18.92 % 18.78/18.92 fof(fact_zmult__int,axiom, % 18.78/18.92 ! [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)) ). % 18.78/18.92 % 18.78/18.92 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom, % 18.78/18.92 ! [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)) ). % 18.78/18.92 % 18.78/18.92 fof(fact_zle__iff__zadd,axiom, % 18.78/18.92 ! [V_z_2,V_w_2] : % 18.78/18.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) % 18.78/18.92 <=> ? [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)) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_int__1,axiom, % 18.78/18.92 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) ). % 18.78/18.92 % 18.78/18.92 fof(fact_transfer__int__nat__numerals_I2_J,axiom, % 18.78/18.92 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)) ). % 18.78/18.92 % 18.78/18.92 fof(fact_transfer__nat__int__numerals_I2_J,axiom, % 18.78/18.92 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 18.78/18.92 % 18.78/18.92 fof(fact_add__nonpos__neg,axiom, % 18.78/18.92 ! [V_b,V_a,T_a] : % 18.78/18.92 ( class_Groups_Oordered__comm__monoid__add(T_a) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 18.78/18.92 => 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))) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_add__neg__nonpos,axiom, % 18.78/18.92 ! [V_b,V_a,T_a] : % 18.78/18.92 ( class_Groups_Oordered__comm__monoid__add(T_a) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 18.78/18.92 => 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))) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_add__strict__increasing2,axiom, % 18.78/18.92 ! [V_c,V_b,V_a,T_a] : % 18.78/18.92 ( class_Groups_Oordered__comm__monoid__add(T_a) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 18.78/18.92 => 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))) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_add__strict__increasing,axiom, % 18.78/18.92 ! [V_c,V_b,V_a,T_a] : % 18.78/18.92 ( class_Groups_Oordered__comm__monoid__add(T_a) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c)) % 18.78/18.92 => 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))) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_add__nonneg__pos,axiom, % 18.78/18.92 ! [V_b,V_a,T_a] : % 18.78/18.92 ( class_Groups_Oordered__comm__monoid__add(T_a) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 18.78/18.92 => 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))) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_add__pos__nonneg,axiom, % 18.78/18.92 ! [V_b,V_a,T_a] : % 18.78/18.92 ( class_Groups_Oordered__comm__monoid__add(T_a) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 18.78/18.92 => 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))) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_mult__left__le__imp__le,axiom, % 18.78/18.92 ! [V_b,V_a,V_c,T_a] : % 18.78/18.92 ( class_Rings_Olinordered__semiring__strict(T_a) % 18.78/18.92 => ( 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))) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 18.78/18.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_mult__right__le__imp__le,axiom, % 18.78/18.92 ! [V_b,V_c,V_a,T_a] : % 18.78/18.92 ( class_Rings_Olinordered__semiring__strict(T_a) % 18.78/18.92 => ( 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))) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 18.78/18.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_mult__less__imp__less__left,axiom, % 18.78/18.92 ! [V_b,V_a,V_c,T_a] : % 18.78/18.92 ( class_Rings_Olinordered__semiring__strict(T_a) % 18.78/18.92 => ( 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))) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 18.78/18.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_mult__left__less__imp__less,axiom, % 18.78/18.92 ! [V_b,V_a,V_c,T_a] : % 18.78/18.92 ( class_Rings_Olinordered__semiring(T_a) % 18.78/18.92 => ( 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))) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 18.78/18.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_mult__less__imp__less__right,axiom, % 18.78/18.92 ! [V_b,V_c,V_a,T_a] : % 18.78/18.92 ( class_Rings_Olinordered__semiring__strict(T_a) % 18.78/18.92 => ( 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))) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 18.78/18.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_mult__right__less__imp__less,axiom, % 18.78/18.92 ! [V_b,V_c,V_a,T_a] : % 18.78/18.92 ( class_Rings_Olinordered__semiring(T_a) % 18.78/18.92 => ( 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))) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 18.78/18.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_mult__le__less__imp__less,axiom, % 18.78/18.92 ! [V_d,V_c,V_b,V_a,T_a] : % 18.78/18.92 ( class_Rings_Olinordered__semiring__strict(T_a) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 18.78/18.92 => 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))) ) ) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_mult__less__le__imp__less,axiom, % 18.78/18.92 ! [V_d,V_c,V_b,V_a,T_a] : % 18.78/18.92 ( class_Rings_Olinordered__semiring__strict(T_a) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 18.78/18.92 => 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))) ) ) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_mult__strict__mono_H,axiom, % 18.78/18.92 ! [V_d,V_c,V_b,V_a,T_a] : % 18.78/18.92 ( class_Rings_Olinordered__semiring__strict(T_a) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 18.78/18.92 => 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))) ) ) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_mult__strict__mono,axiom, % 18.78/18.92 ! [V_d,V_c,V_b,V_a,T_a] : % 18.78/18.92 ( class_Rings_Olinordered__semiring__strict(T_a) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 18.78/18.92 => 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))) ) ) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_mult__le__cancel__left__neg,axiom, % 18.78/18.92 ! [V_b_2,V_a_2,V_c_2,T_b] : % 18.78/18.92 ( class_Rings_Olinordered__ring__strict(T_b) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2))) % 18.78/18.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2)) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_mult__le__cancel__left__pos,axiom, % 18.78/18.92 ! [V_b_2,V_a_2,V_c_2,T_b] : % 18.78/18.92 ( class_Rings_Olinordered__ring__strict(T_b) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2))) % 18.78/18.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_sum__squares__ge__zero,axiom, % 18.78/18.92 ! [V_y,V_x,T_a] : % 18.78/18.92 ( class_Rings_Olinordered__ring(T_a) % 18.78/18.92 => 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)))) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_sum__squares__le__zero__iff,axiom, % 18.78/18.92 ! [V_y_2,V_x_2,T_b] : % 18.78/18.92 ( class_Rings_Olinordered__ring__strict(T_b) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2))),c_Groups_Ozero__class_Ozero(T_b))) % 18.78/18.92 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b) % 18.78/18.92 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_mult__left__le__one__le,axiom, % 18.78/18.92 ! [V_y,V_x,T_a] : % 18.78/18.92 ( class_Rings_Olinordered__idom(T_a) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a))) % 18.78/18.92 => 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)) ) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_mult__right__le__one__le,axiom, % 18.78/18.92 ! [V_y,V_x,T_a] : % 18.78/18.92 ( class_Rings_Olinordered__idom(T_a) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a))) % 18.78/18.92 => 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)) ) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_sgn__less,axiom, % 18.78/18.92 ! [V_a_2,T_b] : % 18.78/18.92 ( class_Rings_Olinordered__idom(T_b) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Osgn__class_Osgn(T_b,V_a_2)),c_Groups_Ozero__class_Ozero(T_b))) % 18.78/18.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_sgn__greater,axiom, % 18.78/18.92 ! [V_a_2,T_b] : % 18.78/18.92 ( class_Rings_Olinordered__idom(T_b) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Groups_Osgn__class_Osgn(T_b,V_a_2))) % 18.78/18.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_one__less__mult,axiom, % 18.78/18.92 ! [V_m,V_n] : % 18.78/18.92 ( 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)) % 18.78/18.92 => ( 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)) % 18.78/18.92 => 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))) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_n__less__n__mult__m,axiom, % 18.78/18.92 ! [V_m,V_n] : % 18.78/18.92 ( 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)) % 18.78/18.92 => ( 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)) % 18.78/18.92 => 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))) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_n__less__m__mult__n,axiom, % 18.78/18.92 ! [V_m,V_n] : % 18.78/18.92 ( 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)) % 18.78/18.92 => ( 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)) % 18.78/18.92 => 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))) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_int__le__0__conv,axiom, % 18.78/18.92 ! [V_n_2] : % 18.78/18.92 ( 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))) % 18.78/18.92 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_nat__0__iff,axiom, % 18.78/18.92 ! [V_i_2] : % 18.78/18.92 ( hAPP(c_Int_Onat,V_i_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 18.78/18.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_nat__le__0,axiom, % 18.78/18.92 ! [V_z] : % 18.78/18.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 18.78/18.92 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_int__one__le__iff__zero__less,axiom, % 18.78/18.92 ! [V_z_2] : % 18.78/18.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) % 18.78/18.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_nat__0__le,axiom, % 18.78/18.92 ! [V_z] : % 18.78/18.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 18.78/18.92 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_int__eq__iff,axiom, % 18.78/18.92 ! [V_z_2,V_m_2] : % 18.78/18.92 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = V_z_2 % 18.78/18.92 <=> ( V_m_2 = hAPP(c_Int_Onat,V_z_2) % 18.78/18.92 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_int__nat__eq,axiom, % 18.78/18.92 ! [V_z] : % 18.78/18.92 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 18.78/18.92 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) % 18.78/18.92 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 18.78/18.92 => 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) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_zle__add1__eq__le,axiom, % 18.78/18.92 ! [V_z_2,V_w_2] : % 18.78/18.92 ( 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)))) % 18.78/18.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_add1__zle__eq,axiom, % 18.78/18.92 ! [V_z_2,V_w_2] : % 18.78/18.92 ( 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)) % 18.78/18.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_zless__imp__add1__zle,axiom, % 18.78/18.92 ! [V_z,V_w] : % 18.78/18.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w),V_z)) % 18.78/18.92 => 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)) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_int__zle__neg,axiom, % 18.78/18.92 ! [V_m_2,V_n_2] : % 18.78/18.92 ( 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)))) % 18.78/18.92 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 18.78/18.92 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_negative__zle__0,axiom, % 18.78/18.92 ! [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))) ). % 18.78/18.92 % 18.78/18.92 fof(fact_convex__bound__le,axiom, % 18.78/18.92 ! [V_v,V_u,V_y,V_a,V_x,T_a] : % 18.78/18.92 ( class_Rings_Olinordered__semiring__1(T_a) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_a)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v)) % 18.78/18.92 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a) % 18.78/18.92 => 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)) ) ) ) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_transfer__nat__int__relations_I2_J,axiom, % 18.78/18.92 ! [V_y_2,V_x_2] : % 18.78/18.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) % 18.78/18.92 => ( 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))) % 18.78/18.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_nat__less__eq__zless,axiom, % 18.78/18.92 ! [V_z_2,V_w_2] : % 18.78/18.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 18.78/18.92 => ( 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))) % 18.78/18.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_nat__eq__iff,axiom, % 18.78/18.92 ! [V_m_2,V_w_2] : % 18.78/18.92 ( hAPP(c_Int_Onat,V_w_2) = V_m_2 % 18.78/18.92 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 18.78/18.92 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) ) % 18.78/18.92 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 18.78/18.92 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_nat__eq__iff2,axiom, % 18.78/18.92 ! [V_w_2,V_m_2] : % 18.78/18.92 ( V_m_2 = hAPP(c_Int_Onat,V_w_2) % 18.78/18.92 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 18.78/18.92 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) ) % 18.78/18.92 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 18.78/18.92 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J,axiom, % 18.78/18.92 ! [V_y,V_x] : % 18.78/18.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 18.78/18.92 => 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)) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_nat__add__distrib,axiom, % 18.78/18.92 ! [V_z_H,V_z] : % 18.78/18.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H)) % 18.78/18.92 => 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)) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_le__imp__0__less,axiom, % 18.78/18.92 ! [V_z] : % 18.78/18.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 18.78/18.92 => 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))) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_not__zle__0__negative,axiom, % 18.78/18.92 ! [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))))) ). % 18.78/18.92 % 18.78/18.92 fof(fact_of__nat__nat,axiom, % 18.78/18.92 ! [V_z,T_a] : % 18.78/18.92 ( class_Rings_Oring__1(T_a) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 18.78/18.92 => 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) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_sgn__pos,axiom, % 18.78/18.92 ! [V_a,T_a] : % 18.78/18.92 ( class_Rings_Olinordered__idom(T_a) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 18.78/18.92 => c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_self__quotient__aux1,axiom, % 18.78/18.92 ! [V_q,V_r,V_a] : % 18.78/18.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 18.78/18.92 => ( 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)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_a)) % 18.78/18.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q)) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_self__quotient__aux2,axiom, % 18.78/18.92 ! [V_q,V_r,V_a] : % 18.78/18.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 18.78/18.92 => ( 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)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 18.78/18.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_zdiv__mono2__neg__lemma,axiom, % 18.78/18.92 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] : % 18.78/18.92 ( 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) % 18.78/18.92 => ( 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))) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 18.78/18.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_unique__quotient__lemma__neg,axiom, % 18.78/18.92 ! [V_r,V_q,V_r_H,V_q_H,V_b] : % 18.78/18.92 ( 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))) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r_H)) % 18.78/18.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_zdiv__mono2__lemma,axiom, % 18.78/18.92 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] : % 18.78/18.92 ( 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) % 18.78/18.92 => ( 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))) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 18.78/18.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_unique__quotient__lemma,axiom, % 18.78/18.92 ! [V_r,V_q,V_r_H,V_q_H,V_b] : % 18.78/18.92 ( 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))) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 18.78/18.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_q__neg__lemma,axiom, % 18.78/18.92 ! [V_r_H,V_q_H,V_b_H] : % 18.78/18.92 ( 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))) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 18.78/18.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_q__pos__lemma,axiom, % 18.78/18.92 ! [V_r_H,V_q_H,V_b_H] : % 18.78/18.92 ( 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))) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 18.78/18.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H)) ) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_nat__mult__le__cancel1,axiom, % 18.78/18.92 ! [V_n_2,V_m_2,V_k_2] : % 18.78/18.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 18.78/18.92 => ( 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))) % 18.78/18.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_le__antisym,axiom, % 18.78/18.92 ! [V_n,V_m] : % 18.78/18.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 18.78/18.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 18.78/18.92 => V_m = V_n ) ) ). % 18.78/18.92 % 18.78/18.92 fof(fact_le__trans,axiom, % 18.78/18.92 ! [V_k,V_j,V_i] : % 18.78/18.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 18.78/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_k)) % 18.78/18.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_k)) ) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_eq__imp__le,axiom, % 18.78/18.93 ! [V_n,V_m] : % 18.78/18.93 ( V_m = V_n % 18.78/18.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_nat__le__linear,axiom, % 18.78/18.93 ! [V_n,V_m] : % 18.78/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 18.78/18.93 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_le__refl,axiom, % 18.78/18.93 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_n)) ). % 18.78/18.93 % 18.78/18.93 fof(fact_less__fun__def,axiom, % 18.78/18.93 ! [V_g_2,V_f_2,T_b,T_c] : % 18.78/18.93 ( class_Orderings_Oord(T_c) % 18.78/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c)),V_f_2),V_g_2)) % 18.78/18.93 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) % 18.78/18.93 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_g_2),V_f_2)) ) ) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_nat__mult__eq__cancel__disj,axiom, % 18.78/18.93 ! [V_n_2,V_m_2,V_k_2] : % 18.78/18.93 ( 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) % 18.78/18.93 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 18.78/18.93 | V_m_2 = V_n_2 ) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_left__add__mult__distrib,axiom, % 18.78/18.93 ! [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) ). % 18.78/18.93 % 18.78/18.93 fof(fact_nat__mult__eq__cancel1,axiom, % 18.78/18.93 ! [V_n_2,V_m_2,V_k_2] : % 18.78/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 18.78/18.93 => ( 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) % 18.78/18.93 <=> V_m_2 = V_n_2 ) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_nat__mult__less__cancel1,axiom, % 18.78/18.93 ! [V_n_2,V_m_2,V_k_2] : % 18.78/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 18.78/18.93 => ( 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))) % 18.78/18.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_transfer__morphism__nat__int,axiom, % 18.78/18.93 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))) ). % 18.78/18.93 % 18.78/18.93 fof(fact_compl__mono,axiom, % 18.78/18.93 ! [V_y,V_x,T_a] : % 18.78/18.93 ( class_Lattices_Oboolean__algebra(T_a) % 18.78/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 18.78/18.93 => 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))) ) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_compl__le__compl__iff,axiom, % 18.78/18.93 ! [V_y_2,V_x_2,T_b] : % 18.78/18.93 ( class_Lattices_Oboolean__algebra(T_b) % 18.78/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2))) % 18.78/18.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_ex__least__nat__less,axiom, % 18.78/18.93 ! [V_n_2,V_Pa_2] : % 18.78/18.93 ( ~ hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) % 18.78/18.93 => ( hBOOL(hAPP(V_Pa_2,V_n_2)) % 18.78/18.93 => ? [B_k] : % 18.78/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_k),V_n_2)) % 18.78/18.93 & ! [B_i] : % 18.78/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_k)) % 18.78/18.93 => ~ hBOOL(hAPP(V_Pa_2,B_i)) ) % 18.78/18.93 & hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_k),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_split__zmod,axiom, % 18.78/18.93 ! [V_k_2,V_n_2,V_Pa_2] : % 18.78/18.93 ( hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2))) % 18.78/18.93 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 18.78/18.93 => hBOOL(hAPP(V_Pa_2,V_n_2)) ) % 18.78/18.93 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 18.78/18.93 => ! [B_i,B_j] : % 18.78/18.93 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) % 18.78/18.93 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) % 18.78/18.93 & 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) ) % 18.78/18.93 => hBOOL(hAPP(V_Pa_2,B_j)) ) ) % 18.78/18.93 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 18.78/18.93 => ! [B_i,B_j] : % 18.78/18.93 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) % 18.78/18.93 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 18.78/18.93 & 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) ) % 18.78/18.93 => hBOOL(hAPP(V_Pa_2,B_j)) ) ) ) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_zmult2__lemma__aux3,axiom, % 18.78/18.93 ! [V_q,V_b,V_r,V_c] : % 18.78/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 18.78/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 18.78/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 18.78/18.93 => 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))) ) ) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_zmult2__lemma__aux4,axiom, % 18.78/18.93 ! [V_q,V_b,V_r,V_c] : % 18.78/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 18.78/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 18.78/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 18.78/18.93 => 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))) ) ) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_zmult2__lemma__aux1,axiom, % 18.78/18.93 ! [V_q,V_r,V_b,V_c] : % 18.78/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 18.78/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 18.78/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 18.78/18.93 => 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))) ) ) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_mod__mod__trivial,axiom, % 18.78/18.93 ! [V_b,V_a,T_a] : % 18.78/18.93 ( class_Divides_Osemiring__div(T_a) % 18.78/18.93 => 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) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_mod__0,axiom, % 18.78/18.93 ! [V_a,T_a] : % 18.78/18.93 ( class_Divides_Osemiring__div(T_a) % 18.78/18.93 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_mod__by__0,axiom, % 18.78/18.93 ! [V_a,T_a] : % 18.78/18.93 ( class_Divides_Osemiring__div(T_a) % 18.78/18.93 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_mod__self,axiom, % 18.78/18.93 ! [V_a,T_a] : % 18.78/18.93 ( class_Divides_Osemiring__div(T_a) % 18.78/18.93 => c_Divides_Odiv__class_Omod(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_mod__add__cong,axiom, % 18.78/18.93 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] : % 18.78/18.93 ( class_Divides_Osemiring__div(T_a) % 18.78/18.93 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) % 18.78/18.93 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) % 18.78/18.93 => 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) ) ) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_zmod__simps_I1_J,axiom, % 18.78/18.93 ! [V_b,V_c,V_a,T_a] : % 18.78/18.93 ( class_Divides_Osemiring__div(T_a) % 18.78/18.93 => 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) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_zmod__simps_I2_J,axiom, % 18.78/18.93 ! [V_c,V_b,V_a,T_a] : % 18.78/18.93 ( class_Divides_Osemiring__div(T_a) % 18.78/18.93 => 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) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_mod__add__eq,axiom, % 18.78/18.93 ! [V_c,V_b,V_a,T_a] : % 18.78/18.93 ( class_Divides_Osemiring__div(T_a) % 18.78/18.93 => 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) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_mod__add__left__eq,axiom, % 18.78/18.93 ! [V_c,V_b,V_a,T_a] : % 18.78/18.93 ( class_Divides_Osemiring__div(T_a) % 18.78/18.93 => 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) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_mod__add__right__eq,axiom, % 18.78/18.93 ! [V_c,V_b,V_a,T_a] : % 18.78/18.93 ( class_Divides_Osemiring__div(T_a) % 18.78/18.93 => 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) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_mod__add__self1,axiom, % 18.78/18.93 ! [V_a,V_b,T_a] : % 18.78/18.93 ( class_Divides_Osemiring__div(T_a) % 18.78/18.93 => 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) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_mod__add__self2,axiom, % 18.78/18.93 ! [V_b,V_a,T_a] : % 18.78/18.93 ( class_Divides_Osemiring__div(T_a) % 18.78/18.93 => 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) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_mod__mult__cong,axiom, % 18.78/18.93 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] : % 18.78/18.93 ( class_Divides_Osemiring__div(T_a) % 18.78/18.93 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) % 18.78/18.93 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) % 18.78/18.93 => 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) ) ) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_zmod__simps_I4_J,axiom, % 18.78/18.93 ! [V_b,V_c,V_a,T_a] : % 18.78/18.93 ( class_Divides_Osemiring__div(T_a) % 18.78/18.93 => 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) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_mod__mult__mult2,axiom, % 18.78/18.93 ! [V_b,V_c,V_a,T_a] : % 18.78/18.93 ( class_Divides_Osemiring__div(T_a) % 18.78/18.93 => 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) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_mod__mult__mult1,axiom, % 18.78/18.93 ! [V_b,V_a,V_c,T_a] : % 18.78/18.93 ( class_Divides_Osemiring__div(T_a) % 18.78/18.93 => 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)) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_mod__mult__eq,axiom, % 18.78/18.93 ! [V_c,V_b,V_a,T_a] : % 18.78/18.93 ( class_Divides_Osemiring__div(T_a) % 18.78/18.93 => 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) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_mod__mult__left__eq,axiom, % 18.78/18.93 ! [V_c,V_b,V_a,T_a] : % 18.78/18.93 ( class_Divides_Osemiring__div(T_a) % 18.78/18.93 => 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) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_mod__mult__right__eq,axiom, % 18.78/18.93 ! [V_c,V_b,V_a,T_a] : % 18.78/18.93 ( class_Divides_Osemiring__div(T_a) % 18.78/18.93 => 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) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_mod__minus__cong,axiom, % 18.78/18.93 ! [V_a_H,V_b,V_a,T_a] : % 18.78/18.93 ( class_Divides_Oring__div(T_a) % 18.78/18.93 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_b) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_b) % 18.78/18.93 => 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) ) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_mod__minus__eq,axiom, % 18.78/18.93 ! [V_b,V_a,T_a] : % 18.78/18.93 ( class_Divides_Oring__div(T_a) % 18.78/18.93 => 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) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_zmod__zero,axiom, % 18.78/18.93 ! [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) ). % 18.78/18.93 % 18.78/18.93 fof(fact_zmod__self,axiom, % 18.78/18.93 ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 18.78/18.93 % 18.78/18.93 fof(fact_zmod__zmult1__eq,axiom, % 18.78/18.93 ! [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) ). % 18.78/18.93 % 18.78/18.93 fof(fact_zmod__simps_I3_J,axiom, % 18.78/18.93 ! [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) ). % 18.78/18.93 % 18.78/18.93 fof(fact_zmod__zminus2,axiom, % 18.78/18.93 ! [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)) ). % 18.78/18.93 % 18.78/18.93 fof(fact_zmod__zminus__zminus,axiom, % 18.78/18.93 ! [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)) ). % 18.78/18.93 % 18.78/18.93 fof(fact_zminus__zmod,axiom, % 18.78/18.93 ! [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) ). % 18.78/18.93 % 18.78/18.93 fof(fact_mod__mult__self2__is__0,axiom, % 18.78/18.93 ! [V_b,V_a,T_a] : % 18.78/18.93 ( class_Divides_Osemiring__div(T_a) % 18.78/18.93 => 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) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_mod__mult__self1__is__0,axiom, % 18.78/18.93 ! [V_a,V_b,T_a] : % 18.78/18.93 ( class_Divides_Osemiring__div(T_a) % 18.78/18.93 => 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) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_mod__mult__self1,axiom, % 18.78/18.93 ! [V_b,V_c,V_a,T_a] : % 18.78/18.93 ( class_Divides_Osemiring__div(T_a) % 18.78/18.93 => 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) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_mod__mult__self2,axiom, % 18.78/18.93 ! [V_c,V_b,V_a,T_a] : % 18.78/18.93 ( class_Divides_Osemiring__div(T_a) % 18.78/18.93 => 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) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_mod__by__1,axiom, % 18.78/18.93 ! [V_a,T_a] : % 18.78/18.93 ( class_Divides_Osemiring__div(T_a) % 18.78/18.93 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_zmod__le__nonneg__dividend,axiom, % 18.78/18.93 ! [V_k,V_m] : % 18.78/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m)) % 18.78/18.93 => 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)) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_Divides_Otransfer__nat__int__function__closures_I2_J,axiom, % 18.78/18.93 ! [V_y,V_x] : % 18.78/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 18.78/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 18.78/18.93 => 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))) ) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_neg__mod__bound,axiom, % 18.78/18.93 ! [V_a,V_b] : % 18.78/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 18.78/18.93 => 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))) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_pos__mod__bound,axiom, % 18.78/18.93 ! [V_a,V_b] : % 18.78/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 18.78/18.93 => 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)) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_zmod__eq__0__iff,axiom, % 18.78/18.93 ! [V_d_2,V_m_2] : % 18.78/18.93 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 18.78/18.93 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),B_q) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_zmod__zminus2__not__zero,axiom, % 18.78/18.93 ! [V_l,V_k] : % 18.78/18.93 ( 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) % 18.78/18.93 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_zmod__zminus1__not__zero,axiom, % 18.78/18.93 ! [V_l,V_k] : % 18.78/18.93 ( 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) % 18.78/18.93 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_mod__neg__neg__trivial,axiom, % 18.78/18.93 ! [V_b,V_a] : % 18.78/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 18.78/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a)) % 18.78/18.93 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_neg__mod__conj,axiom, % 18.78/18.93 ! [V_a,V_b] : % 18.78/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 18.78/18.93 => ( 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))) % 18.78/18.93 & 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))) ) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_neg__mod__sign,axiom, % 18.78/18.93 ! [V_a,V_b] : % 18.78/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 18.78/18.93 => 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))) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_mod__pos__pos__trivial,axiom, % 18.78/18.93 ! [V_b,V_a] : % 18.78/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 18.78/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 18.78/18.93 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_pos__mod__conj,axiom, % 18.78/18.93 ! [V_a,V_b] : % 18.78/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 18.78/18.93 => ( 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))) % 18.78/18.93 & 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)) ) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_pos__mod__sign,axiom, % 18.78/18.93 ! [V_a,V_b] : % 18.78/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 18.78/18.93 => 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))) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_times_Oidem,axiom, % 18.78/18.93 ! [V_a,T_a] : % 18.78/18.93 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 18.78/18.93 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) = V_a ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_mult__idem,axiom, % 18.78/18.93 ! [V_x,T_a] : % 18.78/18.93 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 18.78/18.93 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = V_x ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_mult__left__idem,axiom, % 18.78/18.93 ! [V_b,V_a,T_a] : % 18.78/18.93 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 18.78/18.93 => 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) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_double__compl,axiom, % 18.78/18.93 ! [V_x,T_a] : % 18.78/18.93 ( class_Lattices_Oboolean__algebra(T_a) % 18.78/18.93 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = V_x ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_uminus__apply,axiom, % 18.78/18.93 ! [V_x_2,V_A_2,T_c,T_b] : % 18.78/18.93 ( class_Groups_Ouminus(T_b) % 18.78/18.93 => hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,T_b)),V_A_2),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(V_A_2,V_x_2)) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_compl__eq__compl__iff,axiom, % 18.78/18.93 ! [V_y_2,V_x_2,T_b] : % 18.78/18.93 ( class_Lattices_Oboolean__algebra(T_b) % 18.78/18.93 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2) % 18.78/18.93 <=> V_x_2 = V_y_2 ) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_mod__pos__neg__trivial,axiom, % 18.78/18.93 ! [V_b,V_a] : % 18.78/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 18.78/18.93 => ( 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))) % 18.78/18.93 => 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) ) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_divmod__int__rel__mod__eq,axiom, % 18.78/18.93 ! [V_y,V_q_1,V_b_1,V_a_1] : % 18.78/18.93 ( 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) % 18.78/18.93 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 18.78/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 18.78/18.93 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_b_1)) ) ) % 18.78/18.93 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 18.78/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_y)) % 18.78/18.93 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) % 18.78/18.93 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 18.78/18.93 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a_1,V_b_1) = V_y ) ) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_zmult2__lemma__aux2,axiom, % 18.78/18.93 ! [V_q,V_r,V_b,V_c] : % 18.78/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 18.78/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 18.78/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 18.78/18.93 => 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))) ) ) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_z3mod__def,axiom, % 18.78/18.93 ! [V_k,V_l] : % 18.78/18.93 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 18.78/18.93 => c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) ) % 18.78/18.93 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 18.78/18.93 => 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)) ) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_split__pos__lemma,axiom, % 18.78/18.93 ! [V_n_2,V_Pa_2,V_k_2] : % 18.78/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 18.78/18.93 => ( hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2))) % 18.78/18.93 <=> ! [B_i,B_j] : % 18.78/18.93 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) % 18.78/18.93 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) % 18.78/18.93 & 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) ) % 18.78/18.93 => hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j)) ) ) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_split__neg__lemma,axiom, % 18.78/18.93 ! [V_n_2,V_Pa_2,V_k_2] : % 18.78/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 18.78/18.93 => ( hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2))) % 18.78/18.93 <=> ! [B_i,B_j] : % 18.78/18.93 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) % 18.78/18.93 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 18.78/18.93 & 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) ) % 18.78/18.93 => hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j)) ) ) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_zmod__zmult2__eq,axiom, % 18.78/18.93 ! [V_b,V_a,V_c] : % 18.78/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 18.78/18.93 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b),V_c))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom, % 18.78/18.93 ! [V_y,V_x] : % 18.78/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 18.78/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 18.78/18.93 => 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))) ) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_divmod__int__rel__div__eq,axiom, % 18.78/18.93 ! [V_r_1,V_y,V_b_1,V_a_1] : % 18.78/18.93 ( 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) % 18.78/18.93 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 18.78/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1)) % 18.78/18.93 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_1),V_b_1)) ) ) % 18.78/18.93 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 18.78/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_r_1)) % 18.78/18.93 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) % 18.78/18.93 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 18.78/18.93 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_1),V_b_1) = V_y ) ) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_split__zdiv,axiom, % 18.78/18.93 ! [V_k_2,V_n_2,V_Pa_2] : % 18.78/18.93 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2))) % 18.78/18.93 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 18.78/18.93 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 18.78/18.93 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 18.78/18.93 => ! [B_i] : % 18.78/18.93 ( ? [B_j] : % 18.78/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) % 18.78/18.93 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) % 18.78/18.93 & 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) ) % 18.78/18.93 => hBOOL(hAPP(V_Pa_2,B_i)) ) ) % 18.78/18.93 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 18.78/18.93 => ! [B_i] : % 18.78/18.93 ( ? [B_j] : % 18.78/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) % 18.78/18.93 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 18.78/18.93 & 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) ) % 18.78/18.93 => hBOOL(hAPP(V_Pa_2,B_i)) ) ) ) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_split__div_H,axiom, % 18.78/18.93 ! [V_n_2,V_m_2,V_Pa_2] : % 18.78/18.93 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2))) % 18.78/18.93 <=> ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 18.78/18.93 & hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 18.78/18.93 | ? [B_q] : % 18.78/18.93 ( 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)) % 18.78/18.93 & 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)))) % 18.78/18.93 & hBOOL(hAPP(V_Pa_2,B_q)) ) ) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_div__add1__eq,axiom, % 18.78/18.93 ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_c)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,V_c)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_b,V_c))),V_c)) ). % 18.78/18.93 % 18.78/18.93 fof(fact_zdiv__int,axiom, % 18.78/18.93 ! [V_b,V_a] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_b)) ). % 18.78/18.93 % 18.78/18.93 fof(fact_Divides_Otransfer__int__nat__functions_I1_J,axiom, % 18.78/18.93 ! [V_y,V_x] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_x),V_y)) ). % 18.78/18.93 % 18.78/18.93 fof(fact_div__mult1__eq,axiom, % 18.78/18.93 ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_b,V_c))),V_c)) ). % 18.78/18.93 % 18.78/18.93 fof(fact_mod__mult2__eq,axiom, % 18.78/18.93 ! [V_c,V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_b),V_c))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,V_b)) ). % 18.78/18.93 % 18.78/18.93 fof(fact_div__le__dividend,axiom, % 18.78/18.93 ! [V_n,V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_m)) ). % 18.78/18.93 % 18.78/18.93 fof(fact_div__le__mono,axiom, % 18.78/18.93 ! [V_k,V_n,V_m] : % 18.78/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 18.78/18.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n),V_k))) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_zdiv__zero,axiom, % 18.78/18.93 ! [V_b] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 18.78/18.93 % 18.78/18.93 fof(fact_mod__Suc__eq__Suc__mod,axiom, % 18.78/18.93 ! [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) ). % 18.78/18.93 % 18.78/18.93 fof(fact_div__mult2__eq,axiom, % 18.78/18.93 ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_b)),V_c) ). % 18.78/18.93 % 18.78/18.93 fof(fact_mod__less,axiom, % 18.78/18.93 ! [V_n,V_m] : % 18.78/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 18.78/18.93 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_mod__less__eq__dividend,axiom, % 18.78/18.93 ! [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)) ). % 18.78/18.93 % 18.78/18.93 fof(fact_mod__mult__distrib2,axiom, % 18.78/18.93 ! [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)) ). % 18.78/18.93 % 18.78/18.93 fof(fact_mod__mult__distrib,axiom, % 18.78/18.93 ! [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)) ). % 18.78/18.93 % 18.78/18.93 fof(fact_zdiv__zminus__zminus,axiom, % 18.78/18.93 ! [V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) ). % 18.78/18.93 % 18.78/18.93 fof(fact_zdiv__zminus2,axiom, % 18.78/18.93 ! [V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),V_b) ). % 18.78/18.93 % 18.78/18.93 fof(fact_div__0,axiom, % 18.78/18.93 ! [V_a,T_a] : % 18.78/18.93 ( class_Divides_Osemiring__div(T_a) % 18.78/18.93 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_div__by__0,axiom, % 18.78/18.93 ! [V_a,T_a] : % 18.78/18.93 ( class_Divides_Osemiring__div(T_a) % 18.78/18.93 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_div__by__1,axiom, % 18.78/18.93 ! [V_a,T_a] : % 18.78/18.93 ( class_Divides_Osemiring__div(T_a) % 18.78/18.93 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_nat__div__distrib,axiom, % 18.78/18.93 ! [V_y,V_x] : % 18.78/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 18.78/18.93 => hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_Divides_Otransfer__nat__int__functions_I1_J,axiom, % 18.78/18.93 ! [V_y,V_x] : % 18.78/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 18.78/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 18.78/18.93 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) ) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_div__1,axiom, % 18.78/18.93 ! [V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = V_m ). % 18.78/18.93 % 18.78/18.93 fof(fact_div__less,axiom, % 18.78/18.93 ! [V_n,V_m] : % 18.78/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 18.78/18.93 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_nat__mult__div__cancel__disj,axiom, % 18.78/18.93 ! [V_n,V_m,V_k] : % 18.78/18.93 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 18.78/18.93 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 18.78/18.93 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 18.78/18.93 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) ) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_mod__1,axiom, % 18.78/18.93 ! [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) ). % 18.78/18.93 % 18.78/18.93 fof(fact_mod__Suc,axiom, % 18.78/18.93 ! [V_n,V_m] : % 18.78/18.93 ( ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = V_n % 18.78/18.93 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 18.78/18.93 & ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) != V_n % 18.78/18.93 => 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)) ) ) ). % 18.78/18.93 % 18.78/18.93 fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom, % 18.78/18.93 ! [V_y,V_x] : % 18.78/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 18.97/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 18.97/18.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y))) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_mod__less__divisor,axiom, % 18.97/18.93 ! [V_m,V_n] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 18.97/18.93 => 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)) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_pos__imp__zdiv__neg__iff,axiom, % 18.97/18.93 ! [V_a_2,V_b_2] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) % 18.97/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 18.97/18.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_neg__imp__zdiv__neg__iff,axiom, % 18.97/18.93 ! [V_a_2,V_b_2] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 18.97/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 18.97/18.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_div__neg__pos__less0,axiom, % 18.97/18.93 ! [V_b,V_a] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 18.97/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 18.97/18.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_zdiv__self,axiom, % 18.97/18.93 ! [V_a] : % 18.97/18.93 ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 18.97/18.93 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_mod__eq__0__iff,axiom, % 18.97/18.93 ! [V_d_2,V_m_2] : % 18.97/18.93 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 18.97/18.93 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_d_2),B_q) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_DIVISION__BY__ZERO,axiom, % 18.97/18.93 ! [V_a] : % 18.97/18.93 ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 18.97/18.93 & c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_a ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_zmod__zdiv__trivial,axiom, % 18.97/18.93 ! [V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 18.97/18.93 % 18.97/18.93 fof(fact_mod__mult__self3,axiom, % 18.97/18.93 ! [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) ). % 18.97/18.93 % 18.97/18.93 fof(fact_zdiv__zadd1__eq,axiom, % 18.97/18.93 ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_c)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_c)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c))),V_c)) ). % 18.97/18.93 % 18.97/18.93 fof(fact_zmod__int,axiom, % 18.97/18.93 ! [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)) ). % 18.97/18.93 % 18.97/18.93 fof(fact_Divides_Otransfer__int__nat__functions_I2_J,axiom, % 18.97/18.93 ! [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)) ). % 18.97/18.93 % 18.97/18.93 fof(fact_div__mult__mult1,axiom, % 18.97/18.93 ! [V_b,V_a,V_c,T_a] : % 18.97/18.93 ( class_Divides_Osemiring__div(T_a) % 18.97/18.93 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 18.97/18.93 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_div__mult__mult2,axiom, % 18.97/18.93 ! [V_b,V_a,V_c,T_a] : % 18.97/18.93 ( class_Divides_Osemiring__div(T_a) % 18.97/18.93 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 18.97/18.93 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_div__mult__self1__is__id,axiom, % 18.97/18.93 ! [V_a,V_b,T_a] : % 18.97/18.93 ( class_Divides_Osemiring__div(T_a) % 18.97/18.93 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 18.97/18.93 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)),V_b) = V_a ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_div__mult__self2__is__id,axiom, % 18.97/18.93 ! [V_a,V_b,T_a] : % 18.97/18.93 ( class_Divides_Osemiring__div(T_a) % 18.97/18.93 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 18.97/18.93 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_b) = V_a ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_div__mult__mult1__if,axiom, % 18.97/18.93 ! [V_b,V_a,V_c,T_a] : % 18.97/18.93 ( class_Divides_Osemiring__div(T_a) % 18.97/18.93 => ( ( V_c = c_Groups_Ozero__class_Ozero(T_a) % 18.97/18.93 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = c_Groups_Ozero__class_Ozero(T_a) ) % 18.97/18.93 & ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 18.97/18.93 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b) ) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_div__self,axiom, % 18.97/18.93 ! [V_a,T_a] : % 18.97/18.93 ( class_Divides_Osemiring__div(T_a) % 18.97/18.93 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 18.97/18.93 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_mod__div__trivial,axiom, % 18.97/18.93 ! [V_b,V_a,T_a] : % 18.97/18.93 ( class_Divides_Osemiring__div(T_a) % 18.97/18.93 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_b) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_div__le__mono2,axiom, % 18.97/18.93 ! [V_k,V_n,V_m] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 18.97/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 18.97/18.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_k),V_n)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_k),V_m))) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_div__mult__self__is__m,axiom, % 18.97/18.93 ! [V_m,V_n] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 18.97/18.93 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),V_n) = V_m ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_div__mult__self1__is__m,axiom, % 18.97/18.93 ! [V_m,V_n] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 18.97/18.93 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m)),V_n) = V_m ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_nat__mult__div__cancel1,axiom, % 18.97/18.93 ! [V_n,V_m,V_k] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 18.97/18.93 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_div__less__dividend,axiom, % 18.97/18.93 ! [V_m,V_n] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) % 18.97/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 18.97/18.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_m)) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_zdiv__eq__0__iff,axiom, % 18.97/18.93 ! [V_k_2,V_i_2] : % 18.97/18.93 ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 18.97/18.93 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 18.97/18.93 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2)) % 18.97/18.93 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),V_k_2)) ) % 18.97/18.93 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 18.97/18.93 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_i_2)) ) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_pos__imp__zdiv__nonneg__iff,axiom, % 18.97/18.93 ! [V_a_2,V_b_2] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) % 18.97/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2))) % 18.97/18.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_pos__imp__zdiv__pos__iff,axiom, % 18.97/18.93 ! [V_i_2,V_k_2] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 18.97/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2))) % 18.97/18.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_i_2)) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_nonneg1__imp__zdiv__pos__iff,axiom, % 18.97/18.93 ! [V_b_2,V_a_2] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) % 18.97/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2))) % 18.97/18.93 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),V_a_2)) % 18.97/18.93 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) ) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_zdiv__mono2,axiom, % 18.97/18.93 ! [V_b,V_b_H,V_a] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 18.97/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 18.97/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 18.97/18.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b_H))) ) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_div__nonneg__neg__le0,axiom, % 18.97/18.93 ! [V_b,V_a] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 18.97/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 18.97/18.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_div__pos__pos__trivial,axiom, % 18.97/18.93 ! [V_b,V_a] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 18.97/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 18.97/18.93 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_neg__imp__zdiv__nonneg__iff,axiom, % 18.97/18.93 ! [V_a_2,V_b_2] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 18.97/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2))) % 18.97/18.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_div__nonpos__pos__le0,axiom, % 18.97/18.93 ! [V_b,V_a] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 18.97/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 18.97/18.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_zdiv__mono2__neg,axiom, % 18.97/18.93 ! [V_b,V_b_H,V_a] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 18.97/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 18.97/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 18.97/18.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b_H)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))) ) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_div__neg__neg__trivial,axiom, % 18.97/18.93 ! [V_b,V_a] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 18.97/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a)) % 18.97/18.93 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_zdiv__mono1,axiom, % 18.97/18.93 ! [V_b,V_a_H,V_a] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H)) % 18.97/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 18.97/18.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_H),V_b))) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_zdiv__mono1__neg,axiom, % 18.97/18.93 ! [V_b,V_a_H,V_a] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H)) % 18.97/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 18.97/18.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_H),V_b)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_mod__le__divisor,axiom, % 18.97/18.93 ! [V_m,V_n] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 18.97/18.93 => 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)) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_int__div__less__self,axiom, % 18.97/18.93 ! [V_k,V_x] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 18.97/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k)) % 18.97/18.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_k)),V_x)) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_zdiv__zmult2__eq,axiom, % 18.97/18.93 ! [V_b,V_a,V_c] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 18.97/18.93 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),V_c) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_mod__mult__self4,axiom, % 18.97/18.93 ! [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) ). % 18.97/18.93 % 18.97/18.93 fof(fact_zmod__zdiv__equality,axiom, % 18.97/18.93 ! [V_b,V_a] : V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)) ). % 18.97/18.93 % 18.97/18.93 fof(fact_zdiv__zmult1__eq,axiom, % 18.97/18.93 ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c))),V_c)) ). % 18.97/18.93 % 18.97/18.93 fof(fact_zdiv__zmod__equality,axiom, % 18.97/18.93 ! [V_k,V_a,V_b] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_k) ). % 18.97/18.93 % 18.97/18.93 fof(fact_zdiv__zmod__equality2,axiom, % 18.97/18.93 ! [V_k,V_b,V_a] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_k) ). % 18.97/18.93 % 18.97/18.93 fof(fact_div__mult__self2,axiom, % 18.97/18.93 ! [V_c,V_a,V_b,T_a] : % 18.97/18.93 ( class_Divides_Osemiring__div(T_a) % 18.97/18.93 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 18.97/18.93 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_div__mult__self1,axiom, % 18.97/18.93 ! [V_c,V_a,V_b,T_a] : % 18.97/18.93 ( class_Divides_Osemiring__div(T_a) % 18.97/18.93 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 18.97/18.93 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_div__add__self2,axiom, % 18.97/18.93 ! [V_a,V_b,T_a] : % 18.97/18.93 ( class_Divides_Osemiring__div(T_a) % 18.97/18.93 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 18.97/18.93 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),c_Groups_Oone__class_Oone(T_a)) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_div__add__self1,axiom, % 18.97/18.93 ! [V_a,V_b,T_a] : % 18.97/18.93 ( class_Divides_Osemiring__div(T_a) % 18.97/18.93 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 18.97/18.93 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a)),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),c_Groups_Oone__class_Oone(T_a)) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_semiring__div__class_Omod__div__equality_H,axiom, % 18.97/18.93 ! [V_b,V_a,T_a] : % 18.97/18.93 ( class_Divides_Osemiring__div(T_a) % 18.97/18.93 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)) = V_a ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_mod__div__equality2,axiom, % 18.97/18.93 ! [V_a,V_b,T_a] : % 18.97/18.93 ( class_Divides_Osemiring__div(T_a) % 18.97/18.93 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b))),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) = V_a ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_mod__div__equality,axiom, % 18.97/18.93 ! [V_b,V_a,T_a] : % 18.97/18.93 ( class_Divides_Osemiring__div(T_a) % 18.97/18.93 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) = V_a ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_div__mod__equality2,axiom, % 18.97/18.93 ! [V_c,V_a,V_b,T_a] : % 18.97/18.93 ( class_Divides_Osemiring__div(T_a) % 18.97/18.93 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b))),c_Divides_Odiv__class_Omod(T_a,V_a,V_b))),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_div__mod__equality,axiom, % 18.97/18.93 ! [V_c,V_b,V_a,T_a] : % 18.97/18.93 ( class_Divides_Osemiring__div(T_a) % 18.97/18.93 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b))),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_split__div,axiom, % 18.97/18.93 ! [V_k_2,V_n_2,V_Pa_2] : % 18.97/18.93 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n_2),V_k_2))) % 18.97/18.93 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 18.97/18.93 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 18.97/18.93 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 18.97/18.93 => ! [B_i,B_j] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2)) % 18.97/18.93 => ( 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) % 18.97/18.93 => hBOOL(hAPP(V_Pa_2,B_i)) ) ) ) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_split__mod,axiom, % 18.97/18.93 ! [V_k_2,V_n_2,V_Pa_2] : % 18.97/18.93 ( hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2))) % 18.97/18.93 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 18.97/18.93 => hBOOL(hAPP(V_Pa_2,V_n_2)) ) % 18.97/18.93 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 18.97/18.93 => ! [B_i,B_j] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2)) % 18.97/18.93 => ( 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) % 18.97/18.93 => hBOOL(hAPP(V_Pa_2,B_j)) ) ) ) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_mod__lemma,axiom, % 18.97/18.93 ! [V_q,V_b,V_r,V_c] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 18.97/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_r),V_b)) % 18.97/18.93 => 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))) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_Suc__times__mod__eq,axiom, % 18.97/18.93 ! [V_m,V_k] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_k)) % 18.97/18.93 => 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) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_nat__mod__distrib,axiom, % 18.97/18.93 ! [V_y,V_x] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 18.97/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 18.97/18.93 => 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)) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_Divides_Otransfer__nat__int__functions_I2_J,axiom, % 18.97/18.93 ! [V_y,V_x] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 18.97/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 18.97/18.93 => 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)) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_split__div__lemma,axiom, % 18.97/18.93 ! [V_m_2,V_q_2,V_n_2] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 18.97/18.93 => ( ( 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)) % 18.97/18.93 & 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)))) ) % 18.97/18.93 <=> V_q_2 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_z3div__def,axiom, % 18.97/18.93 ! [V_k,V_l] : % 18.97/18.93 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 18.97/18.93 => c_SMT_Oz3div(V_k,V_l) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l) ) % 18.97/18.93 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 18.97/18.93 => c_SMT_Oz3div(V_k,V_l) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_l))) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_zdiv__zminus1__eq__if,axiom, % 18.97/18.93 ! [V_a,V_b] : % 18.97/18.93 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 18.97/18.93 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 18.97/18.93 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),V_b) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)) ) % 18.97/18.93 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 18.97/18.93 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),V_b) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_zdiv__zminus2__eq__if,axiom, % 18.97/18.93 ! [V_a,V_b] : % 18.97/18.93 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 18.97/18.93 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 18.97/18.93 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)) ) % 18.97/18.93 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 18.97/18.93 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_le__div__geq,axiom, % 18.97/18.93 ! [V_m,V_n] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 18.97/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 18.97/18.93 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n)) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_mod__div__decomp,axiom, % 18.97/18.93 ! [V_b,V_a,T_a] : % 18.97/18.93 ( class_Divides_Osemiring__div(T_a) % 18.97/18.93 => V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J,axiom, % 18.97/18.93 ! [V_y,V_x] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 18.97/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 18.97/18.93 => 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)) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_incr__mult__lemma,axiom, % 18.97/18.93 ! [V_k_2,V_Pa_2,V_d_2] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) % 18.97/18.93 => ( ! [B_x] : % 18.97/18.93 ( hBOOL(hAPP(V_Pa_2,B_x)) % 18.97/18.93 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_d_2))) ) % 18.97/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 18.97/18.93 => ! [B_x] : % 18.97/18.93 ( hBOOL(hAPP(V_Pa_2,B_x)) % 18.97/18.93 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2)))) ) ) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_field__le__mult__one__interval,axiom, % 18.97/18.93 ! [V_y,V_x,T_a] : % 18.97/18.93 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 18.97/18.93 => ( ! [B_z] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_z)) % 18.97/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_z),c_Groups_Oone__class_Oone(T_a))) % 18.97/18.93 => 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)) ) ) % 18.97/18.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_diff__commute,axiom, % 18.97/18.93 ! [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) ). % 18.97/18.93 % 18.97/18.93 fof(fact_diff__eq__diff__eq,axiom, % 18.97/18.93 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] : % 18.97/18.93 ( class_Groups_Oab__group__add(T_b) % 18.97/18.93 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_c_2),V_d_2) % 18.97/18.93 => ( V_a_2 = V_b_2 % 18.97/18.93 <=> V_c_2 = V_d_2 ) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_of__int__diff,axiom, % 18.97/18.93 ! [V_z,V_w,T_a] : % 18.97/18.93 ( class_Rings_Oring__1(T_a) % 18.97/18.93 => 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)) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_minus__apply,axiom, % 18.97/18.93 ! [V_x_2,V_B_2,V_A_2,T_c,T_b] : % 18.97/18.93 ( class_Groups_Ominus(T_b) % 18.97/18.93 => hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,T_b)),V_A_2),V_B_2),V_x_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2)) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_of__nat__diff,axiom, % 18.97/18.93 ! [V_m,V_n,T_a] : % 18.97/18.93 ( class_Rings_Oring__1(T_a) % 18.97/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 18.97/18.93 => 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)) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_zdiff__int,axiom, % 18.97/18.93 ! [V_m,V_n] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 18.97/18.93 => 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)) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_diff__eq__diff__less__eq,axiom, % 18.97/18.93 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] : % 18.97/18.93 ( class_Groups_Oordered__ab__group__add(T_b) % 18.97/18.93 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_c_2),V_d_2) % 18.97/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) % 18.97/18.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_d_2)) ) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_right__minus__eq,axiom, % 18.97/18.93 ! [V_b_2,V_a_2,T_b] : % 18.97/18.93 ( class_Groups_Ogroup__add(T_b) % 18.97/18.93 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b) % 18.97/18.93 <=> V_a_2 = V_b_2 ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_eq__iff__diff__eq__0,axiom, % 18.97/18.93 ! [V_b_2,V_a_2,T_b] : % 18.97/18.93 ( class_Groups_Oab__group__add(T_b) % 18.97/18.93 => ( V_a_2 = V_b_2 % 18.97/18.93 <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_diff__self,axiom, % 18.97/18.93 ! [V_a,T_a] : % 18.97/18.93 ( class_Groups_Ogroup__add(T_a) % 18.97/18.93 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_diff__0__right,axiom, % 18.97/18.93 ! [V_a,T_a] : % 18.97/18.93 ( class_Groups_Ogroup__add(T_a) % 18.97/18.93 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_diff__eq__diff__less,axiom, % 18.97/18.93 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] : % 18.97/18.93 ( class_Groups_Oordered__ab__group__add(T_b) % 18.97/18.93 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_c_2),V_d_2) % 18.97/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) % 18.97/18.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2)) ) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_add__diff__cancel,axiom, % 18.97/18.93 ! [V_b,V_a,T_a] : % 18.97/18.93 ( class_Groups_Ogroup__add(T_a) % 18.97/18.93 => 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 ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_diff__add__cancel,axiom, % 18.97/18.93 ! [V_b,V_a,T_a] : % 18.97/18.93 ( class_Groups_Ogroup__add(T_a) % 18.97/18.93 => 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 ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_minus__diff__eq,axiom, % 18.97/18.93 ! [V_b,V_a,T_a] : % 18.97/18.93 ( class_Groups_Oab__group__add(T_a) % 18.97/18.93 => 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) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_mod__diff__cong,axiom, % 18.97/18.93 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] : % 18.97/18.93 ( class_Divides_Oring__div(T_a) % 18.97/18.93 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) % 18.97/18.93 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) % 18.97/18.93 => 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) ) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_mod__diff__eq,axiom, % 18.97/18.93 ! [V_c,V_b,V_a,T_a] : % 18.97/18.93 ( class_Divides_Oring__div(T_a) % 18.97/18.93 => 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) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_mod__diff__left__eq,axiom, % 18.97/18.93 ! [V_c,V_b,V_a,T_a] : % 18.97/18.93 ( class_Divides_Oring__div(T_a) % 18.97/18.93 => 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) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_mod__diff__right__eq,axiom, % 18.97/18.93 ! [V_c,V_b,V_a,T_a] : % 18.97/18.93 ( class_Divides_Oring__div(T_a) % 18.97/18.93 => 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) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_diffs0__imp__equal,axiom, % 18.97/18.93 ! [V_n,V_m] : % 18.97/18.93 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 18.97/18.93 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 18.97/18.93 => V_m = V_n ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_diff__self__eq__0,axiom, % 18.97/18.93 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 18.97/18.93 % 18.97/18.93 fof(fact_minus__nat_Odiff__0,axiom, % 18.97/18.93 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ). % 18.97/18.93 % 18.97/18.93 fof(fact_diff__0__eq__0,axiom, % 18.97/18.93 ! [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) ). % 18.97/18.93 % 18.97/18.93 fof(fact_diff__Suc__Suc,axiom, % 18.97/18.93 ! [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) ). % 18.97/18.93 % 18.97/18.93 fof(fact_Suc__diff__diff,axiom, % 18.97/18.93 ! [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) ). % 18.97/18.93 % 18.97/18.93 fof(fact_diff__less__mono2,axiom, % 18.97/18.93 ! [V_l,V_n,V_m] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 18.97/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_l)) % 18.97/18.93 => 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))) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_less__imp__diff__less,axiom, % 18.97/18.93 ! [V_n,V_k,V_j] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k)) % 18.97/18.93 => 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)) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_mod__geq,axiom, % 18.97/18.93 ! [V_n,V_m] : % 18.97/18.93 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 18.97/18.93 => 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) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_mod__if,axiom, % 18.97/18.93 ! [V_n,V_m] : % 18.97/18.93 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 18.97/18.93 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) % 18.97/18.93 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 18.97/18.93 => 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) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_diff__add__inverse2,axiom, % 18.97/18.93 ! [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 ). % 18.97/18.93 % 18.97/18.93 fof(fact_diff__add__inverse,axiom, % 18.97/18.93 ! [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 ). % 18.97/18.93 % 18.97/18.93 fof(fact_diff__diff__left,axiom, % 18.97/18.93 ! [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)) ). % 18.97/18.93 % 18.97/18.93 fof(fact_diff__cancel,axiom, % 18.97/18.93 ! [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) ). % 18.97/18.93 % 18.97/18.93 fof(fact_diff__cancel2,axiom, % 18.97/18.93 ! [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) ). % 18.97/18.93 % 18.97/18.93 fof(fact_diff__le__self,axiom, % 18.97/18.93 ! [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)) ). % 18.97/18.93 % 18.97/18.93 fof(fact_diff__le__mono2,axiom, % 18.97/18.93 ! [V_l,V_n,V_m] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 18.97/18.93 => 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))) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_diff__le__mono,axiom, % 18.97/18.93 ! [V_l,V_n,V_m] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 18.97/18.93 => 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))) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_diff__diff__cancel,axiom, % 18.97/18.93 ! [V_n,V_i] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_n)) % 18.97/18.93 => 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 ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_eq__diff__iff,axiom, % 18.97/18.93 ! [V_n_2,V_m_2,V_k_2] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) % 18.97/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2)) % 18.97/18.93 => ( 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) % 18.97/18.93 <=> V_m_2 = V_n_2 ) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_Nat_Odiff__diff__eq,axiom, % 18.97/18.93 ! [V_n,V_m,V_k] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_m)) % 18.97/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) % 18.97/18.93 => 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) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_le__diff__iff,axiom, % 18.97/18.93 ! [V_n_2,V_m_2,V_k_2] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) % 18.97/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2)) % 18.97/18.93 => ( 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))) % 18.97/18.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_le__mod__geq,axiom, % 18.97/18.93 ! [V_m,V_n] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 18.97/18.93 => 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) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_zdiff__zmult__distrib,axiom, % 18.97/18.93 ! [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)) ). % 18.97/18.93 % 18.97/18.93 fof(fact_zdiff__zmult__distrib2,axiom, % 18.97/18.93 ! [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)) ). % 18.97/18.93 % 18.97/18.93 fof(fact_diff__mult__distrib2,axiom, % 18.97/18.93 ! [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)) ). % 18.97/18.93 % 18.97/18.93 fof(fact_diff__mult__distrib,axiom, % 18.97/18.93 ! [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)) ). % 18.97/18.93 % 18.97/18.93 fof(fact_zdiff__zmod__left,axiom, % 18.97/18.93 ! [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) ). % 18.97/18.93 % 18.97/18.93 fof(fact_zdiff__zmod__right,axiom, % 18.97/18.93 ! [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) ). % 18.97/18.93 % 18.97/18.93 fof(fact_nat__diff__distrib,axiom, % 18.97/18.93 ! [V_z,V_z_H] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H)) % 18.97/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z)) % 18.97/18.93 => 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)) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_zdiff__int__split,axiom, % 18.97/18.93 ! [V_y_2,V_x_2,V_Pa_2] : % 18.97/18.93 ( hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_y_2)))) % 18.97/18.93 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),V_x_2)) % 18.97/18.93 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2)))) ) % 18.97/18.93 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) % 18.97/18.93 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_le__iff__diff__le__0,axiom, % 18.97/18.93 ! [V_b_2,V_a_2,T_b] : % 18.97/18.93 ( class_Groups_Oordered__ab__group__add(T_b) % 18.97/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) % 18.97/18.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_less__iff__diff__less__0,axiom, % 18.97/18.93 ! [V_b_2,V_a_2,T_b] : % 18.97/18.93 ( class_Groups_Oordered__ab__group__add(T_b) % 18.97/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) % 18.97/18.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_eq__add__iff2,axiom, % 18.97/18.93 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] : % 18.97/18.93 ( class_Rings_Oring(T_b) % 18.97/18.93 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2) % 18.97/18.93 <=> V_c_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_eq__add__iff1,axiom, % 18.97/18.93 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] : % 18.97/18.93 ( class_Rings_Oring(T_b) % 18.97/18.93 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2) % 18.97/18.93 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_c_2) = V_d_2 ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_diff__0,axiom, % 18.97/18.93 ! [V_a,T_a] : % 18.97/18.93 ( class_Groups_Ogroup__add(T_a) % 18.97/18.93 => 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) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_diff__def,axiom, % 18.97/18.93 ! [V_b,V_a,T_a] : % 18.97/18.93 ( class_Groups_Ogroup__add(T_a) % 18.97/18.93 => 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)) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_ab__diff__minus,axiom, % 18.97/18.93 ! [V_b,V_a,T_a] : % 18.97/18.93 ( class_Groups_Oab__group__add(T_a) % 18.97/18.93 => 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)) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_diff__minus__eq__add,axiom, % 18.97/18.93 ! [V_b,V_a,T_a] : % 18.97/18.93 ( class_Groups_Ogroup__add(T_a) % 18.97/18.93 => 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) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom, % 18.97/18.93 ! [V_y,V_x,T_a] : % 18.97/18.93 ( class_Rings_Ocomm__ring__1(T_a) % 18.97/18.93 => 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)) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_less__bin__lemma,axiom, % 18.97/18.93 ! [V_l_2,V_k_2] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) % 18.97/18.93 <=> 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))) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_diff__less,axiom, % 18.97/18.93 ! [V_m,V_n] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 18.97/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 18.97/18.93 => 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)) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_zero__less__diff,axiom, % 18.97/18.93 ! [V_m_2,V_n_2] : % 18.97/18.93 ( 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))) % 18.97/18.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_diff__less__Suc,axiom, % 18.97/18.93 ! [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))) ). % 18.97/18.93 % 18.97/18.93 fof(fact_diff__add__0,axiom, % 18.97/18.93 ! [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) ). % 18.97/18.93 % 18.97/18.93 fof(fact_diff__is__0__eq_H,axiom, % 18.97/18.93 ! [V_n,V_m] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 18.97/18.93 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_diff__is__0__eq,axiom, % 18.97/18.93 ! [V_n_2,V_m_2] : % 18.97/18.93 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 18.97/18.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_less__diff__conv,axiom, % 18.97/18.93 ! [V_k_2,V_j_2,V_i_2] : % 18.97/18.93 ( 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))) % 18.97/18.93 <=> 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)) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_add__diff__inverse,axiom, % 18.97/18.93 ! [V_n,V_m] : % 18.97/18.93 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 18.97/18.93 => 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 ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_Suc__diff__le,axiom, % 18.97/18.93 ! [V_m,V_n] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 18.97/18.93 => 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)) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_less__diff__iff,axiom, % 18.97/18.93 ! [V_n_2,V_m_2,V_k_2] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) % 18.97/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2)) % 18.97/18.93 => ( 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))) % 18.97/18.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_diff__less__mono,axiom, % 18.97/18.93 ! [V_c,V_b,V_a] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a),V_b)) % 18.97/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_c),V_a)) % 18.97/18.93 => 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))) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_diff__add__assoc2,axiom, % 18.97/18.93 ! [V_i,V_j,V_k] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 18.97/18.93 => 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) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_add__diff__assoc2,axiom, % 18.97/18.93 ! [V_i,V_j,V_k] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 18.97/18.93 => 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) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_diff__add__assoc,axiom, % 18.97/18.93 ! [V_i,V_j,V_k] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 18.97/18.93 => 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)) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_le__imp__diff__is__add,axiom, % 18.97/18.93 ! [V_k_2,V_j_2,V_i_2] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 18.97/18.93 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2) = V_k_2 % 18.97/18.93 <=> V_j_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_le__add__diff__inverse2,axiom, % 18.97/18.93 ! [V_m,V_n] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 18.97/18.93 => 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 ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_le__diff__conv2,axiom, % 18.97/18.93 ! [V_i_2,V_j_2,V_k_2] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_j_2)) % 18.97/18.93 => ( 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))) % 18.97/18.93 <=> 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)) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_add__diff__assoc,axiom, % 18.97/18.93 ! [V_i,V_j,V_k] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 18.97/18.93 => 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) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_le__add__diff__inverse,axiom, % 18.97/18.93 ! [V_m,V_n] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 18.97/18.93 => 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 ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_le__add__diff,axiom, % 18.97/18.93 ! [V_m,V_n,V_k] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) % 18.97/18.93 => 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))) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_le__diff__conv,axiom, % 18.97/18.93 ! [V_i_2,V_k_2,V_j_2] : % 18.97/18.93 ( 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)) % 18.97/18.93 <=> 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))) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_diff__diff__right,axiom, % 18.97/18.93 ! [V_i,V_j,V_k] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 18.97/18.93 => 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) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_diff__int__def__symmetric,axiom, % 18.97/18.93 ! [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) ). % 18.97/18.93 % 18.97/18.93 fof(fact_diff__int__def,axiom, % 18.97/18.93 ! [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)) ). % 18.97/18.93 % 18.97/18.93 fof(fact_diff__Suc__eq__diff__pred,axiom, % 18.97/18.93 ! [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) ). % 18.97/18.93 % 18.97/18.93 fof(fact_diff__Suc__1,axiom, % 18.97/18.93 ! [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 ). % 18.97/18.93 % 18.97/18.93 fof(fact_Divides_Omod__div__equality_H,axiom, % 18.97/18.93 ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_n)) ). % 18.97/18.93 % 18.97/18.93 fof(fact_mult__div__cancel,axiom, % 18.97/18.93 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) ). % 18.97/18.93 % 18.97/18.93 fof(fact_div__mod__equality_H,axiom, % 18.97/18.93 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) ). % 18.97/18.93 % 18.97/18.93 fof(fact_tsub__eq,axiom, % 18.97/18.93 ! [V_x,V_y] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) % 18.97/18.93 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom, % 18.97/18.93 ! [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)) ). % 18.97/18.93 % 18.97/18.93 fof(fact_le__add__iff2,axiom, % 18.97/18.93 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] : % 18.97/18.93 ( class_Rings_Oordered__ring(T_b) % 18.97/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2))) % 18.97/18.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2))) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_le__add__iff1,axiom, % 18.97/18.93 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] : % 18.97/18.93 ( class_Rings_Oordered__ring(T_b) % 18.97/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2))) % 18.97/18.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_c_2)),V_d_2)) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_less__add__iff2,axiom, % 18.97/18.93 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] : % 18.97/18.93 ( class_Rings_Oordered__ring(T_b) % 18.97/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2))) % 18.97/18.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2))) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_less__add__iff1,axiom, % 18.97/18.93 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] : % 18.97/18.93 ( class_Rings_Oordered__ring(T_b) % 18.97/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2))) % 18.97/18.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_c_2)),V_d_2)) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_diff__Suc__less,axiom, % 18.97/18.93 ! [V_i,V_n] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 18.97/18.93 => 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)) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_Suc__pred,axiom, % 18.97/18.93 ! [V_n] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 18.97/18.93 => 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 ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_nat__diff__split,axiom, % 18.97/18.93 ! [V_b_2,V_a_2,V_Pa_2] : % 18.97/18.93 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2))) % 18.97/18.93 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) % 18.97/18.93 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 18.97/18.93 & ! [B_d] : % 18.97/18.93 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) % 18.97/18.93 => hBOOL(hAPP(V_Pa_2,B_d)) ) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_nat__diff__split__asm,axiom, % 18.97/18.93 ! [V_b_2,V_a_2,V_Pa_2] : % 18.97/18.93 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2))) % 18.97/18.93 <=> ~ ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) % 18.97/18.93 & ~ hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 18.97/18.93 | ? [B_d] : % 18.97/18.93 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) % 18.97/18.93 & ~ hBOOL(hAPP(V_Pa_2,B_d)) ) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_zle__diff1__eq,axiom, % 18.97/18.93 ! [V_z_2,V_w_2] : % 18.97/18.93 ( 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)))) % 18.97/18.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_diff__Suc__diff__eq2,axiom, % 18.97/18.93 ! [V_m,V_j,V_k] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 18.97/18.93 => 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)) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_diff__Suc__diff__eq1,axiom, % 18.97/18.93 ! [V_m,V_j,V_k] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 18.97/18.93 => 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)) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_nat__eq__add__iff2,axiom, % 18.97/18.93 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 18.97/18.93 => ( 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) % 18.97/18.93 <=> 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) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_nat__diff__add__eq2,axiom, % 18.97/18.93 ! [V_n,V_m,V_u,V_j,V_i] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 18.97/18.93 => 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)) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_nat__le__add__iff2,axiom, % 18.97/18.93 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 18.97/18.93 => ( 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))) % 18.97/18.93 <=> 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))) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_nat__eq__add__iff1,axiom, % 18.97/18.93 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) % 18.97/18.93 => ( 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) % 18.97/18.93 <=> 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 ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_nat__diff__add__eq1,axiom, % 18.97/18.93 ! [V_n,V_m,V_u,V_i,V_j] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i)) % 18.97/18.93 => 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) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_nat__le__add__iff1,axiom, % 18.97/18.93 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) % 18.97/18.93 => ( 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))) % 18.97/18.93 <=> 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)) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_zmod__zminus2__eq__if,axiom, % 18.97/18.93 ! [V_b,V_a] : % 18.97/18.93 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 18.97/18.93 => 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) ) % 18.97/18.93 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 18.97/18.93 => 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) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_zmod__zminus1__eq__if,axiom, % 18.97/18.93 ! [V_b,V_a] : % 18.97/18.93 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 18.97/18.93 => 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) ) % 18.97/18.93 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 18.97/18.93 => 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)) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_zmult__div__cancel,axiom, % 18.97/18.93 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_n),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_m),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_m),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n)) ). % 18.97/18.93 % 18.97/18.93 fof(fact_zmod__zdiv__equality_H,axiom, % 18.97/18.93 ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_m),V_n)),V_n)) ). % 18.97/18.93 % 18.97/18.93 fof(fact_tsub__def,axiom, % 18.97/18.93 ! [V_x,V_y] : % 18.97/18.93 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) % 18.97/18.93 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) % 18.97/18.93 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) % 18.97/18.93 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_Suc__pred_H,axiom, % 18.97/18.93 ! [V_n] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 18.97/18.93 => 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))) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_Suc__diff__1,axiom, % 18.97/18.93 ! [V_n] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 18.97/18.93 => 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 ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_nat__less__add__iff2,axiom, % 18.97/18.93 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 18.97/18.93 => ( 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))) % 18.97/18.93 <=> 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))) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_nat__less__add__iff1,axiom, % 18.97/18.93 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) % 18.97/18.93 => ( 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))) % 18.97/18.93 <=> 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)) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_add__eq__if,axiom, % 18.97/18.93 ! [V_n,V_m] : % 18.97/18.93 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 18.97/18.93 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_n ) % 18.97/18.93 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 18.97/18.93 => 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)) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_div__if,axiom, % 18.97/18.93 ! [V_m,V_n] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 18.97/18.93 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 18.97/18.93 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 18.97/18.93 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 18.97/18.93 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n)) ) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_div__geq,axiom, % 18.97/18.93 ! [V_m,V_n] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 18.97/18.93 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 18.97/18.93 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n)) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_mult__eq__if,axiom, % 18.97/18.93 ! [V_n,V_m] : % 18.97/18.93 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 18.97/18.93 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 18.97/18.93 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 18.97/18.93 => 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)) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_int__power__div__base,axiom, % 18.97/18.93 ! [V_k,V_m] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 18.97/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 18.97/18.93 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),V_m)),V_k) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_decr__mult__lemma,axiom, % 18.97/18.93 ! [V_k_2,V_Pa_2,V_d_2] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) % 18.97/18.93 => ( ! [B_x] : % 18.97/18.93 ( hBOOL(hAPP(V_Pa_2,B_x)) % 18.97/18.93 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_d_2))) ) % 18.97/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 18.97/18.93 => ! [B_x] : % 18.97/18.93 ( hBOOL(hAPP(V_Pa_2,B_x)) % 18.97/18.93 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2)))) ) ) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_decr__lemma,axiom, % 18.97/18.93 ! [V_z,V_x,V_d] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d)) % 18.97/18.93 => 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)) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_incr__lemma,axiom, % 18.97/18.93 ! [V_x,V_z,V_d] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d)) % 18.97/18.93 => 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)))) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_nat__mod__eq__lemma,axiom, % 18.97/18.93 ! [V_y,V_n,V_x] : % 18.97/18.93 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_y,V_n) % 18.97/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y),V_x)) % 18.97/18.93 => ? [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)) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_mod__induct__0,axiom, % 18.97/18.93 ! [V_i_2,V_Pa_2,V_p_2] : % 18.97/18.93 ( ! [B_i] : % 18.97/18.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_p_2)) % 18.97/18.93 => ( hBOOL(hAPP(V_Pa_2,B_i)) % 18.97/18.93 => hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_i),V_p_2))) ) ) % 18.97/18.93 => ( hBOOL(hAPP(V_Pa_2,V_i_2)) % 18.97/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_p_2)) % 18.97/18.93 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_expand__Suc,axiom, % 18.97/18.93 ! [V_v] : % 18.97/18.93 ( 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))) % 18.97/18.93 => 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))) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_nat__gcd_Osimps,axiom, % 18.97/18.93 ! [V_x,V_y] : % 18.97/18.93 ( ( V_y = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 18.97/18.93 => c_Nitpick_Onat__gcd(V_x,V_y) = V_x ) % 18.97/18.93 & ( V_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 18.97/18.93 => 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)) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_of__int__power,axiom, % 18.97/18.93 ! [V_n,V_z,T_a] : % 18.97/18.93 ( class_Rings_Oring__1(T_a) % 18.97/18.93 => 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) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_of__int__number__of__eq,axiom, % 18.97/18.93 ! [V_v,T_a] : % 18.97/18.93 ( class_Int_Onumber__ring(T_a) % 18.97/18.93 => 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) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_number__of__reorient,axiom, % 18.97/18.93 ! [V_x_2,V_w_2,T_b] : % 18.97/18.93 ( class_Int_Onumber(T_b) % 18.97/18.93 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = V_x_2 % 18.97/18.93 <=> V_x_2 = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_eq__number__of,axiom, % 18.97/18.93 ! [V_y_2,V_x_2,T_b] : % 18.97/18.93 ( ( class_Int_Onumber__ring(T_b) % 18.97/18.93 & class_Int_Oring__char__0(T_b) ) % 18.97/18.93 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2) % 18.97/18.93 <=> V_x_2 = V_y_2 ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_abs__idempotent,axiom, % 18.97/18.93 ! [V_a,T_a] : % 18.97/18.93 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 18.97/18.93 => 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) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_zero__le__zpower__abs,axiom, % 18.97/18.93 ! [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))) ). % 18.97/18.93 % 18.97/18.93 fof(fact_abs__ge__self,axiom, % 18.97/18.93 ! [V_a,T_a] : % 18.97/18.93 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 18.97/18.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_abs__le__D1,axiom, % 18.97/18.93 ! [V_b,V_a,T_a] : % 18.97/18.93 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 18.97/18.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) % 18.97/18.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_abs__zero,axiom, % 18.97/18.93 ! [T_a] : % 18.97/18.93 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 18.97/18.93 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_abs__eq__0,axiom, % 18.97/18.93 ! [V_a_2,T_b] : % 18.97/18.93 ( class_Groups_Oordered__ab__group__add__abs(T_b) % 18.97/18.93 => ( hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b) % 18.97/18.93 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_abs__add__abs,axiom, % 18.97/18.93 ! [V_b,V_a,T_a] : % 18.97/18.93 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 18.97/18.93 => 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)) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_abs__mult,axiom, % 18.97/18.93 ! [V_b,V_a,T_a] : % 18.97/18.93 ( class_Rings_Olinordered__idom(T_a) % 18.97/18.93 => 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)) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_abs__mult__self,axiom, % 18.97/18.93 ! [V_a,T_a] : % 18.97/18.93 ( class_Rings_Olinordered__idom(T_a) % 18.97/18.93 => 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) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_abs__minus__commute,axiom, % 18.97/18.93 ! [V_b,V_a,T_a] : % 18.97/18.93 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 18.97/18.93 => 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)) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_abs__one,axiom, % 18.97/18.93 ! [T_a] : % 18.97/18.93 ( class_Rings_Olinordered__idom(T_a) % 18.97/18.93 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_abs__minus__cancel,axiom, % 18.97/18.93 ! [V_a,T_a] : % 18.97/18.93 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 18.97/18.93 => 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) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom, % 18.97/18.93 ! [V_q,V_y,V_x,T_a] : % 18.97/18.93 ( class_Rings_Ocomm__semiring__1(T_a) % 18.97/18.93 => 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)) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_abs__of__nat,axiom, % 18.97/18.93 ! [V_n,T_a] : % 18.97/18.93 ( class_Rings_Olinordered__idom(T_a) % 18.97/18.93 => 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) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_abs__int__eq,axiom, % 18.97/18.93 ! [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) ). % 18.97/18.93 % 18.97/18.93 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom, % 18.97/18.93 ! [V_q,V_p,V_x,T_a] : % 18.97/18.93 ( class_Rings_Ocomm__semiring__1(T_a) % 18.97/18.93 => 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)) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_zpower__zpower,axiom, % 18.97/18.93 ! [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)) ). % 18.97/18.93 % 18.97/18.93 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom, % 18.97/18.93 ! [V_x,T_a] : % 18.97/18.93 ( class_Rings_Ocomm__semiring__1(T_a) % 18.97/18.93 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_zpower__zmod,axiom, % 18.97/18.93 ! [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) ). % 18.97/18.93 % 18.97/18.93 fof(fact_of__nat__number__of__lemma,axiom, % 18.97/18.93 ! [V_v,T_a] : % 18.97/18.93 ( class_Int_Onumber__ring(T_a) % 18.97/18.93 => ( ( 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))) % 18.97/18.93 => 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) ) % 18.97/18.93 & ( ~ 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))) % 18.97/18.93 => 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) ) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_number__of__eq,axiom, % 18.97/18.93 ! [V_k,T_a] : % 18.97/18.93 ( class_Int_Onumber__ring(T_a) % 18.97/18.93 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_abs__number__of,axiom, % 18.97/18.93 ! [V_x,T_a] : % 18.97/18.93 ( ( class_Int_Onumber__ring(T_a) % 18.97/18.93 & class_Rings_Olinordered__idom(T_a) ) % 18.97/18.93 => ( ( 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))) % 18.97/18.93 => 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)) ) % 18.97/18.93 & ( ~ 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))) % 18.97/18.93 => 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) ) ) ) ). % 18.97/18.93 % 18.97/18.93 fof(fact_zero__less__zpower__abs__iff,axiom, % 18.97/18.93 ! [V_n_2,V_x_2] : % 18.97/18.93 ( 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))) % 18.97/18.93 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 18.97/18.93 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_abs__of__nonneg,axiom, % 18.97/18.94 ! [V_a,T_a] : % 18.97/18.94 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 18.97/18.94 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_abs__le__zero__iff,axiom, % 18.97/18.94 ! [V_a_2,T_b] : % 18.97/18.94 ( class_Groups_Oordered__ab__group__add__abs(T_b) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),c_Groups_Ozero__class_Ozero(T_b))) % 18.97/18.94 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_abs__ge__zero,axiom, % 18.97/18.94 ! [V_a,T_a] : % 18.97/18.94 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 18.97/18.94 => 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))) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_abs__not__less__zero,axiom, % 18.97/18.94 ! [V_a,T_a] : % 18.97/18.94 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 18.97/18.94 => ~ 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))) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_zero__less__abs__iff,axiom, % 18.97/18.94 ! [V_a_2,T_b] : % 18.97/18.94 ( class_Groups_Oordered__ab__group__add__abs(T_b) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2))) % 18.97/18.94 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_abs__of__pos,axiom, % 18.97/18.94 ! [V_a,T_a] : % 18.97/18.94 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 18.97/18.94 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_abs__triangle__ineq,axiom, % 18.97/18.94 ! [V_b,V_a,T_a] : % 18.97/18.94 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 18.97/18.94 => 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)))) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_abs__mult__less,axiom, % 18.97/18.94 ! [V_d,V_b,V_c,V_a,T_a] : % 18.97/18.94 ( class_Rings_Olinordered__idom(T_a) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_c)) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)),V_d)) % 18.97/18.94 => 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))) ) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_abs__triangle__ineq3,axiom, % 18.97/18.94 ! [V_b,V_a,T_a] : % 18.97/18.94 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 18.97/18.94 => 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)))) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_abs__triangle__ineq2,axiom, % 18.97/18.94 ! [V_b,V_a,T_a] : % 18.97/18.94 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 18.97/18.94 => 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)))) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_abs__triangle__ineq2__sym,axiom, % 18.97/18.94 ! [V_b,V_a,T_a] : % 18.97/18.94 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 18.97/18.94 => 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)))) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_abs__le__D2,axiom, % 18.97/18.94 ! [V_b,V_a,T_a] : % 18.97/18.94 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) % 18.97/18.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_abs__leI,axiom, % 18.97/18.94 ! [V_b,V_a,T_a] : % 18.97/18.94 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) % 18.97/18.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) ) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_abs__le__iff,axiom, % 18.97/18.94 ! [V_b_2,V_a_2,T_b] : % 18.97/18.94 ( class_Groups_Oordered__ab__group__add__abs(T_b) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),V_b_2)) % 18.97/18.94 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) % 18.97/18.94 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2)) ) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_abs__ge__minus__self,axiom, % 18.97/18.94 ! [V_a,T_a] : % 18.97/18.94 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 18.97/18.94 => 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))) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_abs__less__iff,axiom, % 18.97/18.94 ! [V_b_2,V_a_2,T_b] : % 18.97/18.94 ( class_Rings_Olinordered__idom(T_b) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),V_b_2)) % 18.97/18.94 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) % 18.97/18.94 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2)) ) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_le__number__of__eq__not__less,axiom, % 18.97/18.94 ! [V_w_2,V_v_2,T_b] : % 18.97/18.94 ( ( class_Int_Onumber(T_b) % 18.97/18.94 & class_Orderings_Olinorder(T_b) ) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) % 18.97/18.94 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2))) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_right__distrib__number__of,axiom, % 18.97/18.94 ! [V_c,V_b,V_v,T_b] : % 18.97/18.94 ( ( class_Int_Onumber(T_b) % 18.97/18.94 & class_Rings_Osemiring(T_b) ) % 18.97/18.94 => 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)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_left__distrib__number__of,axiom, % 18.97/18.94 ! [V_v,V_b,V_a,T_b] : % 18.97/18.94 ( ( class_Int_Onumber(T_b) % 18.97/18.94 & class_Rings_Osemiring(T_b) ) % 18.97/18.94 => 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))) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom, % 18.97/18.94 ! [V_q,V_x,T_a] : % 18.97/18.94 ( class_Rings_Ocomm__semiring__1(T_a) % 18.97/18.94 => 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)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom, % 18.97/18.94 ! [V_q,V_x,T_a] : % 18.97/18.94 ( class_Rings_Ocomm__semiring__1(T_a) % 18.97/18.94 => 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)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom, % 18.97/18.94 ! [V_q,V_x,T_a] : % 18.97/18.94 ( class_Rings_Ocomm__semiring__1(T_a) % 18.97/18.94 => 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)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_right__diff__distrib__number__of,axiom, % 18.97/18.94 ! [V_c,V_b,V_v,T_b] : % 18.97/18.94 ( ( class_Int_Onumber(T_b) % 18.97/18.94 & class_Rings_Oring(T_b) ) % 18.97/18.94 => 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)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_left__diff__distrib__number__of,axiom, % 18.97/18.94 ! [V_v,V_b,V_a,T_b] : % 18.97/18.94 ( ( class_Int_Onumber(T_b) % 18.97/18.94 & class_Rings_Oring(T_b) ) % 18.97/18.94 => 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))) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_le__number__of,axiom, % 18.97/18.94 ! [V_y_2,V_x_2,T_b] : % 18.97/18.94 ( ( class_Int_Onumber__ring(T_b) % 18.97/18.94 & class_Rings_Olinordered__idom(T_b) ) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2))) % 18.97/18.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom, % 18.97/18.94 ! [V_x,T_a] : % 18.97/18.94 ( class_Rings_Ocomm__semiring__1(T_a) % 18.97/18.94 => 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) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom, % 18.97/18.94 ! [V_q,V_p,V_x,T_a] : % 18.97/18.94 ( class_Rings_Ocomm__semiring__1(T_a) % 18.97/18.94 => 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)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_less__number__of,axiom, % 18.97/18.94 ! [V_y_2,V_x_2,T_b] : % 18.97/18.94 ( ( class_Int_Onumber__ring(T_b) % 18.97/18.94 & class_Rings_Olinordered__idom(T_b) ) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2))) % 18.97/18.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_add__number__of__left,axiom, % 18.97/18.94 ! [V_z,V_w,V_v,T_a] : % 18.97/18.94 ( class_Int_Onumber__ring(T_a) % 18.97/18.94 => 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) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_add__number__of__eq,axiom, % 18.97/18.94 ! [V_w,V_v,T_a] : % 18.97/18.94 ( class_Int_Onumber__ring(T_a) % 18.97/18.94 => 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)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_number__of__add,axiom, % 18.97/18.94 ! [V_w,V_v,T_a] : % 18.97/18.94 ( class_Int_Onumber__ring(T_a) % 18.97/18.94 => 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)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom, % 18.97/18.94 ! [V_n,V_x] : % 18.97/18.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 18.97/18.94 => 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))) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_number__of__mult,axiom, % 18.97/18.94 ! [V_w,V_v,T_a] : % 18.97/18.94 ( class_Int_Onumber__ring(T_a) % 18.97/18.94 => 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)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_arith__simps_I32_J,axiom, % 18.97/18.94 ! [V_w,V_v,T_a] : % 18.97/18.94 ( class_Int_Onumber__ring(T_a) % 18.97/18.94 => 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)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_mult__number__of__left,axiom, % 18.97/18.94 ! [V_z,V_w,V_v,T_a] : % 18.97/18.94 ( class_Int_Onumber__ring(T_a) % 18.97/18.94 => 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) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_abs__zmult__eq__1,axiom, % 18.97/18.94 ! [V_n,V_m] : % 18.97/18.94 ( 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) % 18.97/18.94 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_number__of__diff,axiom, % 18.97/18.94 ! [V_w,V_v,T_a] : % 18.97/18.94 ( class_Int_Onumber__ring(T_a) % 18.97/18.94 => 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)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_zpower__zadd__distrib,axiom, % 18.97/18.94 ! [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)) ). % 18.97/18.94 % 18.97/18.94 fof(fact_arith__simps_I30_J,axiom, % 18.97/18.94 ! [V_w,T_a] : % 18.97/18.94 ( class_Int_Onumber__ring(T_a) % 18.97/18.94 => 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)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_number__of__minus,axiom, % 18.97/18.94 ! [V_w,T_a] : % 18.97/18.94 ( class_Int_Onumber__ring(T_a) % 18.97/18.94 => 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)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_abs__sgn,axiom, % 18.97/18.94 ! [V_k,T_a] : % 18.97/18.94 ( class_Rings_Olinordered__idom(T_a) % 18.97/18.94 => 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)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_mult__sgn__abs,axiom, % 18.97/18.94 ! [V_x,T_a] : % 18.97/18.94 ( class_Rings_Olinordered__idom(T_a) % 18.97/18.94 => 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 ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_abs__mult__pos,axiom, % 18.97/18.94 ! [V_y,V_x,T_a] : % 18.97/18.94 ( class_Rings_Olinordered__idom(T_a) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 18.97/18.94 => 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)) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_abs__eq__mult,axiom, % 18.97/18.94 ! [V_b,V_a,T_a] : % 18.97/18.94 ( class_Rings_Oordered__ring__abs(T_a) % 18.97/18.94 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 18.97/18.94 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) ) % 18.97/18.94 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 18.97/18.94 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) ) % 18.97/18.94 => 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)) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_abs__diff__triangle__ineq,axiom, % 18.97/18.94 ! [V_d,V_c,V_b,V_a,T_a] : % 18.97/18.94 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 18.97/18.94 => 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))))) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_abs__triangle__ineq4,axiom, % 18.97/18.94 ! [V_b,V_a,T_a] : % 18.97/18.94 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 18.97/18.94 => 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)))) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_abs__of__nonpos,axiom, % 18.97/18.94 ! [V_a,T_a] : % 18.97/18.94 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 18.97/18.94 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_abs__minus__le__zero,axiom, % 18.97/18.94 ! [V_a,T_a] : % 18.97/18.94 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 18.97/18.94 => 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))) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_abs__if,axiom, % 18.97/18.94 ! [V_a,T_a] : % 18.97/18.94 ( class_Groups_Oabs__if(T_a) % 18.97/18.94 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 18.97/18.94 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) % 18.97/18.94 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 18.97/18.94 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_abs__of__neg,axiom, % 18.97/18.94 ! [V_a,T_a] : % 18.97/18.94 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 18.97/18.94 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_zabs__less__one__iff,axiom, % 18.97/18.94 ! [V_z_2] : % 18.97/18.94 ( 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))) % 18.97/18.94 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_add__number__of__diff1,axiom, % 18.97/18.94 ! [V_c,V_w,V_v,T_a] : % 18.97/18.94 ( class_Int_Onumber__ring(T_a) % 18.97/18.94 => 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) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_zabs__def,axiom, % 18.97/18.94 ! [V_i] : % 18.97/18.94 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 18.97/18.94 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_i) ) % 18.97/18.94 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 18.97/18.94 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = V_i ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_minus__number__of__mult,axiom, % 18.97/18.94 ! [V_z,V_w,T_a] : % 18.97/18.94 ( class_Int_Onumber__ring(T_a) % 18.97/18.94 => 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) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_nat__abs__mult__distrib,axiom, % 18.97/18.94 ! [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))) ). % 18.97/18.94 % 18.97/18.94 fof(fact_diff__number__of__eq,axiom, % 18.97/18.94 ! [V_w,V_v,T_a] : % 18.97/18.94 ( class_Int_Onumber__ring(T_a) % 18.97/18.94 => 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))) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_add__number__of__diff2,axiom, % 18.97/18.94 ! [V_w,V_c,V_v,T_a] : % 18.97/18.94 ( class_Int_Onumber__ring(T_a) % 18.97/18.94 => 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) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_power__strict__mono,axiom, % 18.97/18.94 ! [V_n,V_b,V_a,T_a] : % 18.97/18.94 ( class_Rings_Olinordered__semidom(T_a) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 18.97/18.94 => 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))) ) ) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_one__less__power,axiom, % 18.97/18.94 ! [V_n,V_a,T_a] : % 18.97/18.94 ( class_Rings_Olinordered__semidom(T_a) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 18.97/18.94 => 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))) ) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_power__le__imp__le__exp,axiom, % 18.97/18.94 ! [V_n,V_m,V_a,T_a] : % 18.97/18.94 ( class_Rings_Olinordered__semidom(T_a) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 18.97/18.94 => ( 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))) % 18.97/18.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_power__increasing__iff,axiom, % 18.97/18.94 ! [V_y_2,V_x_2,V_b_2,T_b] : % 18.97/18.94 ( class_Rings_Olinordered__semidom(T_b) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_b_2)) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_y_2))) % 18.97/18.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_power__decreasing,axiom, % 18.97/18.94 ! [V_a,V_N,V_n,T_a] : % 18.97/18.94 ( class_Rings_Olinordered__semidom(T_a) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N)) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 18.97/18.94 => 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))) ) ) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_power__strict__decreasing,axiom, % 18.97/18.94 ! [V_a,V_N,V_n,T_a] : % 18.97/18.94 ( class_Rings_Olinordered__semidom(T_a) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N)) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 18.97/18.94 => 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))) ) ) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_power__Suc__less__one,axiom, % 18.97/18.94 ! [V_n,V_a,T_a] : % 18.97/18.94 ( class_Rings_Olinordered__semidom(T_a) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 18.97/18.94 => 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))) ) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_number__of__is__id,axiom, % 18.97/18.94 ! [V_k] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k) = V_k ). % 18.97/18.94 % 18.97/18.94 fof(fact_less__eq__number__of__int__code,axiom, % 18.97/18.94 ! [V_l_2,V_k_2] : % 18.97/18.94 ( 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))) % 18.97/18.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_less__number__of__int__code,axiom, % 18.97/18.94 ! [V_l_2,V_k_2] : % 18.97/18.94 ( 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))) % 18.97/18.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_plus__numeral__code_I9_J,axiom, % 18.97/18.94 ! [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)) ). % 18.97/18.94 % 18.97/18.94 fof(fact_times__numeral__code_I5_J,axiom, % 18.97/18.94 ! [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)) ). % 18.97/18.94 % 18.97/18.94 fof(fact_minus__numeral__code_I5_J,axiom, % 18.97/18.94 ! [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)) ). % 18.97/18.94 % 18.97/18.94 fof(fact_nat__power__eq__Suc__0__iff,axiom, % 18.97/18.94 ! [V_m_2,V_x_2] : % 18.97/18.94 ( 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)) % 18.97/18.94 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 18.97/18.94 | V_x_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_power__Suc__0,axiom, % 18.97/18.94 ! [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)) ). % 18.97/18.94 % 18.97/18.94 fof(fact_nat__power__less__imp__less,axiom, % 18.97/18.94 ! [V_n,V_m,V_i] : % 18.97/18.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i)) % 18.97/18.94 => ( 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))) % 18.97/18.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_nat__zero__less__power__iff,axiom, % 18.97/18.94 ! [V_n_2,V_x_2] : % 18.97/18.94 ( 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))) % 18.97/18.94 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2)) % 18.97/18.94 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_int__number__of__def,axiom, % 18.97/18.94 ! [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) ). % 18.97/18.94 % 18.97/18.94 fof(fact_nat__one__le__power,axiom, % 18.97/18.94 ! [V_n,V_i] : % 18.97/18.94 ( 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)) % 18.97/18.94 => 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))) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_nat__number__of__def,axiom, % 18.97/18.94 ! [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)) ). % 18.97/18.94 % 18.97/18.94 fof(fact_nat__number__of,axiom, % 18.97/18.94 ! [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) ). % 18.97/18.94 % 18.97/18.94 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J,axiom, % 18.97/18.94 ! [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)) ). % 18.97/18.94 % 18.97/18.94 fof(fact_zpower__int,axiom, % 18.97/18.94 ! [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)) ). % 18.97/18.94 % 18.97/18.94 fof(fact_int__power,axiom, % 18.97/18.94 ! [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) ). % 18.97/18.94 % 18.97/18.94 fof(fact_minus__numeral__code_I6_J,axiom, % 18.97/18.94 ! [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))) ). % 18.97/18.94 % 18.97/18.94 fof(fact_power__eq__if,axiom, % 18.97/18.94 ! [V_p,V_m] : % 18.97/18.94 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 18.97/18.94 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) % 18.97/18.94 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 18.97/18.94 => 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)))) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_int__eq__iff__number__of,axiom, % 18.97/18.94 ! [V_v_2,V_m_2] : % 18.97/18.94 ( 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) % 18.97/18.94 <=> ( V_m_2 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)) % 18.97/18.94 & 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))) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_nat__power__eq,axiom, % 18.97/18.94 ! [V_n,V_z] : % 18.97/18.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 18.97/18.94 => 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) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J,axiom, % 18.97/18.94 ! [V_n,V_x] : % 18.97/18.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 18.97/18.94 => 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)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_field__power__not__zero,axiom, % 18.97/18.94 ! [V_n,V_a,T_a] : % 18.97/18.94 ( class_Rings_Oring__1__no__zero__divisors(T_a) % 18.97/18.94 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 18.97/18.94 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_power__mult__distrib,axiom, % 18.97/18.94 ! [V_n,V_b,V_a,T_a] : % 18.97/18.94 ( class_Groups_Ocomm__monoid__mult(T_a) % 18.97/18.94 => 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)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_power__commutes,axiom, % 18.97/18.94 ! [V_n,V_a,T_a] : % 18.97/18.94 ( class_Groups_Omonoid__mult(T_a) % 18.97/18.94 => 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)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_power__one,axiom, % 18.97/18.94 ! [V_n,T_a] : % 18.97/18.94 ( class_Groups_Omonoid__mult(T_a) % 18.97/18.94 => 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) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_of__nat__power,axiom, % 18.97/18.94 ! [V_n,V_m,T_a] : % 18.97/18.94 ( class_Rings_Osemiring__1(T_a) % 18.97/18.94 => 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) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_power__mult,axiom, % 18.97/18.94 ! [V_n,V_m,V_a,T_a] : % 18.97/18.94 ( class_Groups_Omonoid__mult(T_a) % 18.97/18.94 => 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) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_one__div__nat__number__of,axiom, % 18.97/18.94 ! [V_v_H] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) ). % 18.97/18.94 % 18.97/18.94 fof(fact_power__abs,axiom, % 18.97/18.94 ! [V_n,V_a,T_a] : % 18.97/18.94 ( class_Rings_Olinordered__idom(T_a) % 18.97/18.94 => 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) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_power__one__right,axiom, % 18.97/18.94 ! [V_a,T_a] : % 18.97/18.94 ( class_Groups_Omonoid__mult(T_a) % 18.97/18.94 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_zero__le__power,axiom, % 18.97/18.94 ! [V_n,V_a,T_a] : % 18.97/18.94 ( class_Rings_Olinordered__semidom(T_a) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 18.97/18.94 => 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))) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_power__mono,axiom, % 18.97/18.94 ! [V_n,V_b,V_a,T_a] : % 18.97/18.94 ( class_Rings_Olinordered__semidom(T_a) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 18.97/18.94 => 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))) ) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_zero__less__power,axiom, % 18.97/18.94 ! [V_n,V_a,T_a] : % 18.97/18.94 ( class_Rings_Olinordered__semidom(T_a) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 18.97/18.94 => 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))) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_power__eq__0__iff,axiom, % 18.97/18.94 ! [V_n_2,V_a_2,T_b] : % 18.97/18.94 ( ( class_Power_Opower(T_b) % 18.97/18.94 & class_Rings_Omult__zero(T_b) % 18.97/18.94 & class_Rings_Ono__zero__divisors(T_b) % 18.97/18.94 & class_Rings_Ozero__neq__one(T_b) ) % 18.97/18.94 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_b) % 18.97/18.94 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b) % 18.97/18.94 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_one__le__power,axiom, % 18.97/18.94 ! [V_n,V_a,T_a] : % 18.97/18.94 ( class_Rings_Olinordered__semidom(T_a) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 18.97/18.94 => 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))) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_power__0__Suc,axiom, % 18.97/18.94 ! [V_n,T_a] : % 18.97/18.94 ( ( class_Power_Opower(T_a) % 18.97/18.94 & class_Rings_Osemiring__0(T_a) ) % 18.97/18.94 => 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) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_power__inject__exp,axiom, % 18.97/18.94 ! [V_n_2,V_m_2,V_a_2,T_b] : % 18.97/18.94 ( class_Rings_Olinordered__semidom(T_b) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2)) % 18.97/18.94 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_m_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2) % 18.97/18.94 <=> V_m_2 = V_n_2 ) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_power__Suc2,axiom, % 18.97/18.94 ! [V_n,V_a,T_a] : % 18.97/18.94 ( class_Groups_Omonoid__mult(T_a) % 18.97/18.94 => 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) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_power__Suc,axiom, % 18.97/18.94 ! [V_n,V_a,T_a] : % 18.97/18.94 ( class_Power_Opower(T_a) % 18.97/18.94 => 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)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_power__0,axiom, % 18.97/18.94 ! [V_a,T_a] : % 18.97/18.94 ( class_Power_Opower(T_a) % 18.97/18.94 => 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) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_power__add,axiom, % 18.97/18.94 ! [V_n,V_m,V_a,T_a] : % 18.97/18.94 ( class_Groups_Omonoid__mult(T_a) % 18.97/18.94 => 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)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_abs__power__minus,axiom, % 18.97/18.94 ! [V_n,V_a,T_a] : % 18.97/18.94 ( class_Rings_Olinordered__idom(T_a) % 18.97/18.94 => 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)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_power__less__imp__less__base,axiom, % 18.97/18.94 ! [V_b,V_n,V_a,T_a] : % 18.97/18.94 ( class_Rings_Olinordered__semidom(T_a) % 18.97/18.94 => ( 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))) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 18.97/18.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_power__inject__base,axiom, % 18.97/18.94 ! [V_b,V_n,V_a,T_a] : % 18.97/18.94 ( class_Rings_Olinordered__semidom(T_a) % 18.97/18.94 => ( 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)) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 18.97/18.94 => V_a = V_b ) ) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_power__le__imp__le__base,axiom, % 18.97/18.94 ! [V_b,V_n,V_a,T_a] : % 18.97/18.94 ( class_Rings_Olinordered__semidom(T_a) % 18.97/18.94 => ( 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)))) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 18.97/18.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_power__less__power__Suc,axiom, % 18.97/18.94 ! [V_n,V_a,T_a] : % 18.97/18.94 ( class_Rings_Olinordered__semidom(T_a) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 18.97/18.94 => 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)))) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_power__gt1__lemma,axiom, % 18.97/18.94 ! [V_n,V_a,T_a] : % 18.97/18.94 ( class_Rings_Olinordered__semidom(T_a) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 18.97/18.94 => 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)))) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_power__0__left,axiom, % 18.97/18.94 ! [V_n,T_a] : % 18.97/18.94 ( ( class_Power_Opower(T_a) % 18.97/18.94 & class_Rings_Osemiring__0(T_a) ) % 18.97/18.94 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 18.97/18.94 => 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) ) % 18.97/18.94 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 18.97/18.94 => 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) ) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_power__gt1,axiom, % 18.97/18.94 ! [V_n,V_a,T_a] : % 18.97/18.94 ( class_Rings_Olinordered__semidom(T_a) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 18.97/18.94 => 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)))) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_power__strict__increasing__iff,axiom, % 18.97/18.94 ! [V_y_2,V_x_2,V_b_2,T_b] : % 18.97/18.94 ( class_Rings_Olinordered__semidom(T_b) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_b_2)) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_y_2))) % 18.97/18.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_power__less__imp__less__exp,axiom, % 18.97/18.94 ! [V_n,V_m,V_a,T_a] : % 18.97/18.94 ( class_Rings_Olinordered__semidom(T_a) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 18.97/18.94 => ( 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))) % 18.97/18.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_power__strict__increasing,axiom, % 18.97/18.94 ! [V_a,V_N,V_n,T_a] : % 18.97/18.94 ( class_Rings_Olinordered__semidom(T_a) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N)) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 18.97/18.94 => 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))) ) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_zero__le__power__abs,axiom, % 18.97/18.94 ! [V_n,V_a,T_a] : % 18.97/18.94 ( class_Rings_Olinordered__idom(T_a) % 18.97/18.94 => 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))) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_power__increasing,axiom, % 18.97/18.94 ! [V_a,V_N,V_n,T_a] : % 18.97/18.94 ( class_Rings_Olinordered__semidom(T_a) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N)) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 18.97/18.94 => 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))) ) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_power__minus,axiom, % 18.97/18.94 ! [V_n,V_a,T_a] : % 18.97/18.94 ( class_Rings_Oring__1(T_a) % 18.97/18.94 => 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)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_power__Suc__less,axiom, % 18.97/18.94 ! [V_n,V_a,T_a] : % 18.97/18.94 ( class_Rings_Olinordered__semidom(T_a) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 18.97/18.94 => 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))) ) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_power__eq__imp__eq__base,axiom, % 18.97/18.94 ! [V_b,V_n,V_a,T_a] : % 18.97/18.94 ( class_Rings_Olinordered__semidom(T_a) % 18.97/18.94 => ( 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) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 18.97/18.94 => V_a = V_b ) ) ) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_Nitpick_Onat__lcm__def,axiom, % 18.97/18.94 ! [V_y,V_x] : c_Nitpick_Onat__lcm(V_x,V_y) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x),V_y)),c_Nitpick_Onat__gcd(V_x,V_y)) ). % 18.97/18.94 % 18.97/18.94 fof(fact_Nitpick_Oint__gcd__def,axiom, % 18.97/18.94 ! [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)))) ). % 18.97/18.94 % 18.97/18.94 fof(fact_one__mod__nat__number__of,axiom, % 18.97/18.94 ! [V_v_H] : % 18.97/18.94 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 18.97/18.94 => 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)) ) % 18.97/18.94 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 18.97/18.94 => 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))) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_power__power__power,axiom, % 18.97/18.94 ! [T_b] : % 18.97/18.94 ( class_Power_Opower(T_b) % 18.97/18.94 => c_Power_Opower__class_Opower(T_b) = c_Power_Opower_Opower(T_b,c_Groups_Oone__class_Oone(T_b),c_Groups_Otimes__class_Otimes(T_b)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_div__nat__number__of,axiom, % 18.97/18.94 ! [V_v_H,V_v] : % 18.97/18.94 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 18.97/18.94 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 18.97/18.94 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 18.97/18.94 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_mod__nat__number__of,axiom, % 18.97/18.94 ! [V_v_H,V_v] : % 18.97/18.94 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 18.97/18.94 => 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) ) % 18.97/18.94 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 18.97/18.94 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 18.97/18.94 => 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) ) % 18.97/18.94 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 18.97/18.94 => 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))) ) ) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_Nitpick_Oint__lcm__def,axiom, % 18.97/18.94 ! [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)))) ). % 18.97/18.94 % 18.97/18.94 fof(fact_not__neg__0,axiom, % 18.97/18.94 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 18.97/18.94 % 18.97/18.94 fof(fact_not__neg__int,axiom, % 18.97/18.94 ! [V_n] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) ). % 18.97/18.94 % 18.97/18.94 fof(fact_not__neg__1,axiom, % 18.97/18.94 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))) ). % 18.97/18.94 % 18.97/18.94 fof(fact_not__neg__eq__ge__0,axiom, % 18.97/18.94 ! [V_x_2] : % 18.97/18.94 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_x_2)) % 18.97/18.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_neg__def,axiom, % 18.97/18.94 ! [V_Z_2] : % 18.97/18.94 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_Z_2)) % 18.97/18.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_Z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_neg__nat,axiom, % 18.97/18.94 ! [V_z] : % 18.97/18.94 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z)) % 18.97/18.94 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_not__neg__nat,axiom, % 18.97/18.94 ! [V_z] : % 18.97/18.94 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z)) % 18.97/18.94 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_power_Opower_Opower__0,axiom, % 18.97/18.94 ! [V_a_2,V_times_2,V_one_2,T_b] : hAPP(hAPP(c_Power_Opower_Opower(T_b,V_one_2,V_times_2),V_a_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_one_2 ). % 18.97/18.94 % 18.97/18.94 fof(fact_power_Opower_Opower__Suc,axiom, % 18.97/18.94 ! [V_n_2,V_a_2,V_times_2,V_one_2,T_b] : hAPP(hAPP(c_Power_Opower_Opower(T_b,V_one_2,V_times_2),V_a_2),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(V_times_2,V_a_2),hAPP(hAPP(c_Power_Opower_Opower(T_b,V_one_2,V_times_2),V_a_2),V_n_2)) ). % 18.97/18.94 % 18.97/18.94 fof(fact_neg__imp__number__of__eq__0,axiom, % 18.97/18.94 ! [V_v] : % 18.97/18.94 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 18.97/18.94 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_neg__zminus__int,axiom, % 18.97/18.94 ! [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))))) ). % 18.97/18.94 % 18.97/18.94 fof(fact_eq__nat__number__of,axiom, % 18.97/18.94 ! [V_v_H_2,V_v_2] : % 18.97/18.94 ( 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) % 18.97/18.94 <=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) % 18.97/18.94 => 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))) ) % 18.97/18.94 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) % 18.97/18.94 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2))) % 18.97/18.94 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 18.97/18.94 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2))) % 18.97/18.94 => V_v_2 = V_v_H_2 ) ) ) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_nat__number__of__add__left,axiom, % 18.97/18.94 ! [V_k,V_v_H,V_v] : % 18.97/18.94 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 18.97/18.94 => 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) ) % 18.97/18.94 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 18.97/18.94 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 18.97/18.94 => 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) ) % 18.97/18.94 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 18.97/18.94 => 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) ) ) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_int__nat__number__of,axiom, % 18.97/18.94 ! [V_v] : % 18.97/18.94 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 18.97/18.94 => 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) ) % 18.97/18.94 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 18.97/18.94 => 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) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_of__nat__number__of__eq,axiom, % 18.97/18.94 ! [V_v,T_a] : % 18.97/18.94 ( class_Int_Onumber__ring(T_a) % 18.97/18.94 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 18.97/18.94 => 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) ) % 18.97/18.94 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 18.97/18.94 => 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) ) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_power__nat__number__of__number__of,axiom, % 18.97/18.94 ! [V_w,V_v] : % 18.97/18.94 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 18.97/18.94 => 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)) ) % 18.97/18.94 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 18.97/18.94 => 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))) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_power__nat__number__of,axiom, % 18.97/18.94 ! [V_n,V_v] : % 18.97/18.94 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 18.97/18.94 => 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) ) % 18.97/18.94 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 18.97/18.94 => 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)) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_Suc__nat__number__of__add,axiom, % 18.97/18.94 ! [V_n,V_v] : % 18.97/18.94 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 18.97/18.94 => 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) ) % 18.97/18.94 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 18.97/18.94 => 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) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_Suc__nat__number__of,axiom, % 18.97/18.94 ! [V_v] : % 18.97/18.94 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 18.97/18.94 => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) % 18.97/18.94 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 18.97/18.94 => 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)) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_zmod__minus1,axiom, % 18.97/18.94 ! [V_b] : % 18.97/18.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 18.97/18.94 => 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)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_div__pos__neg__trivial,axiom, % 18.97/18.94 ! [V_b,V_a] : % 18.97/18.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 18.97/18.94 => ( 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))) % 18.97/18.94 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_int__val__lemma,axiom, % 18.97/18.94 ! [V_k_2,V_f_2,V_n_2] : % 18.97/18.94 ( ! [B_i] : % 18.97/18.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) % 18.97/18.94 => 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))) ) % 18.97/18.94 => ( 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)) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2))) % 18.97/18.94 => ? [B_i] : % 18.97/18.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) % 18.97/18.94 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_nat0__intermed__int__val,axiom, % 18.97/18.94 ! [V_k_2,V_f_2,V_n_2] : % 18.97/18.94 ( ! [B_i] : % 18.97/18.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) % 18.97/18.94 => 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))) ) % 18.97/18.94 => ( 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)) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2))) % 18.97/18.94 => ? [B_i] : % 18.97/18.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) % 18.97/18.94 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_eq__number__of__eq,axiom, % 18.97/18.94 ! [V_y_2,V_x_2,T_b] : % 18.97/18.94 ( class_Int_Onumber__ring(T_b) % 18.97/18.94 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2) % 18.97/18.94 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_y_2)))) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_diff__bin__simps_I2_J,axiom, % 18.97/18.94 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Osucc(V_k) ). % 18.97/18.94 % 18.97/18.94 fof(fact_nonzero__number__of__Min,axiom, % 18.97/18.94 ! [T_a] : % 18.97/18.94 ( class_Int_Onumber__ring(T_a) % 18.97/18.94 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_rel__simps_I24_J,axiom, % 18.97/18.94 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ). % 18.97/18.94 % 18.97/18.94 fof(fact_rel__simps_I7_J,axiom, % 18.97/18.94 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ). % 18.97/18.94 % 18.97/18.94 fof(fact_iszero__def,axiom, % 18.97/18.94 ! [V_z_2,T_b] : % 18.97/18.94 ( class_Rings_Osemiring__1(T_b) % 18.97/18.94 => ( c_Int_Oiszero(T_b,V_z_2) % 18.97/18.94 <=> V_z_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_iszero__0,axiom, % 18.97/18.94 ! [T_a] : % 18.97/18.94 ( class_Rings_Osemiring__1(T_a) % 18.97/18.94 => c_Int_Oiszero(T_a,c_Groups_Ozero__class_Ozero(T_a)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_not__iszero__1,axiom, % 18.97/18.94 ! [T_a] : % 18.97/18.94 ( class_Rings_Osemiring__1(T_a) % 18.97/18.94 => ~ c_Int_Oiszero(T_a,c_Groups_Oone__class_Oone(T_a)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_bin__less__0__simps_I2_J,axiom, % 18.97/18.94 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 18.97/18.94 % 18.97/18.94 fof(fact_Int_OMin__def,axiom, % 18.97/18.94 c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 18.97/18.94 % 18.97/18.94 fof(fact_mult__Min,axiom, % 18.97/18.94 ! [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) ). % 18.97/18.94 % 18.97/18.94 fof(fact_neg__number__of__Min,axiom, % 18.97/18.94 hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))) ). % 18.97/18.94 % 18.97/18.94 fof(fact_mult__minus1,axiom, % 18.97/18.94 ! [V_z,T_a] : % 18.97/18.94 ( class_Int_Onumber__ring(T_a) % 18.97/18.94 => 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) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_mult__minus1__right,axiom, % 18.97/18.94 ! [V_z,T_a] : % 18.97/18.94 ( class_Int_Onumber__ring(T_a) % 18.97/18.94 => 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) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_number__of__Min,axiom, % 18.97/18.94 ! [T_a] : % 18.97/18.94 ( class_Int_Onumber__ring(T_a) % 18.97/18.94 => 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)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_arith__simps_I31_J,axiom, % 18.97/18.94 ! [T_a] : % 18.97/18.94 ( class_Int_Onumber__ring(T_a) % 18.97/18.94 => 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) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_abs__minus__one,axiom, % 18.97/18.94 ! [T_a] : % 18.97/18.94 ( ( class_Int_Onumber__ring(T_a) % 18.97/18.94 & class_Rings_Olinordered__idom(T_a) ) % 18.97/18.94 => 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) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_zmod__minus1__right,axiom, % 18.97/18.94 ! [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) ). % 18.97/18.94 % 18.97/18.94 fof(fact_pos__zmult__eq__1__iff__lemma,axiom, % 18.97/18.94 ! [V_n,V_m] : % 18.97/18.94 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 18.97/18.94 => ( V_m = c_Groups_Oone__class_Oone(tc_Int_Oint) % 18.97/18.94 | V_m = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_zmult__eq__1__iff,axiom, % 18.97/18.94 ! [V_n_2,V_m_2] : % 18.97/18.94 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 18.97/18.94 <=> ( ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) % 18.97/18.94 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) % 18.97/18.94 | ( V_m_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) % 18.97/18.94 & V_n_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_of__int__m1,axiom, % 18.97/18.94 ! [T_a] : % 18.97/18.94 ( class_Int_Onumber__ring(T_a) % 18.97/18.94 => 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) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_zdiv__minus1__right,axiom, % 18.97/18.94 ! [V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a) ). % 18.97/18.94 % 18.97/18.94 fof(fact_succ__def,axiom, % 18.97/18.94 ! [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)) ). % 18.97/18.94 % 18.97/18.94 fof(fact_abs__power__minus__one,axiom, % 18.97/18.94 ! [V_n,T_a] : % 18.97/18.94 ( ( class_Int_Onumber__ring(T_a) % 18.97/18.94 & class_Rings_Olinordered__idom(T_a) ) % 18.97/18.94 => 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) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_div__eq__minus1,axiom, % 18.97/18.94 ! [V_b] : % 18.97/18.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 18.97/18.94 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),V_b) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_number__of__succ,axiom, % 18.97/18.94 ! [V_k,T_a] : % 18.97/18.94 ( class_Int_Onumber__ring(T_a) % 18.97/18.94 => 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)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_nat__number__of__add__1,axiom, % 18.97/18.94 ! [V_v] : % 18.97/18.94 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 18.97/18.94 => 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) ) % 18.97/18.94 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 18.97/18.94 => 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)) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_nat__1__add__number__of,axiom, % 18.97/18.94 ! [V_v] : % 18.97/18.94 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 18.97/18.94 => 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) ) % 18.97/18.94 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 18.97/18.94 => 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)) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_eq__special_I1_J,axiom, % 18.97/18.94 ! [V_y_2,T_b] : % 18.97/18.94 ( class_Int_Onumber__ring(T_b) % 18.97/18.94 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2) % 18.97/18.94 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_y_2)))) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_eq__special_I3_J,axiom, % 18.97/18.94 ! [V_x_2,T_b] : % 18.97/18.94 ( class_Int_Onumber__ring(T_b) % 18.97/18.94 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Ozero__class_Ozero(T_b) % 18.97/18.94 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls)))) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_neg__number__of__pred__iff__0,axiom, % 18.97/18.94 ! [V_v_2] : % 18.97/18.94 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2)))) % 18.97/18.94 <=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_nat__number__of__mult__left,axiom, % 18.97/18.94 ! [V_k,V_v_H,V_v] : % 18.97/18.94 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 18.97/18.94 => 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) ) % 18.97/18.94 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 18.97/18.94 => 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) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_mult__nat__number__of,axiom, % 18.97/18.94 ! [V_v_H,V_v] : % 18.97/18.94 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 18.97/18.94 => 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) ) % 18.97/18.94 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 18.97/18.94 => 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)) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_pred__Pls,axiom, % 18.97/18.94 c_Int_Opred(c_Int_OPls) = c_Int_OMin ). % 18.97/18.94 % 18.97/18.94 fof(fact_Pls__def,axiom, % 18.97/18.94 c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 18.97/18.94 % 18.97/18.94 fof(fact_rel__simps_I19_J,axiom, % 18.97/18.94 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ). % 18.97/18.94 % 18.97/18.94 fof(fact_rel__simps_I2_J,axiom, % 18.97/18.94 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ). % 18.97/18.94 % 18.97/18.94 fof(fact_add__Pls__right,axiom, % 18.97/18.94 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ). % 18.97/18.94 % 18.97/18.94 fof(fact_add__Pls,axiom, % 18.97/18.94 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),V_k) = V_k ). % 18.97/18.94 % 18.97/18.94 fof(fact_mult__Pls,axiom, % 18.97/18.94 ! [V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),V_w) = c_Int_OPls ). % 18.97/18.94 % 18.97/18.94 fof(fact_diff__bin__simps_I1_J,axiom, % 18.97/18.94 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ). % 18.97/18.94 % 18.97/18.94 fof(fact_minus__Pls,axiom, % 18.97/18.94 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls ). % 18.97/18.94 % 18.97/18.94 fof(fact_rel__simps_I40_J,axiom, % 18.97/18.94 c_Int_OMin != c_Int_OPls ). % 18.97/18.94 % 18.97/18.94 fof(fact_rel__simps_I37_J,axiom, % 18.97/18.94 c_Int_OPls != c_Int_OMin ). % 18.97/18.94 % 18.97/18.94 fof(fact_succ__pred,axiom, % 18.97/18.94 ! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x ). % 18.97/18.94 % 18.97/18.94 fof(fact_semiring__norm_I112_J,axiom, % 18.97/18.94 ! [T_a] : % 18.97/18.94 ( class_Int_Onumber__ring(T_a) % 18.97/18.94 => c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_number__of__Pls,axiom, % 18.97/18.94 ! [T_a] : % 18.97/18.94 ( class_Int_Onumber__ring(T_a) % 18.97/18.94 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_add__numeral__0__right,axiom, % 18.97/18.94 ! [V_a,T_a] : % 18.97/18.94 ( class_Int_Onumber__ring(T_a) % 18.97/18.94 => 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 ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_add__numeral__0,axiom, % 18.97/18.94 ! [V_a,T_a] : % 18.97/18.94 ( class_Int_Onumber__ring(T_a) % 18.97/18.94 => 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 ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_bin__less__0__simps_I1_J,axiom, % 18.97/18.94 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 18.97/18.94 % 18.97/18.94 fof(fact_semiring__norm_I113_J,axiom, % 18.97/18.94 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) ). % 18.97/18.94 % 18.97/18.94 fof(fact_nat__number__of__Pls,axiom, % 18.97/18.94 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 18.97/18.94 % 18.97/18.94 fof(fact_zero__is__num__zero,axiom, % 18.97/18.94 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) ). % 18.97/18.94 % 18.97/18.94 fof(fact_Suc__diff__number__of,axiom, % 18.97/18.94 ! [V_m,V_v] : % 18.97/18.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v)) % 18.97/18.94 => 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))) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_rel__simps_I23_J,axiom, % 18.97/18.94 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ). % 18.97/18.94 % 18.97/18.94 fof(fact_rel__simps_I20_J,axiom, % 18.97/18.94 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ). % 18.97/18.94 % 18.97/18.94 fof(fact_rel__simps_I6_J,axiom, % 18.97/18.94 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ). % 18.97/18.94 % 18.97/18.94 fof(fact_rel__simps_I3_J,axiom, % 18.97/18.94 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ). % 18.97/18.94 % 18.97/18.94 fof(fact_eq__number__of__Pls__Min,axiom, % 18.97/18.94 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) ). % 18.97/18.94 % 18.97/18.94 fof(fact_not__neg__number__of__Pls,axiom, % 18.97/18.94 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))) ). % 18.97/18.94 % 18.97/18.94 fof(fact_iszero__Numeral0,axiom, % 18.97/18.94 ! [T_a] : % 18.97/18.94 ( class_Int_Onumber__ring(T_a) % 18.97/18.94 => c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_succ__Min,axiom, % 18.97/18.94 c_Int_Osucc(c_Int_OMin) = c_Int_OPls ). % 18.97/18.94 % 18.97/18.94 fof(fact_le__iff__pred__less,axiom, % 18.97/18.94 ! [V_l_2,V_k_2] : % 18.97/18.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) % 18.97/18.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(V_k_2)),V_l_2)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_pred__def,axiom, % 18.97/18.94 ! [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)) ). % 18.97/18.94 % 18.97/18.94 fof(fact_add__Min,axiom, % 18.97/18.94 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),V_k) = c_Int_Opred(V_k) ). % 18.97/18.94 % 18.97/18.94 fof(fact_add__Min__right,axiom, % 18.97/18.94 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Opred(V_k) ). % 18.97/18.94 % 18.97/18.94 fof(fact_nat__number__of__diff__1,axiom, % 18.97/18.94 ! [V_v] : % 18.97/18.94 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls)) % 18.97/18.94 => 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) ) % 18.97/18.94 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls)) % 18.97/18.94 => 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)) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_eq__0__number__of,axiom, % 18.97/18.94 ! [V_v_2] : % 18.97/18.94 ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) % 18.97/18.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_eq__number__of__0,axiom, % 18.97/18.94 ! [V_v_2] : % 18.97/18.94 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 18.97/18.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_number__of2,axiom, % 18.97/18.94 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))) ). % 18.97/18.94 % 18.97/18.94 fof(fact_less__nat__number__of,axiom, % 18.97/18.94 ! [V_v_H_2,V_v_2] : % 18.97/18.94 ( 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))) % 18.97/18.94 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) % 18.97/18.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_H_2)) ) % 18.97/18.94 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_le__nat__number__of,axiom, % 18.97/18.94 ! [V_v_H_2,V_v_2] : % 18.97/18.94 ( 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))) % 18.97/18.94 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),V_v_H_2)) % 18.97/18.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_le__special_I1_J,axiom, % 18.97/18.94 ! [V_y_2,T_b] : % 18.97/18.94 ( ( class_Int_Onumber__ring(T_b) % 18.97/18.94 & class_Rings_Olinordered__idom(T_b) ) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2))) % 18.97/18.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_le__special_I3_J,axiom, % 18.97/18.94 ! [V_x_2,T_b] : % 18.97/18.94 ( ( class_Int_Onumber__ring(T_b) % 18.97/18.94 & class_Rings_Olinordered__idom(T_b) ) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Ozero__class_Ozero(T_b))) % 18.97/18.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_less__special_I3_J,axiom, % 18.97/18.94 ! [V_x_2,T_b] : % 18.97/18.94 ( ( class_Int_Onumber__ring(T_b) % 18.97/18.94 & class_Rings_Olinordered__idom(T_b) ) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Ozero__class_Ozero(T_b))) % 18.97/18.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_less__special_I1_J,axiom, % 18.97/18.94 ! [V_y_2,T_b] : % 18.97/18.94 ( ( class_Int_Onumber__ring(T_b) % 18.97/18.94 & class_Rings_Olinordered__idom(T_b) ) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2))) % 18.97/18.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_less__0__number__of,axiom, % 18.97/18.94 ! [V_v_2] : % 18.97/18.94 ( 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))) % 18.97/18.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_2)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_add__nat__number__of,axiom, % 18.97/18.94 ! [V_v_H,V_v] : % 18.97/18.94 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 18.97/18.94 => 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) ) % 18.97/18.94 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 18.97/18.94 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls)) % 18.97/18.94 => 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) ) % 18.97/18.94 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls)) % 18.97/18.94 => 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)) ) ) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_number__of__pred,axiom, % 18.97/18.94 ! [V_w,T_a] : % 18.97/18.94 ( class_Int_Onumber__ring(T_a) % 18.97/18.94 => 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)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_eq__special_I2_J,axiom, % 18.97/18.94 ! [V_y_2,T_b] : % 18.97/18.94 ( class_Int_Onumber__ring(T_b) % 18.97/18.94 => ( c_Groups_Oone__class_Oone(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2) % 18.97/18.94 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_y_2)))) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_eq__special_I4_J,axiom, % 18.97/18.94 ! [V_x_2,T_b] : % 18.97/18.94 ( class_Int_Onumber__ring(T_b) % 18.97/18.94 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Oone__class_Oone(T_b) % 18.97/18.94 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_diff__special_I1_J,axiom, % 18.97/18.94 ! [V_w,T_a] : % 18.97/18.94 ( class_Int_Onumber__ring(T_a) % 18.97/18.94 => 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))) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_diff__special_I2_J,axiom, % 18.97/18.94 ! [V_v,T_a] : % 18.97/18.94 ( class_Int_Onumber__ring(T_a) % 18.97/18.94 => 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)))) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_div__Suc__eq__div__add3,axiom, % 18.97/18.94 ! [V_n,V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_n)) ). % 18.97/18.94 % 18.97/18.94 fof(fact_Suc__div__eq__add3__div,axiom, % 18.97/18.94 ! [V_n,V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m)))),V_n) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_m)),V_n) ). % 18.97/18.94 % 18.97/18.94 fof(fact_rel__simps_I51_J,axiom, % 18.97/18.94 ! [V_l_2,V_k_2] : % 18.97/18.94 ( c_Int_OBit1(V_k_2) = c_Int_OBit1(V_l_2) % 18.97/18.94 <=> V_k_2 = V_l_2 ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_less__eq__int__code_I16_J,axiom, % 18.97/18.94 ! [V_k2_2,V_k1_2] : % 18.97/18.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2))) % 18.97/18.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_rel__simps_I34_J,axiom, % 18.97/18.94 ! [V_l_2,V_k_2] : % 18.97/18.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2))) % 18.97/18.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_less__int__code_I16_J,axiom, % 18.97/18.94 ! [V_k2_2,V_k1_2] : % 18.97/18.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2))) % 18.97/18.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_rel__simps_I17_J,axiom, % 18.97/18.94 ! [V_l_2,V_k_2] : % 18.97/18.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2))) % 18.97/18.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_rel__simps_I46_J,axiom, % 18.97/18.94 ! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls ). % 18.97/18.94 % 18.97/18.94 fof(fact_rel__simps_I39_J,axiom, % 18.97/18.94 ! [V_l] : c_Int_OPls != c_Int_OBit1(V_l) ). % 18.97/18.94 % 18.97/18.94 fof(fact_rel__simps_I47_J,axiom, % 18.97/18.94 ! [V_k_2] : % 18.97/18.94 ( c_Int_OBit1(V_k_2) = c_Int_OMin % 18.97/18.94 <=> V_k_2 = c_Int_OMin ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_rel__simps_I43_J,axiom, % 18.97/18.94 ! [V_l_2] : % 18.97/18.94 ( c_Int_OMin = c_Int_OBit1(V_l_2) % 18.97/18.94 <=> c_Int_OMin = V_l_2 ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_Bit1__Min,axiom, % 18.97/18.94 c_Int_OBit1(c_Int_OMin) = c_Int_OMin ). % 18.97/18.94 % 18.97/18.94 fof(fact_bin__less__0__simps_I4_J,axiom, % 18.97/18.94 ! [V_w_2] : % 18.97/18.94 ( 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))) % 18.97/18.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_rel__simps_I22_J,axiom, % 18.97/18.94 ! [V_k_2] : % 18.97/18.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2))) % 18.97/18.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_rel__simps_I12_J,axiom, % 18.97/18.94 ! [V_k_2] : % 18.97/18.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls)) % 18.97/18.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_Bit1__def,axiom, % 18.97/18.94 ! [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) ). % 18.97/18.94 % 18.97/18.94 fof(fact_rel__simps_I30_J,axiom, % 18.97/18.94 ! [V_k_2] : % 18.97/18.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin)) % 18.97/18.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_rel__simps_I26_J,axiom, % 18.97/18.94 ! [V_k_2] : % 18.97/18.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2))) % 18.97/18.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_rel__simps_I13_J,axiom, % 18.97/18.94 ! [V_k_2] : % 18.97/18.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin)) % 18.97/18.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_rel__simps_I9_J,axiom, % 18.97/18.94 ! [V_k_2] : % 18.97/18.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2))) % 18.97/18.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_neg__number__of__Bit1,axiom, % 18.97/18.94 ! [V_w_2] : % 18.97/18.94 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_w_2)))) % 18.97/18.94 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_minus__Bit1,axiom, % 18.97/18.94 ! [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))) ). % 18.97/18.94 % 18.97/18.94 fof(fact_iszero__number__of__Bit1,axiom, % 18.97/18.94 ! [V_w,T_a] : % 18.97/18.94 ( ( class_Int_Onumber__ring(T_a) % 18.97/18.94 & class_Int_Oring__char__0(T_a) ) % 18.97/18.94 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w))) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_succ__Pls,axiom, % 18.97/18.94 c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls) ). % 18.97/18.94 % 18.97/18.94 fof(fact_number__of__Bit1,axiom, % 18.97/18.94 ! [V_w,T_a] : % 18.97/18.94 ( class_Int_Onumber__ring(T_a) % 18.97/18.94 => 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)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_mult__numeral__1,axiom, % 18.97/18.94 ! [V_a,T_a] : % 18.97/18.94 ( class_Int_Onumber__ring(T_a) % 18.97/18.94 => 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 ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_mult__numeral__1__right,axiom, % 18.97/18.94 ! [V_a,T_a] : % 18.97/18.94 ( class_Int_Onumber__ring(T_a) % 18.97/18.94 => 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 ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_semiring__norm_I110_J,axiom, % 18.97/18.94 ! [T_a] : % 18.97/18.94 ( class_Int_Onumber__ring(T_a) % 18.97/18.94 => c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_numeral__1__eq__1,axiom, % 18.97/18.94 ! [T_a] : % 18.97/18.94 ( class_Int_Onumber__ring(T_a) % 18.97/18.94 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(T_a) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_rel__simps_I5_J,axiom, % 18.97/18.94 ! [V_k_2] : % 18.97/18.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2))) % 18.97/18.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_rel__simps_I29_J,axiom, % 18.97/18.94 ! [V_k_2] : % 18.97/18.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls)) % 18.97/18.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_one__is__num__one,axiom, % 18.97/18.94 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)) ). % 18.97/18.94 % 18.97/18.94 fof(fact_nat__numeral__1__eq__1,axiom, % 18.97/18.94 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ). % 18.97/18.94 % 18.97/18.94 fof(fact_Numeral1__eq1__nat,axiom, % 18.97/18.94 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) ). % 18.97/18.94 % 18.97/18.94 fof(fact_diff__bin__simps_I4_J,axiom, % 18.97/18.94 ! [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)) ). % 18.97/18.94 % 18.97/18.94 fof(fact_minus__Min,axiom, % 18.97/18.94 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls) ). % 18.97/18.94 % 18.97/18.94 fof(fact_not__iszero__Numeral1,axiom, % 18.97/18.94 ! [T_a] : % 18.97/18.94 ( class_Int_Onumber__ring(T_a) % 18.97/18.94 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_numeral__3__eq__3,axiom, % 18.97/18.94 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)))) ). % 18.97/18.94 % 18.97/18.94 fof(fact_numeral__1__eq__Suc__0,axiom, % 18.97/18.94 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)) ). % 18.97/18.94 % 18.97/18.94 fof(fact_power3__eq__cube,axiom, % 18.97/18.94 ! [V_a,T_a] : % 18.97/18.94 ( class_Groups_Omonoid__mult(T_a) % 18.97/18.94 => 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) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom, % 18.97/18.94 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))))) ). % 18.97/18.94 % 18.97/18.94 fof(fact_Suc3__eq__add__3,axiom, % 18.97/18.94 ! [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) ). % 18.97/18.94 % 18.97/18.94 fof(fact_transfer__int__nat__numerals_I4_J,axiom, % 18.97/18.94 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)))) ). % 18.97/18.94 % 18.97/18.94 fof(fact_transfer__nat__int__numerals_I4_J,axiom, % 18.97/18.94 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)))) ). % 18.97/18.94 % 18.97/18.94 fof(fact_le__special_I2_J,axiom, % 18.97/18.94 ! [V_y_2,T_b] : % 18.97/18.94 ( ( class_Int_Onumber__ring(T_b) % 18.97/18.94 & class_Rings_Olinordered__idom(T_b) ) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Oone__class_Oone(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2))) % 18.97/18.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_le__special_I4_J,axiom, % 18.97/18.94 ! [V_x_2,T_b] : % 18.97/18.94 ( ( class_Int_Onumber__ring(T_b) % 18.97/18.94 & class_Rings_Olinordered__idom(T_b) ) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Oone__class_Oone(T_b))) % 18.97/18.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_less__special_I2_J,axiom, % 18.97/18.94 ! [V_y_2,T_b] : % 18.97/18.94 ( ( class_Int_Onumber__ring(T_b) % 18.97/18.94 & class_Rings_Olinordered__idom(T_b) ) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2))) % 18.97/18.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_less__special_I4_J,axiom, % 18.97/18.94 ! [V_x_2,T_b] : % 18.97/18.94 ( ( class_Int_Onumber__ring(T_b) % 18.97/18.94 & class_Rings_Olinordered__idom(T_b) ) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Oone__class_Oone(T_b))) % 18.97/18.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_add__special_I3_J,axiom, % 18.97/18.94 ! [V_v,T_a] : % 18.97/18.94 ( class_Int_Onumber__ring(T_a) % 18.97/18.94 => 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))) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_add__special_I2_J,axiom, % 18.97/18.94 ! [V_w,T_a] : % 18.97/18.94 ( class_Int_Onumber__ring(T_a) % 18.97/18.94 => 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)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_Suc__diff__eq__diff__pred,axiom, % 18.97/18.94 ! [V_m,V_n] : % 18.97/18.94 ( 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)) % 18.97/18.94 => 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)))) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_Suc__mod__eq__add3__mod__number__of,axiom, % 18.97/18.94 ! [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)) ). % 18.97/18.94 % 18.97/18.94 fof(fact_Suc__mod__eq__add3__mod,axiom, % 18.97/18.94 ! [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) ). % 18.97/18.94 % 18.97/18.94 fof(fact_mod__Suc__eq__mod__add3,axiom, % 18.97/18.94 ! [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)) ). % 18.97/18.94 % 18.97/18.94 fof(fact_Suc__div__eq__add3__div__number__of,axiom, % 18.97/18.94 ! [V_v,V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) ). % 18.97/18.94 % 18.97/18.94 fof(fact_neg__zmod__mult__2,axiom, % 18.97/18.94 ! [V_b,V_a] : % 18.97/18.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 18.97/18.94 => 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)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_zmod__number__of__Bit1,axiom, % 18.97/18.94 ! [V_v,V_w] : % 18.97/18.94 ( ( 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))) % 18.97/18.94 => 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)) ) % 18.97/18.94 & ( ~ 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))) % 18.97/18.94 => 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)) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_neg__zdiv__mult__2,axiom, % 18.97/18.94 ! [V_b,V_a] : % 18.97/18.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 18.97/18.94 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_b),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_a) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_pos__zdiv__mult__2,axiom, % 18.97/18.94 ! [V_b,V_a] : % 18.97/18.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 18.97/18.94 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b),V_a) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_pos__zmod__mult__2,axiom, % 18.97/18.94 ! [V_b,V_a] : % 18.97/18.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 18.97/18.94 => 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))) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_of__nat__double,axiom, % 18.97/18.94 ! [V_x,T_a] : % 18.97/18.94 ( class_Rings_Osemiring__1(T_a) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 18.97/18.94 => 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))) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_rel__simps_I48_J,axiom, % 18.97/18.94 ! [V_l_2,V_k_2] : % 18.97/18.94 ( c_Int_OBit0(V_k_2) = c_Int_OBit0(V_l_2) % 18.97/18.94 <=> V_k_2 = V_l_2 ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_rel__simps_I31_J,axiom, % 18.97/18.94 ! [V_l_2,V_k_2] : % 18.97/18.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2))) % 18.97/18.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_less__eq__int__code_I13_J,axiom, % 18.97/18.94 ! [V_k2_2,V_k1_2] : % 18.97/18.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2))) % 18.97/18.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_rel__simps_I14_J,axiom, % 18.97/18.94 ! [V_l_2,V_k_2] : % 18.97/18.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2))) % 18.97/18.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_less__int__code_I13_J,axiom, % 18.97/18.94 ! [V_k2_2,V_k1_2] : % 18.97/18.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2))) % 18.97/18.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_Bit0__Pls,axiom, % 18.97/18.94 c_Int_OBit0(c_Int_OPls) = c_Int_OPls ). % 18.97/18.94 % 18.97/18.94 fof(fact_rel__simps_I38_J,axiom, % 18.97/18.94 ! [V_l_2] : % 18.97/18.94 ( c_Int_OPls = c_Int_OBit0(V_l_2) % 18.97/18.94 <=> c_Int_OPls = V_l_2 ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_rel__simps_I44_J,axiom, % 18.97/18.94 ! [V_k_2] : % 18.97/18.94 ( c_Int_OBit0(V_k_2) = c_Int_OPls % 18.97/18.94 <=> V_k_2 = c_Int_OPls ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_rel__simps_I49_J,axiom, % 18.97/18.94 ! [V_l,V_k] : c_Int_OBit0(V_k) != c_Int_OBit1(V_l) ). % 18.97/18.94 % 18.97/18.94 fof(fact_rel__simps_I50_J,axiom, % 18.97/18.94 ! [V_l,V_k] : c_Int_OBit1(V_k) != c_Int_OBit0(V_l) ). % 18.97/18.94 % 18.97/18.94 fof(fact_add__Bit0__Bit0,axiom, % 18.97/18.94 ! [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)) ). % 18.97/18.94 % 18.97/18.94 fof(fact_Bit0__def,axiom, % 18.97/18.94 ! [V_k] : c_Int_OBit0(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_k) ). % 18.97/18.94 % 18.97/18.94 fof(fact_mult__Bit0,axiom, % 18.97/18.94 ! [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)) ). % 18.97/18.94 % 18.97/18.94 fof(fact_diff__bin__simps_I7_J,axiom, % 18.97/18.94 ! [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)) ). % 18.97/18.94 % 18.97/18.94 fof(fact_minus__Bit0,axiom, % 18.97/18.94 ! [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)) ). % 18.97/18.94 % 18.97/18.94 fof(fact_rel__simps_I42_J,axiom, % 18.97/18.94 ! [V_l] : c_Int_OMin != c_Int_OBit0(V_l) ). % 18.97/18.94 % 18.97/18.94 fof(fact_rel__simps_I45_J,axiom, % 18.97/18.94 ! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin ). % 18.97/18.94 % 18.97/18.94 fof(fact_bin__less__0__simps_I3_J,axiom, % 18.97/18.94 ! [V_w_2] : % 18.97/18.94 ( 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))) % 18.97/18.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_rel__simps_I21_J,axiom, % 18.97/18.94 ! [V_k_2] : % 18.97/18.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2))) % 18.97/18.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_rel__simps_I27_J,axiom, % 18.97/18.94 ! [V_k_2] : % 18.97/18.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls)) % 18.97/18.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_rel__simps_I32_J,axiom, % 18.97/18.94 ! [V_l_2,V_k_2] : % 18.97/18.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2))) % 18.97/18.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_less__eq__int__code_I14_J,axiom, % 18.97/18.94 ! [V_k2_2,V_k1_2] : % 18.97/18.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2))) % 18.97/18.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_rel__simps_I4_J,axiom, % 18.97/18.94 ! [V_k_2] : % 18.97/18.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2))) % 18.97/18.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_rel__simps_I10_J,axiom, % 18.97/18.94 ! [V_k_2] : % 18.97/18.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls)) % 18.97/18.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_rel__simps_I16_J,axiom, % 18.97/18.94 ! [V_l_2,V_k_2] : % 18.97/18.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2))) % 18.97/18.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_less__int__code_I15_J,axiom, % 18.97/18.94 ! [V_k2_2,V_k1_2] : % 18.97/18.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2))) % 18.97/18.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_add__Bit0__Bit1,axiom, % 18.97/18.94 ! [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)) ). % 18.97/18.94 % 18.97/18.94 fof(fact_add__Bit1__Bit0,axiom, % 18.97/18.94 ! [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)) ). % 18.97/18.94 % 18.97/18.94 fof(fact_diff__bin__simps_I3_J,axiom, % 18.97/18.94 ! [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)) ). % 18.97/18.94 % 18.97/18.94 fof(fact_diff__bin__simps_I9_J,axiom, % 18.97/18.94 ! [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)) ). % 18.97/18.94 % 18.97/18.94 fof(fact_diff__bin__simps_I10_J,axiom, % 18.97/18.94 ! [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)) ). % 18.97/18.94 % 18.97/18.94 fof(fact_rel__simps_I28_J,axiom, % 18.97/18.94 ! [V_k_2] : % 18.97/18.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin)) % 18.97/18.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_rel__simps_I8_J,axiom, % 18.97/18.94 ! [V_k_2] : % 18.97/18.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2))) % 18.97/18.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_zdiv__number__of__Bit0,axiom, % 18.97/18.94 ! [V_w,V_v] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_v))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) ). % 18.97/18.94 % 18.97/18.94 fof(fact_neg__number__of__Bit0,axiom, % 18.97/18.94 ! [V_w_2] : % 18.97/18.94 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w_2)))) % 18.97/18.94 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_pred__Bit0,axiom, % 18.97/18.94 ! [V_k] : c_Int_Opred(c_Int_OBit0(V_k)) = c_Int_OBit1(c_Int_Opred(V_k)) ). % 18.97/18.94 % 18.97/18.94 fof(fact_pred__Bit1,axiom, % 18.97/18.94 ! [V_k] : c_Int_Opred(c_Int_OBit1(V_k)) = c_Int_OBit0(V_k) ). % 18.97/18.94 % 18.97/18.94 fof(fact_pred__Min,axiom, % 18.97/18.94 c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin) ). % 18.97/18.94 % 18.97/18.94 fof(fact_iszero__number__of__Bit0,axiom, % 18.97/18.94 ! [V_w_2,T_b] : % 18.97/18.94 ( ( class_Int_Onumber__ring(T_b) % 18.97/18.94 & class_Int_Oring__char__0(T_b) ) % 18.97/18.94 => ( c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),c_Int_OBit0(V_w_2))) % 18.97/18.94 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_succ__Bit1,axiom, % 18.97/18.94 ! [V_k] : c_Int_Osucc(c_Int_OBit1(V_k)) = c_Int_OBit0(c_Int_Osucc(V_k)) ). % 18.97/18.94 % 18.97/18.94 fof(fact_succ__Bit0,axiom, % 18.97/18.94 ! [V_k] : c_Int_Osucc(c_Int_OBit0(V_k)) = c_Int_OBit1(V_k) ). % 18.97/18.94 % 18.97/18.94 fof(fact_number__of__Bit0,axiom, % 18.97/18.94 ! [V_w,T_a] : % 18.97/18.94 ( class_Int_Onumber__ring(T_a) % 18.97/18.94 => 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)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_less__eq__int__code_I15_J,axiom, % 18.97/18.94 ! [V_k2_2,V_k1_2] : % 18.97/18.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2))) % 18.97/18.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_rel__simps_I33_J,axiom, % 18.97/18.94 ! [V_l_2,V_k_2] : % 18.97/18.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2))) % 18.97/18.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_less__int__code_I14_J,axiom, % 18.97/18.94 ! [V_k2_2,V_k1_2] : % 18.97/18.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2))) % 18.97/18.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_rel__simps_I15_J,axiom, % 18.97/18.94 ! [V_l_2,V_k_2] : % 18.97/18.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2))) % 18.97/18.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_mult__Bit1,axiom, % 18.97/18.94 ! [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) ). % 18.97/18.94 % 18.97/18.94 fof(fact_rel__simps_I11_J,axiom, % 18.97/18.94 ! [V_k_2] : % 18.97/18.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin)) % 18.97/18.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_rel__simps_I25_J,axiom, % 18.97/18.94 ! [V_k_2] : % 18.97/18.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2))) % 18.97/18.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_diff__bin__simps_I5_J,axiom, % 18.97/18.94 ! [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)) ). % 18.97/18.94 % 18.97/18.94 fof(fact_diff__bin__simps_I6_J,axiom, % 18.97/18.94 ! [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)) ). % 18.97/18.94 % 18.97/18.94 fof(fact_diff__bin__simps_I8_J,axiom, % 18.97/18.94 ! [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)) ). % 18.97/18.94 % 18.97/18.94 fof(fact_add__Bit1__Bit1,axiom, % 18.97/18.94 ! [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))) ). % 18.97/18.94 % 18.97/18.94 fof(fact_double__number__of__Bit0,axiom, % 18.97/18.94 ! [V_w,T_a] : % 18.97/18.94 ( class_Int_Onumber__ring(T_a) % 18.97/18.94 => 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)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_number__of1,axiom, % 18.97/18.94 ! [V_n] : % 18.97/18.94 ( 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))) % 18.97/18.94 => ( 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)))) % 18.97/18.94 & 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)))) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_mult__2,axiom, % 18.97/18.94 ! [V_z,T_a] : % 18.97/18.94 ( class_Int_Onumber__ring(T_a) % 18.97/18.94 => 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) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_mult__2__right,axiom, % 18.97/18.94 ! [V_z,T_a] : % 18.97/18.94 ( class_Int_Onumber__ring(T_a) % 18.97/18.94 => 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) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_one__add__one__is__two,axiom, % 18.97/18.94 ! [T_a] : % 18.97/18.94 ( class_Int_Onumber__ring(T_a) % 18.97/18.94 => 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))) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_zero__power2,axiom, % 18.97/18.94 ! [T_a] : % 18.97/18.94 ( class_Rings_Osemiring__1(T_a) % 18.97/18.94 => 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) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_zero__eq__power2,axiom, % 18.97/18.94 ! [V_a_2,T_b] : % 18.97/18.94 ( class_Rings_Oring__1__no__zero__divisors(T_b) % 18.97/18.94 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(T_b) % 18.97/18.94 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_numeral__2__eq__2,axiom, % 18.97/18.94 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))) ). % 18.97/18.94 % 18.97/18.94 fof(fact_semiring__norm_I115_J,axiom, % 18.97/18.94 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))) ). % 18.97/18.94 % 18.97/18.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom, % 18.97/18.94 ! [V_x,T_a] : % 18.97/18.94 ( class_Rings_Ocomm__semiring__1(T_a) % 18.97/18.94 => 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)))) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_power2__eq__square,axiom, % 18.97/18.94 ! [V_a,T_a] : % 18.97/18.94 ( class_Groups_Omonoid__mult(T_a) % 18.97/18.94 => 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) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom, % 18.97/18.94 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))))) ). % 18.97/18.94 % 18.97/18.94 fof(fact_add__2__eq__Suc_H,axiom, % 18.97/18.94 ! [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)) ). % 18.97/18.94 % 18.97/18.94 fof(fact_add__2__eq__Suc,axiom, % 18.97/18.94 ! [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)) ). % 18.97/18.94 % 18.97/18.94 fof(fact_one__power2,axiom, % 18.97/18.94 ! [T_a] : % 18.97/18.94 ( class_Rings_Osemiring__1(T_a) % 18.97/18.94 => 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) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_power2__minus,axiom, % 18.97/18.94 ! [V_a,T_a] : % 18.97/18.94 ( class_Rings_Oring__1(T_a) % 18.97/18.94 => 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)))) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_nat__mult__2,axiom, % 18.97/18.94 ! [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) ). % 18.97/18.94 % 18.97/18.94 fof(fact_nat__mult__2__right,axiom, % 18.97/18.94 ! [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) ). % 18.97/18.94 % 18.97/18.94 fof(fact_power__even__eq,axiom, % 18.97/18.94 ! [V_n,V_a,T_a] : % 18.97/18.94 ( class_Groups_Omonoid__mult(T_a) % 18.97/18.94 => 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)))) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_transfer__int__nat__numerals_I3_J,axiom, % 18.97/18.94 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)))) ). % 18.97/18.94 % 18.97/18.94 fof(fact_transfer__nat__int__numerals_I3_J,axiom, % 18.97/18.94 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)))) ). % 18.97/18.94 % 18.97/18.94 fof(fact_abs__power2,axiom, % 18.97/18.94 ! [V_a,T_a] : % 18.97/18.94 ( class_Rings_Olinordered__idom(T_a) % 18.97/18.94 => 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)))) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_power2__abs,axiom, % 18.97/18.94 ! [V_a,T_a] : % 18.97/18.94 ( class_Rings_Olinordered__idom(T_a) % 18.97/18.94 => 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)))) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_nat__1__add__1,axiom, % 18.97/18.94 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))) ). % 18.97/18.94 % 18.97/18.94 fof(fact_mod2__Suc__Suc,axiom, % 18.97/18.94 ! [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)))) ). % 18.97/18.94 % 18.97/18.94 fof(fact_div2__Suc__Suc,axiom, % 18.97/18.94 ! [V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ). % 18.97/18.94 % 18.97/18.94 fof(fact_zmod__number__of__Bit0,axiom, % 18.97/18.94 ! [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))) ). % 18.97/18.94 % 18.97/18.94 fof(fact_add__self__div__2,axiom, % 18.97/18.94 ! [V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = V_m ). % 18.97/18.94 % 18.97/18.94 fof(fact_zero__le__power2,axiom, % 18.97/18.94 ! [V_a,T_a] : % 18.97/18.94 ( class_Rings_Olinordered__idom(T_a) % 18.97/18.94 => 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)))))) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_power2__le__imp__le,axiom, % 18.97/18.94 ! [V_y,V_x,T_a] : % 18.97/18.94 ( class_Rings_Olinordered__semidom(T_a) % 18.97/18.94 => ( 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)))))) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 18.97/18.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_power2__eq__imp__eq,axiom, % 18.97/18.94 ! [V_y,V_x,T_a] : % 18.97/18.94 ( class_Rings_Olinordered__semidom(T_a) % 18.97/18.94 => ( 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)))) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 18.97/18.94 => V_x = V_y ) ) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_zero__less__power2,axiom, % 18.97/18.94 ! [V_a_2,T_b] : % 18.97/18.94 ( class_Rings_Olinordered__idom(T_b) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) % 18.97/18.94 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_power2__less__0,axiom, % 18.97/18.94 ! [V_a,T_a] : % 18.97/18.94 ( class_Rings_Olinordered__idom(T_a) % 18.97/18.94 => ~ 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))) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_sum__power2__eq__zero__iff,axiom, % 18.97/18.94 ! [V_y_2,V_x_2,T_b] : % 18.97/18.94 ( class_Rings_Olinordered__idom(T_b) % 18.97/18.94 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(T_b) % 18.97/18.94 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b) % 18.97/18.94 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_power2__eq__square__number__of,axiom, % 18.97/18.94 ! [V_w,T_b] : % 18.97/18.94 ( ( class_Groups_Omonoid__mult(T_b) % 18.97/18.94 & class_Int_Onumber(T_b) ) % 18.97/18.94 => 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)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_less__2__cases,axiom, % 18.97/18.94 ! [V_n] : % 18.97/18.94 ( 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))))) % 18.97/18.94 => ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 18.97/18.94 | V_n = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_nat__2,axiom, % 18.97/18.94 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))) ). % 18.97/18.94 % 18.97/18.94 fof(fact_power2__eq__1__iff,axiom, % 18.97/18.94 ! [V_a_2,T_b] : % 18.97/18.94 ( class_Rings_Oring__1__no__zero__divisors(T_b) % 18.97/18.94 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(T_b) % 18.97/18.94 <=> ( V_a_2 = c_Groups_Oone__class_Oone(T_b) % 18.97/18.94 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b)) ) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom, % 18.97/18.94 ! [V_n,V_x,T_a] : % 18.97/18.94 ( class_Rings_Ocomm__semiring__1(T_a) % 18.97/18.94 => 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)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_power__minus__even,axiom, % 18.97/18.94 ! [V_n,V_a,T_a] : % 18.97/18.94 ( class_Rings_Oring__1(T_a) % 18.97/18.94 => 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)) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_power2__less__imp__less,axiom, % 18.97/18.94 ! [V_y,V_x,T_a] : % 18.97/18.94 ( class_Rings_Olinordered__semidom(T_a) % 18.97/18.94 => ( 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)))))) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 18.97/18.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_sum__power2__ge__zero,axiom, % 18.97/18.94 ! [V_y,V_x,T_a] : % 18.97/18.94 ( class_Rings_Olinordered__idom(T_a) % 18.97/18.94 => 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))))))) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_sum__power2__le__zero__iff,axiom, % 18.97/18.94 ! [V_y_2,V_x_2,T_b] : % 18.97/18.94 ( class_Rings_Olinordered__idom(T_b) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(T_b))) % 18.97/18.94 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b) % 18.97/18.94 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_sum__power2__gt__zero__iff,axiom, % 18.97/18.94 ! [V_y_2,V_x_2,T_b] : % 18.97/18.94 ( class_Rings_Olinordered__idom(T_b) % 18.97/18.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) % 18.97/18.94 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_b) % 18.97/18.94 | V_y_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_not__sum__power2__lt__zero,axiom, % 18.97/18.94 ! [V_y,V_x,T_a] : % 18.97/18.94 ( class_Rings_Olinordered__idom(T_a) % 18.97/18.94 => ~ 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))) ) ). % 18.97/18.94 % 18.97/18.94 fof(fact_power2__sum,axiom, % 18.97/18.94 ! [V_y,V_x,T_a] : % 18.97/18.94 ( class_Int_Onumber__ring(T_a) % 18.97/18.95 => 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)) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_zero__le__even__power_H,axiom, % 18.97/18.95 ! [V_n,V_a,T_a] : % 18.97/18.95 ( class_Rings_Olinordered__idom(T_a) % 18.97/18.95 => 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)))) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J,axiom, % 18.97/18.95 ! [V_n,V_x,T_a] : % 18.97/18.95 ( class_Rings_Ocomm__semiring__1(T_a) % 18.97/18.95 => 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))) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_power__odd__eq,axiom, % 18.97/18.95 ! [V_n,V_a,T_a] : % 18.97/18.95 ( class_Groups_Omonoid__mult(T_a) % 18.97/18.95 => 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))))) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_power__minus1__even,axiom, % 18.97/18.95 ! [V_n,T_a] : % 18.97/18.95 ( class_Rings_Oring__1(T_a) % 18.97/18.95 => 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) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_zdiv__number__of__Bit1,axiom, % 18.97/18.95 ! [V_v,V_w] : % 18.97/18.95 ( ( 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))) % 18.97/18.95 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) ) % 18.97/18.95 & ( ~ 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))) % 18.97/18.95 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_mod2__gr__0,axiom, % 18.97/18.95 ! [V_m_2] : % 18.97/18.95 ( 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)))))) % 18.97/18.95 <=> 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) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_div__2__gt__zero,axiom, % 18.97/18.95 ! [V_n] : % 18.97/18.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) % 18.97/18.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_power2__diff,axiom, % 18.97/18.95 ! [V_y,V_x,T_a] : % 18.97/18.95 ( class_Int_Onumber__ring(T_a) % 18.97/18.95 => 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)) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_odd__0__le__power__imp__0__le,axiom, % 18.97/18.95 ! [V_n,V_a,T_a] : % 18.97/18.95 ( class_Rings_Olinordered__idom(T_a) % 18.97/18.95 => ( 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))))) % 18.97/18.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_odd__power__less__zero,axiom, % 18.97/18.95 ! [V_n,V_a,T_a] : % 18.97/18.95 ( class_Rings_Olinordered__idom(T_a) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 18.97/18.95 => 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))) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_power__minus1__odd,axiom, % 18.97/18.95 ! [V_n,T_a] : % 18.97/18.95 ( class_Rings_Oring__1(T_a) % 18.97/18.95 => 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)) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_power__m1__even,axiom, % 18.97/18.95 ! [V_n,T_a] : % 18.97/18.95 ( class_Int_Onumber__ring(T_a) % 18.97/18.95 => 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) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_power__m1__odd,axiom, % 18.97/18.95 ! [V_n,T_a] : % 18.97/18.95 ( class_Int_Onumber__ring(T_a) % 18.97/18.95 => 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) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_Suc__n__div__2__gt__zero,axiom, % 18.97/18.95 ! [V_n] : % 18.97/18.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 18.97/18.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_int__of__code,axiom, % 18.97/18.95 ! [V_k] : % 18.97/18.95 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 18.97/18.95 => hAPP(c_Code__Numeral_Oint__of,V_k) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 18.97/18.95 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 18.97/18.95 => ( ( 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) % 18.97/18.95 => hAPP(c_Code__Numeral_Oint__of,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_k),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) % 18.97/18.95 & ( 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) % 18.97/18.95 => hAPP(c_Code__Numeral_Oint__of,V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_k),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_one__code__numeral__code,axiom, % 18.97/18.95 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)) ). % 18.97/18.95 % 18.97/18.95 fof(fact_half__gt__zero,axiom, % 18.97/18.95 ! [V_r,T_a] : % 18.97/18.95 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 18.97/18.95 & class_Int_Onumber__ring(T_a) ) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r)) % 18.97/18.95 => 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)))))) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_half__gt__zero__iff,axiom, % 18.97/18.95 ! [V_r_2,T_b] : % 18.97/18.95 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 18.97/18.95 & class_Int_Onumber__ring(T_b) ) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_r_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) % 18.97/18.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_r_2)) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J,axiom, % 18.97/18.95 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ). % 18.97/18.95 % 18.97/18.95 fof(fact_nat__intermed__int__val,axiom, % 18.97/18.95 ! [V_k_2,V_f_2,V_n_2,V_m_2] : % 18.97/18.95 ( ! [B_i] : % 18.97/18.95 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i)) % 18.97/18.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) ) % 18.97/18.95 => 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))) ) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,V_m_2)),V_k_2)) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2))) % 18.97/18.95 => ? [B_i] : % 18.97/18.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i)) % 18.97/18.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) % 18.97/18.95 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_code__numeral__zero__minus__one,axiom, % 18.97/18.95 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) ). % 18.97/18.95 % 18.97/18.95 fof(fact_divide__zero,axiom, % 18.97/18.95 ! [V_a,T_a] : % 18.97/18.95 ( class_Rings_Odivision__ring__inverse__zero(T_a) % 18.97/18.95 => 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) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_divide__zero__left,axiom, % 18.97/18.95 ! [V_a,T_a] : % 18.97/18.95 ( class_Rings_Odivision__ring(T_a) % 18.97/18.95 => 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) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_add__divide__distrib,axiom, % 18.97/18.95 ! [V_c,V_b,V_a,T_a] : % 18.97/18.95 ( class_Rings_Odivision__ring(T_a) % 18.97/18.95 => 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)) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_times__divide__times__eq,axiom, % 18.97/18.95 ! [V_w,V_z,V_y,V_x,T_a] : % 18.97/18.95 ( class_Fields_Ofield__inverse__zero(T_a) % 18.97/18.95 => 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)) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_times__divide__eq__right,axiom, % 18.97/18.95 ! [V_c,V_b,V_a,T_a] : % 18.97/18.95 ( class_Rings_Odivision__ring(T_a) % 18.97/18.95 => 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) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_diff__divide__distrib,axiom, % 18.97/18.95 ! [V_c,V_b,V_a,T_a] : % 18.97/18.95 ( class_Rings_Odivision__ring(T_a) % 18.97/18.95 => 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)) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_divide__1,axiom, % 18.97/18.95 ! [V_a,T_a] : % 18.97/18.95 ( class_Rings_Odivision__ring(T_a) % 18.97/18.95 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_minus__divide__right,axiom, % 18.97/18.95 ! [V_b,V_a,T_a] : % 18.97/18.95 ( class_Fields_Ofield__inverse__zero(T_a) % 18.97/18.95 => 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)) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_minus__divide__divide,axiom, % 18.97/18.95 ! [V_b,V_a,T_a] : % 18.97/18.95 ( class_Fields_Ofield__inverse__zero(T_a) % 18.97/18.95 => 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) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_minus__divide__left,axiom, % 18.97/18.95 ! [V_b,V_a,T_a] : % 18.97/18.95 ( class_Rings_Odivision__ring(T_a) % 18.97/18.95 => 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) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_power__divide,axiom, % 18.97/18.95 ! [V_n,V_b,V_a,T_a] : % 18.97/18.95 ( class_Fields_Ofield__inverse__zero(T_a) % 18.97/18.95 => 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)) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_abs__divide,axiom, % 18.97/18.95 ! [V_b,V_a,T_a] : % 18.97/18.95 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 18.97/18.95 => 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)) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J,axiom, % 18.97/18.95 c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ). % 18.97/18.95 % 18.97/18.95 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J,axiom, % 18.97/18.95 ! [V_y,V_x] : % 18.97/18.95 ( c_Nat__Transfer_Ois__nat(V_x) % 18.97/18.95 => ( c_Nat__Transfer_Ois__nat(V_y) % 18.97/18.95 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J,axiom, % 18.97/18.95 ! [V_z] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z)) ). % 18.97/18.95 % 18.97/18.95 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J,axiom, % 18.97/18.95 c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 18.97/18.95 % 18.97/18.95 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J,axiom, % 18.97/18.95 ! [V_y,V_x] : % 18.97/18.95 ( c_Nat__Transfer_Ois__nat(V_x) % 18.97/18.95 => ( c_Nat__Transfer_Ois__nat(V_y) % 18.97/18.95 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_Divides_Otransfer__int__nat__function__closures_I2_J,axiom, % 18.97/18.95 ! [V_y,V_x] : % 18.97/18.95 ( c_Nat__Transfer_Ois__nat(V_x) % 18.97/18.95 => ( c_Nat__Transfer_Ois__nat(V_y) % 18.97/18.95 => c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_Divides_Otransfer__int__nat__function__closures_I1_J,axiom, % 18.97/18.95 ! [V_y,V_x] : % 18.97/18.95 ( c_Nat__Transfer_Ois__nat(V_x) % 18.97/18.95 => ( c_Nat__Transfer_Ois__nat(V_y) % 18.97/18.95 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J,axiom, % 18.97/18.95 ! [V_n,V_x] : % 18.97/18.95 ( c_Nat__Transfer_Ois__nat(V_x) % 18.97/18.95 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_zero__le__divide__iff,axiom, % 18.97/18.95 ! [V_b_2,V_a_2,T_b] : % 18.97/18.95 ( class_Fields_Olinordered__field__inverse__zero(T_b) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2))) % 18.97/18.95 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) % 18.97/18.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) % 18.97/18.95 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) % 18.97/18.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_divide__le__0__iff,axiom, % 18.97/18.95 ! [V_b_2,V_a_2,T_b] : % 18.97/18.95 ( class_Fields_Olinordered__field__inverse__zero(T_b) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))) % 18.97/18.95 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) % 18.97/18.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) % 18.97/18.95 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) % 18.97/18.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_divide__right__mono,axiom, % 18.97/18.95 ! [V_c,V_b,V_a,T_a] : % 18.97/18.95 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 18.97/18.95 => 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))) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_divide__right__mono__neg,axiom, % 18.97/18.95 ! [V_c,V_b,V_a,T_a] : % 18.97/18.95 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 18.97/18.95 => 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))) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_divide__strict__right__mono__neg,axiom, % 18.97/18.95 ! [V_c,V_a,V_b,T_a] : % 18.97/18.95 ( class_Fields_Olinordered__field(T_a) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 18.97/18.95 => 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))) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_divide__strict__right__mono,axiom, % 18.97/18.95 ! [V_c,V_b,V_a,T_a] : % 18.97/18.95 ( class_Fields_Olinordered__field(T_a) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 18.97/18.95 => 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))) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_divide__neg__neg,axiom, % 18.97/18.95 ! [V_y,V_x,T_a] : % 18.97/18.95 ( class_Fields_Olinordered__field(T_a) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 18.97/18.95 => 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))) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_divide__neg__pos,axiom, % 18.97/18.95 ! [V_y,V_x,T_a] : % 18.97/18.95 ( class_Fields_Olinordered__field(T_a) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 18.97/18.95 => 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))) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_divide__pos__neg,axiom, % 18.97/18.95 ! [V_y,V_x,T_a] : % 18.97/18.95 ( class_Fields_Olinordered__field(T_a) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 18.97/18.95 => 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))) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_divide__pos__pos,axiom, % 18.97/18.95 ! [V_y,V_x,T_a] : % 18.97/18.95 ( class_Fields_Olinordered__field(T_a) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 18.97/18.95 => 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))) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_divide__less__0__iff,axiom, % 18.97/18.95 ! [V_b_2,V_a_2,T_b] : % 18.97/18.95 ( class_Fields_Olinordered__field__inverse__zero(T_b) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))) % 18.97/18.95 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) % 18.97/18.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) % 18.97/18.95 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) % 18.97/18.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_zero__less__divide__iff,axiom, % 18.97/18.95 ! [V_b_2,V_a_2,T_b] : % 18.97/18.95 ( class_Fields_Olinordered__field__inverse__zero(T_b) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2))) % 18.97/18.95 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) % 18.97/18.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) % 18.97/18.95 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) % 18.97/18.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_eq__divide__eq,axiom, % 18.97/18.95 ! [V_c_2,V_b_2,V_a_2,T_b] : % 18.97/18.95 ( class_Fields_Ofield__inverse__zero(T_b) % 18.97/18.95 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) % 18.97/18.95 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b) % 18.97/18.95 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) = V_b_2 ) % 18.97/18.95 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b) % 18.97/18.95 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_divide__eq__eq,axiom, % 18.97/18.95 ! [V_a_2,V_c_2,V_b_2,T_b] : % 18.97/18.95 ( class_Fields_Ofield__inverse__zero(T_b) % 18.97/18.95 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) = V_a_2 % 18.97/18.95 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b) % 18.97/18.95 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) ) % 18.97/18.95 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b) % 18.97/18.95 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_mult__divide__mult__cancel__right,axiom, % 18.97/18.95 ! [V_b,V_a,V_c,T_a] : % 18.97/18.95 ( class_Fields_Ofield__inverse__zero(T_a) % 18.97/18.95 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 18.97/18.95 => 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) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_mult__divide__mult__cancel__left,axiom, % 18.97/18.95 ! [V_b,V_a,V_c,T_a] : % 18.97/18.95 ( class_Fields_Ofield__inverse__zero(T_a) % 18.97/18.95 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 18.97/18.95 => 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) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_frac__eq__eq,axiom, % 18.97/18.95 ! [V_w_2,V_x_2,V_z_2,V_y_2,T_b] : % 18.97/18.95 ( class_Fields_Ofield(T_b) % 18.97/18.95 => ( V_y_2 != c_Groups_Ozero__class_Ozero(T_b) % 18.97/18.95 => ( V_z_2 != c_Groups_Ozero__class_Ozero(T_b) % 18.97/18.95 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_x_2),V_y_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_w_2),V_z_2) % 18.97/18.95 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_z_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_y_2) ) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_eq__divide__imp,axiom, % 18.97/18.95 ! [V_b,V_a,V_c,T_a] : % 18.97/18.95 ( class_Rings_Odivision__ring(T_a) % 18.97/18.95 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 18.97/18.95 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) = V_b % 18.97/18.95 => V_a = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_divide__eq__imp,axiom, % 18.97/18.95 ! [V_a,V_b,V_c,T_a] : % 18.97/18.95 ( class_Rings_Odivision__ring(T_a) % 18.97/18.95 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 18.97/18.95 => ( V_b = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) % 18.97/18.95 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) = V_a ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_nonzero__divide__eq__eq,axiom, % 18.97/18.95 ! [V_a_2,V_b_2,V_c_2,T_b] : % 18.97/18.95 ( class_Rings_Odivision__ring(T_b) % 18.97/18.95 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b) % 18.97/18.95 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) = V_a_2 % 18.97/18.95 <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_nonzero__eq__divide__eq,axiom, % 18.97/18.95 ! [V_b_2,V_a_2,V_c_2,T_b] : % 18.97/18.95 ( class_Rings_Odivision__ring(T_b) % 18.97/18.95 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b) % 18.97/18.95 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) % 18.97/18.95 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) = V_b_2 ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_right__inverse__eq,axiom, % 18.97/18.95 ! [V_a_2,V_b_2,T_b] : % 18.97/18.95 ( class_Rings_Odivision__ring(T_b) % 18.97/18.95 => ( V_b_2 != c_Groups_Ozero__class_Ozero(T_b) % 18.97/18.95 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2) = c_Groups_Oone__class_Oone(T_b) % 18.97/18.95 <=> V_a_2 = V_b_2 ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_divide__self,axiom, % 18.97/18.95 ! [V_a,T_a] : % 18.97/18.95 ( class_Rings_Odivision__ring(T_a) % 18.97/18.95 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 18.97/18.95 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_divide__self__if,axiom, % 18.97/18.95 ! [V_a,T_a] : % 18.97/18.95 ( class_Rings_Odivision__ring__inverse__zero(T_a) % 18.97/18.95 => ( ( V_a = c_Groups_Ozero__class_Ozero(T_a) % 18.97/18.95 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) % 18.97/18.95 & ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 18.97/18.95 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_nonzero__minus__divide__divide,axiom, % 18.97/18.95 ! [V_a,V_b,T_a] : % 18.97/18.95 ( class_Rings_Odivision__ring(T_a) % 18.97/18.95 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 18.97/18.95 => 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) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_nonzero__minus__divide__right,axiom, % 18.97/18.95 ! [V_a,V_b,T_a] : % 18.97/18.95 ( class_Rings_Odivision__ring(T_a) % 18.97/18.95 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 18.97/18.95 => 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)) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_nonzero__power__divide,axiom, % 18.97/18.95 ! [V_n,V_a,V_b,T_a] : % 18.97/18.95 ( class_Fields_Ofield(T_a) % 18.97/18.95 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 18.97/18.95 => 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)) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_nonzero__abs__divide,axiom, % 18.97/18.95 ! [V_a,V_b,T_a] : % 18.97/18.95 ( class_Fields_Olinordered__field(T_a) % 18.97/18.95 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 18.97/18.95 => 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)) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_power__one__over,axiom, % 18.97/18.95 ! [V_n,V_a,T_a] : % 18.97/18.95 ( class_Fields_Ofield__inverse__zero(T_a) % 18.97/18.95 => 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) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J,axiom, % 18.97/18.95 ! [V_y,V_x] : % 18.97/18.95 ( c_Nat__Transfer_Ois__nat(V_x) % 18.97/18.95 => ( c_Nat__Transfer_Ois__nat(V_y) % 18.97/18.95 => c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(V_x,V_y)) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_divide__nonpos__neg,axiom, % 18.97/18.95 ! [V_y,V_x,T_a] : % 18.97/18.95 ( class_Fields_Olinordered__field(T_a) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 18.97/18.95 => 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))) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_divide__nonpos__pos,axiom, % 18.97/18.95 ! [V_y,V_x,T_a] : % 18.97/18.95 ( class_Fields_Olinordered__field(T_a) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 18.97/18.95 => 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))) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_frac__le,axiom, % 18.97/18.95 ! [V_z,V_w,V_y,V_x,T_a] : % 18.97/18.95 ( class_Fields_Olinordered__field(T_a) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w)) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z)) % 18.97/18.95 => 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))) ) ) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_frac__less,axiom, % 18.97/18.95 ! [V_z,V_w,V_y,V_x,T_a] : % 18.97/18.95 ( class_Fields_Olinordered__field(T_a) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w)) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z)) % 18.97/18.95 => 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))) ) ) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_frac__less2,axiom, % 18.97/18.95 ! [V_z,V_w,V_y,V_x,T_a] : % 18.97/18.95 ( class_Fields_Olinordered__field(T_a) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w)) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_w),V_z)) % 18.97/18.95 => 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))) ) ) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_divide__nonneg__neg,axiom, % 18.97/18.95 ! [V_y,V_x,T_a] : % 18.97/18.95 ( class_Fields_Olinordered__field(T_a) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 18.97/18.95 => 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))) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_divide__nonneg__pos,axiom, % 18.97/18.95 ! [V_y,V_x,T_a] : % 18.97/18.95 ( class_Fields_Olinordered__field(T_a) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 18.97/18.95 => 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))) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_divide__strict__left__mono__neg,axiom, % 18.97/18.95 ! [V_c,V_b,V_a,T_a] : % 18.97/18.95 ( class_Fields_Olinordered__field(T_a) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 18.97/18.95 => ( 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))) % 18.97/18.95 => 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))) ) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_divide__strict__left__mono,axiom, % 18.97/18.95 ! [V_c,V_a,V_b,T_a] : % 18.97/18.95 ( class_Fields_Olinordered__field(T_a) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 18.97/18.95 => ( 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))) % 18.97/18.95 => 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))) ) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_neg__divide__less__eq,axiom, % 18.97/18.95 ! [V_a_2,V_b_2,V_c_2,T_b] : % 18.97/18.95 ( class_Fields_Olinordered__field(T_b) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2)) % 18.97/18.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_neg__less__divide__eq,axiom, % 18.97/18.95 ! [V_b_2,V_a_2,V_c_2,T_b] : % 18.97/18.95 ( class_Fields_Olinordered__field(T_b) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2))) % 18.97/18.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_mult__imp__less__div__pos,axiom, % 18.97/18.95 ! [V_x,V_z,V_y,T_a] : % 18.97/18.95 ( class_Fields_Olinordered__field(T_a) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 18.97/18.95 => ( 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)) % 18.97/18.95 => 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))) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_mult__imp__div__pos__less,axiom, % 18.97/18.95 ! [V_z,V_x,V_y,T_a] : % 18.97/18.95 ( class_Fields_Olinordered__field(T_a) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 18.97/18.95 => ( 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))) % 18.97/18.95 => 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)) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_pos__divide__less__eq,axiom, % 18.97/18.95 ! [V_a_2,V_b_2,V_c_2,T_b] : % 18.97/18.95 ( class_Fields_Olinordered__field(T_b) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2)) % 18.97/18.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_pos__less__divide__eq,axiom, % 18.97/18.95 ! [V_b_2,V_a_2,V_c_2,T_b] : % 18.97/18.95 ( class_Fields_Olinordered__field(T_b) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2))) % 18.97/18.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_divide__less__eq,axiom, % 18.97/18.95 ! [V_a_2,V_c_2,V_b_2,T_b] : % 18.97/18.95 ( class_Fields_Olinordered__field__inverse__zero(T_b) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2)) % 18.97/18.95 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 18.97/18.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) % 18.97/18.95 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 18.97/18.95 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 18.97/18.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) % 18.97/18.95 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 18.97/18.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_less__divide__eq,axiom, % 18.97/18.95 ! [V_c_2,V_b_2,V_a_2,T_b] : % 18.97/18.95 ( class_Fields_Olinordered__field__inverse__zero(T_b) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2))) % 18.97/18.95 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 18.97/18.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) % 18.97/18.95 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 18.97/18.95 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 18.97/18.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) % 18.97/18.95 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 18.97/18.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_is__nat__def,axiom, % 18.97/18.95 ! [V_x_2] : % 18.97/18.95 ( c_Nat__Transfer_Ois__nat(V_x_2) % 18.97/18.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_add__frac__eq,axiom, % 18.97/18.95 ! [V_w,V_x,V_z,V_y,T_a] : % 18.97/18.95 ( class_Fields_Ofield(T_a) % 18.97/18.95 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 18.97/18.95 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 18.97/18.95 => 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)) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_divide__add__eq__iff,axiom, % 18.97/18.95 ! [V_y,V_x,V_z,T_a] : % 18.97/18.95 ( class_Fields_Ofield(T_a) % 18.97/18.95 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 18.97/18.95 => 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) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_add__frac__num,axiom, % 18.97/18.95 ! [V_z,V_x,V_y,T_a] : % 18.97/18.95 ( class_Fields_Ofield__inverse__zero(T_a) % 18.97/18.95 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 18.97/18.95 => 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) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_add__divide__eq__iff,axiom, % 18.97/18.95 ! [V_y,V_x,V_z,T_a] : % 18.97/18.95 ( class_Fields_Ofield(T_a) % 18.97/18.95 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 18.97/18.95 => 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) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_add__num__frac,axiom, % 18.97/18.95 ! [V_x,V_z,V_y,T_a] : % 18.97/18.95 ( class_Fields_Ofield__inverse__zero(T_a) % 18.97/18.95 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 18.97/18.95 => 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) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_diff__frac__eq,axiom, % 18.97/18.95 ! [V_w,V_x,V_z,V_y,T_a] : % 18.97/18.95 ( class_Fields_Ofield(T_a) % 18.97/18.95 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 18.97/18.95 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 18.97/18.95 => 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)) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_divide__diff__eq__iff,axiom, % 18.97/18.95 ! [V_y,V_x,V_z,T_a] : % 18.97/18.95 ( class_Fields_Ofield(T_a) % 18.97/18.95 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 18.97/18.95 => 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) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_diff__divide__eq__iff,axiom, % 18.97/18.95 ! [V_y,V_x,V_z,T_a] : % 18.97/18.95 ( class_Fields_Ofield(T_a) % 18.97/18.95 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 18.97/18.95 => 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) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_divide__eq__eq__number__of1,axiom, % 18.97/18.95 ! [V_a_2,V_w_2,V_b_2,T_b] : % 18.97/18.95 ( ( class_Fields_Ofield__inverse__zero(T_b) % 18.97/18.95 & class_Int_Onumber(T_b) ) % 18.97/18.95 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) = V_a_2 % 18.97/18.95 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b) % 18.97/18.95 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) ) % 18.97/18.95 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) % 18.97/18.95 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_divide__eq__eq__number__of,axiom, % 18.97/18.95 ! [V_w_2,V_c_2,V_b_2,T_b] : % 18.97/18.95 ( ( class_Fields_Ofield__inverse__zero(T_b) % 18.97/18.95 & class_Int_Onumber(T_b) ) % 18.97/18.95 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) % 18.97/18.95 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b) % 18.97/18.95 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2) ) % 18.97/18.95 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b) % 18.97/18.95 => hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_eq__divide__eq__number__of,axiom, % 18.97/18.95 ! [V_c_2,V_b_2,V_w_2,T_b] : % 18.97/18.95 ( ( class_Fields_Ofield__inverse__zero(T_b) % 18.97/18.95 & class_Int_Onumber(T_b) ) % 18.97/18.95 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) % 18.97/18.95 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b) % 18.97/18.95 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2) = V_b_2 ) % 18.97/18.95 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b) % 18.97/18.95 => hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_eq__divide__eq__number__of1,axiom, % 18.97/18.95 ! [V_w_2,V_b_2,V_a_2,T_b] : % 18.97/18.95 ( ( class_Fields_Ofield__inverse__zero(T_b) % 18.97/18.95 & class_Int_Onumber(T_b) ) % 18.97/18.95 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) % 18.97/18.95 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b) % 18.97/18.95 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) = V_b_2 ) % 18.97/18.95 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) % 18.97/18.95 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_less__half__sum,axiom, % 18.97/18.95 ! [V_b,V_a,T_a] : % 18.97/18.95 ( class_Fields_Olinordered__field(T_a) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 18.97/18.95 => 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))))) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_gt__half__sum,axiom, % 18.97/18.95 ! [V_b,V_a,T_a] : % 18.97/18.95 ( class_Fields_Olinordered__field(T_a) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 18.97/18.95 => 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)) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_divide__Numeral0,axiom, % 18.97/18.95 ! [V_x,T_a] : % 18.97/18.95 ( ( class_Fields_Ofield__inverse__zero(T_a) % 18.97/18.95 & class_Int_Onumber__ring(T_a) ) % 18.97/18.95 => 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) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_abs__div__pos,axiom, % 18.97/18.95 ! [V_x,V_y,T_a] : % 18.97/18.95 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 18.97/18.95 => 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)) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_divide__Numeral1,axiom, % 18.97/18.95 ! [V_x,T_a] : % 18.97/18.95 ( ( class_Fields_Ofield(T_a) % 18.97/18.95 & class_Int_Onumber__ring(T_a) ) % 18.97/18.95 => 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 ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_divide__numeral__1,axiom, % 18.97/18.95 ! [V_a,T_a] : % 18.97/18.95 ( ( class_Fields_Ofield(T_a) % 18.97/18.95 & class_Int_Onumber__ring(T_a) ) % 18.97/18.95 => 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 ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_divide__minus1,axiom, % 18.97/18.95 ! [V_x,T_a] : % 18.97/18.95 ( ( class_Fields_Ofield__inverse__zero(T_a) % 18.97/18.95 & class_Int_Onumber__ring(T_a) ) % 18.97/18.95 => 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) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_zero__code__numeral__code,axiom, % 18.97/18.95 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) ). % 18.97/18.95 % 18.97/18.95 fof(fact_le__divide__eq,axiom, % 18.97/18.95 ! [V_c_2,V_b_2,V_a_2,T_b] : % 18.97/18.95 ( class_Fields_Olinordered__field__inverse__zero(T_b) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2))) % 18.97/18.95 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 18.97/18.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) % 18.97/18.95 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 18.97/18.95 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 18.97/18.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) % 18.97/18.95 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 18.97/18.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_divide__le__eq,axiom, % 18.97/18.95 ! [V_a_2,V_c_2,V_b_2,T_b] : % 18.97/18.95 ( class_Fields_Olinordered__field__inverse__zero(T_b) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2)) % 18.97/18.95 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 18.97/18.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) % 18.97/18.95 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 18.97/18.95 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 18.97/18.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) % 18.97/18.95 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 18.97/18.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_pos__le__divide__eq,axiom, % 18.97/18.95 ! [V_b_2,V_a_2,V_c_2,T_b] : % 18.97/18.95 ( class_Fields_Olinordered__field(T_b) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2))) % 18.97/18.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_pos__divide__le__eq,axiom, % 18.97/18.95 ! [V_a_2,V_b_2,V_c_2,T_b] : % 18.97/18.95 ( class_Fields_Olinordered__field(T_b) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2)) % 18.97/18.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_mult__imp__div__pos__le,axiom, % 18.97/18.95 ! [V_z,V_x,V_y,T_a] : % 18.97/18.95 ( class_Fields_Olinordered__field(T_a) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 18.97/18.95 => ( 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))) % 18.97/18.95 => 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)) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_mult__imp__le__div__pos,axiom, % 18.97/18.95 ! [V_x,V_z,V_y,T_a] : % 18.97/18.95 ( class_Fields_Olinordered__field(T_a) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 18.97/18.95 => ( 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)) % 18.97/18.95 => 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))) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_neg__le__divide__eq,axiom, % 18.97/18.95 ! [V_b_2,V_a_2,V_c_2,T_b] : % 18.97/18.95 ( class_Fields_Olinordered__field(T_b) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2))) % 18.97/18.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_neg__divide__le__eq,axiom, % 18.97/18.95 ! [V_a_2,V_b_2,V_c_2,T_b] : % 18.97/18.95 ( class_Fields_Olinordered__field(T_b) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2)) % 18.97/18.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_divide__left__mono,axiom, % 18.97/18.95 ! [V_c,V_a,V_b,T_a] : % 18.97/18.95 ( class_Fields_Olinordered__field(T_a) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 18.97/18.95 => ( 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))) % 18.97/18.95 => 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))) ) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_divide__left__mono__neg,axiom, % 18.97/18.95 ! [V_c,V_b,V_a,T_a] : % 18.97/18.95 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 18.97/18.95 => ( 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))) % 18.97/18.95 => 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))) ) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_less__divide__eq__number__of1,axiom, % 18.97/18.95 ! [V_w_2,V_b_2,V_a_2,T_b] : % 18.97/18.95 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 18.97/18.95 & class_Int_Onumber(T_b) ) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) % 18.97/18.95 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) % 18.97/18.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2)) ) % 18.97/18.95 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) % 18.97/18.95 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) % 18.97/18.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) ) % 18.97/18.95 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) % 18.97/18.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_less__divide__eq__number__of,axiom, % 18.97/18.95 ! [V_c_2,V_b_2,V_w_2,T_b] : % 18.97/18.95 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 18.97/18.95 & class_Int_Onumber(T_b) ) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2))) % 18.97/18.95 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 18.97/18.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2)) ) % 18.97/18.95 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 18.97/18.95 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 18.97/18.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2))) ) % 18.97/18.95 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 18.97/18.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_divide__less__eq__number__of,axiom, % 18.97/18.95 ! [V_w_2,V_c_2,V_b_2,T_b] : % 18.97/18.95 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 18.97/18.95 & class_Int_Onumber(T_b) ) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) % 18.97/18.95 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 18.97/18.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2))) ) % 18.97/18.95 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 18.97/18.95 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 18.97/18.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2)) ) % 18.97/18.95 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 18.97/18.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) ) ) ) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_divide__less__eq__number__of1,axiom, % 18.97/18.95 ! [V_a_2,V_w_2,V_b_2,T_b] : % 18.97/18.95 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 18.97/18.95 & class_Int_Onumber(T_b) ) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_a_2)) % 18.97/18.95 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) % 18.97/18.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) ) % 18.97/18.95 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) % 18.97/18.95 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) % 18.97/18.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2)) ) % 18.97/18.95 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) % 18.97/18.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_power__diff,axiom, % 18.97/18.95 ! [V_m,V_n,V_a,T_a] : % 18.97/18.95 ( class_Fields_Ofield(T_a) % 18.97/18.95 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 18.97/18.95 => 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)) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_minus1__divide,axiom, % 18.97/18.95 ! [V_x,T_a] : % 18.97/18.95 ( ( class_Fields_Ofield__inverse__zero(T_a) % 18.97/18.95 & class_Int_Onumber__ring(T_a) ) % 18.97/18.95 => 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)) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J,axiom, % 18.97/18.95 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ). % 18.97/18.95 % 18.97/18.95 fof(fact_divide__le__eq__number__of1,axiom, % 18.97/18.95 ! [V_a_2,V_w_2,V_b_2,T_b] : % 18.97/18.95 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 18.97/18.95 & class_Int_Onumber(T_b) ) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_a_2)) % 18.97/18.95 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) % 18.97/18.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) ) % 18.97/18.95 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) % 18.97/18.95 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) % 18.97/18.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2)) ) % 18.97/18.95 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) % 18.97/18.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_divide__le__eq__number__of,axiom, % 18.97/18.95 ! [V_w_2,V_c_2,V_b_2,T_b] : % 18.97/18.95 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 18.97/18.95 & class_Int_Onumber(T_b) ) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) % 18.97/18.95 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 18.97/18.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2))) ) % 18.97/18.95 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 18.97/18.95 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 18.97/18.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2)) ) % 18.97/18.95 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 18.97/18.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) ) ) ) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_le__divide__eq__number__of,axiom, % 18.97/18.95 ! [V_c_2,V_b_2,V_w_2,T_b] : % 18.97/18.95 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 18.97/18.95 & class_Int_Onumber(T_b) ) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2))) % 18.97/18.95 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 18.97/18.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2)) ) % 18.97/18.95 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 18.97/18.95 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 18.97/18.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2))) ) % 18.97/18.95 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 18.97/18.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_le__divide__eq__number__of1,axiom, % 18.97/18.95 ! [V_w_2,V_b_2,V_a_2,T_b] : % 18.97/18.95 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 18.97/18.95 & class_Int_Onumber(T_b) ) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) % 18.97/18.95 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) % 18.97/18.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2)) ) % 18.97/18.95 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) % 18.97/18.95 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) % 18.97/18.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) ) % 18.97/18.95 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) % 18.97/18.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_nat__of__aux__code,axiom, % 18.97/18.95 ! [V_n,V_i] : % 18.97/18.95 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 18.97/18.95 => c_Code__Numeral_Onat__of__aux(V_i,V_n) = V_n ) % 18.97/18.95 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 18.97/18.95 => 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)) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_code__numeral_Osize_I1_J,axiom, % 18.97/18.95 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) ). % 18.97/18.95 % 18.97/18.95 fof(fact_code__numeral_Osize_I3_J,axiom, % 18.97/18.95 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) ). % 18.97/18.95 % 18.97/18.95 fof(fact_code__numeral_Osimps_I4_J,axiom, % 18.97/18.95 ! [V_f2_2,V_f1_2,T_b] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(T_b,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = V_f1_2 ). % 18.97/18.95 % 18.97/18.95 fof(fact_log_Osimps,axiom, % 18.97/18.95 ! [V_i,V_b] : % 18.97/18.95 ( ( ( 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))) % 18.97/18.95 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) ) % 18.97/18.95 => c_Random_Olog(V_b,V_i) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) ) % 18.97/18.95 & ( ~ ( 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))) % 18.97/18.95 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) ) % 18.97/18.95 => c_Random_Olog(V_b,V_i) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),c_Random_Olog(V_b,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_i),V_b))) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_field__le__epsilon,axiom, % 18.97/18.95 ! [V_y,V_x,T_a] : % 18.97/18.95 ( class_Fields_Olinordered__field(T_a) % 18.97/18.95 => ( ! [B_e] : % 18.97/18.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_e)) % 18.97/18.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),B_e))) ) % 18.97/18.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_minus__shift__def,axiom, % 18.97/18.95 ! [V_r,V_l,V_k] : % 18.97/18.95 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) % 18.97/18.95 => 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) ) % 18.97/18.95 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) % 18.97/18.95 => 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) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_inc__shift__def,axiom, % 18.97/18.95 ! [V_k,V_v] : % 18.97/18.95 ( ( V_v = V_k % 18.97/18.95 => c_Random_Oinc__shift(V_v,V_k) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) ) % 18.97/18.95 & ( V_v != V_k % 18.97/18.95 => 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)) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_code__numeral_Osize_I4_J,axiom, % 18.97/18.95 ! [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))) ). % 18.97/18.95 % 18.97/18.95 fof(fact_code__numeral_Osize_I2_J,axiom, % 18.97/18.95 ! [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))) ). % 18.97/18.95 % 18.97/18.95 fof(fact_subtract__code__numeral__def,axiom, % 18.97/18.95 c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) ). % 18.97/18.95 % 18.97/18.95 fof(fact_minus__code__numeral__code,axiom, % 18.97/18.95 ! [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) ). % 18.97/18.95 % 18.97/18.95 fof(fact_code__numeral_Oinject,axiom, % 18.97/18.95 ! [V_code__numeral_H_2,V_code__numeral_2] : % 18.97/18.95 ( c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2) = c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_2) % 18.97/18.95 <=> V_code__numeral_2 = V_code__numeral_H_2 ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_code__numeral_Osimps_I2_J,axiom, % 18.97/18.95 ! [V_code__numeral_H] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H) ). % 18.97/18.95 % 18.97/18.95 fof(fact_code__numeral_Osimps_I3_J,axiom, % 18.97/18.95 ! [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) ). % 18.97/18.95 % 18.97/18.95 fof(fact_code__numeral_Osimps_I5_J,axiom, % 18.97/18.95 ! [V_code__numeral_2,V_f2_2,V_f1_2,T_b] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(T_b,V_f1_2,V_f2_2,c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2)) = hAPP(V_f2_2,V_code__numeral_2) ). % 18.97/18.95 % 18.97/18.95 fof(fact_Suc__code__numeral__minus__one,axiom, % 18.97/18.95 ! [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 ). % 18.97/18.95 % 18.97/18.95 fof(fact_negDivAlg__eqn__1__number__of,axiom, % 18.97/18.95 ! [V_w] : % 18.97/18.95 ( 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))) % 18.97/18.95 => ( ( 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),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))) % 18.97/18.95 => 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))) ) % 18.97/18.95 & ( ~ 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),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))) % 18.97/18.95 => 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)))) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_diff__nat__number__of,axiom, % 18.97/18.95 ! [V_v_2,V_v_H_2] : % 18.97/18.95 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls)) % 18.97/18.95 => 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) ) % 18.97/18.95 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls)) % 18.97/18.95 => 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)) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_code__numeral_Orecs_I2_J,axiom, % 18.97/18.95 ! [V_code__numeral_2,V_f2_2,V_f1_2,T_b] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(T_b,V_f1_2,V_f2_2,c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2)) = hAPP(hAPP(V_f2_2,V_code__numeral_2),c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(T_b,V_f1_2,V_f2_2,V_code__numeral_2)) ). % 18.97/18.95 % 18.97/18.95 fof(fact_divmod__nat__step,axiom, % 18.97/18.95 ! [V_m,V_n] : % 18.97/18.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 18.97/18.95 => c_Divides_Odivmod__nat(V_m,V_n) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n)) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_code__numeral__not__eq__zero,axiom, % 18.97/18.95 ! [V_i_2] : % 18.97/18.95 ( V_i_2 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 18.97/18.95 <=> 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)) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_divmod__nat__zero,axiom, % 18.97/18.95 ! [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) ). % 18.97/18.95 % 18.97/18.95 fof(fact_Code__Numeral_Oof__nat__inject,axiom, % 18.97/18.95 ! [V_m_2,V_n_2] : % 18.97/18.95 ( hAPP(c_Code__Numeral_Oof__nat,V_n_2) = hAPP(c_Code__Numeral_Oof__nat,V_m_2) % 18.97/18.95 <=> V_n_2 = V_m_2 ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_Code__Numeral_Oof__nat__code,axiom, % 18.97/18.95 c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral) ). % 18.97/18.95 % 18.97/18.95 fof(fact_fun__Compl__def,axiom, % 18.97/18.95 ! [V_x_2,V_A_2,T_c,T_b] : % 18.97/18.95 ( class_Groups_Ouminus(T_b) % 18.97/18.95 => hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,T_b)),V_A_2),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(V_A_2,V_x_2)) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_fun__diff__def,axiom, % 18.97/18.95 ! [V_x_2,V_B_2,V_A_2,T_c,T_b] : % 18.97/18.95 ( class_Groups_Ominus(T_b) % 18.97/18.95 => hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,T_b)),V_A_2),V_B_2),V_x_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2)) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_divmod__nat__base,axiom, % 18.97/18.95 ! [V_n,V_m] : % 18.97/18.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 18.97/18.95 => 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) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_less__eq__Suc__le__raw,axiom, % 18.97/18.95 ! [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)) ). % 18.97/18.95 % 18.97/18.95 fof(fact_nat__number__of__Bit0,axiom, % 18.97/18.95 ! [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))) ). % 18.97/18.95 % 18.97/18.95 fof(fact_times__code__numeral__code,axiom, % 18.97/18.95 ! [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)) ). % 18.97/18.95 % 18.97/18.95 fof(fact_divmod__nat__div__mod,axiom, % 18.97/18.95 ! [V_n,V_m] : c_Divides_Odivmod__nat(V_m,V_n) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) ). % 18.97/18.95 % 18.97/18.95 fof(fact_power__number__of__even,axiom, % 18.97/18.95 ! [V_w_2,V_z_2,T_b] : % 18.97/18.95 ( class_Int_Onumber__ring(T_b) % 18.97/18.95 => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_b,T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),c_Groups_Otimes__class_Otimes(T_b)),c_COMBI(T_b))) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_zpower__number__of__even,axiom, % 18.97/18.95 ! [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))) ). % 18.97/18.95 % 18.97/18.95 fof(fact_power__number__of__even__number__of,axiom, % 18.97/18.95 ! [V_w_2,V_v_2,T_b] : % 18.97/18.95 ( class_Int_Onumber__ring(T_b) % 18.97/18.95 => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_b,T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),c_Groups_Otimes__class_Otimes(T_b)),c_COMBI(T_b))) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_diff__nat__eq__if,axiom, % 18.97/18.95 ! [V_z_2,V_z_H_2] : % 18.97/18.95 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2)) % 18.97/18.95 => 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) ) % 18.97/18.95 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2)) % 18.97/18.95 => 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)) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_negDivAlg__div__mod,axiom, % 18.97/18.95 ! [V_l,V_k] : % 18.97/18.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 18.97/18.95 => c_Divides_OnegDivAlg(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l)) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_negDivAlg__minus1,axiom, % 18.97/18.95 ! [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))) ). % 18.97/18.95 % 18.97/18.95 fof(fact_semiring__1__class_Oof__nat__code,axiom, % 18.97/18.95 ! [V_n_2,T_b] : % 18.97/18.95 ( class_Rings_Osemiring__1(T_b) % 18.97/18.95 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2) = c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,hAPP(hAPP(c_COMBC(T_b,T_b,T_b),c_Groups_Oplus__class_Oplus(T_b)),c_Groups_Oone__class_Oone(T_b)),V_n_2,c_Groups_Ozero__class_Ozero(T_b)) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_adjust__eq,axiom, % 18.97/18.95 ! [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))) ). % 18.97/18.95 % 18.97/18.95 fof(fact_zero__code__numeral__def,axiom, % 18.97/18.95 c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 18.97/18.95 % 18.97/18.95 fof(fact_one__code__numeral__def,axiom, % 18.97/18.95 c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ). % 18.97/18.95 % 18.97/18.95 fof(fact_less__code__numeral__code,axiom, % 18.97/18.95 ! [V_m_2,V_n_2] : % 18.97/18.95 ( 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))) % 18.97/18.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_eq__number__of__Suc,axiom, % 18.97/18.95 ! [V_n_2,V_v_2] : % 18.97/18.95 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Nat_OSuc,V_n_2) % 18.97/18.95 <=> 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))))) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_Suc__eq__number__of,axiom, % 18.97/18.95 ! [V_v_2,V_n_2] : % 18.97/18.95 ( hAPP(c_Nat_OSuc,V_n_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) % 18.97/18.95 <=> 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))))) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_plus__code__numeral__code,axiom, % 18.97/18.95 ! [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)) ). % 18.97/18.95 % 18.97/18.95 fof(fact_less__eq__code__numeral__code,axiom, % 18.97/18.95 ! [V_m_2,V_n_2] : % 18.97/18.95 ( 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))) % 18.97/18.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_nat__number__of__Bit1,axiom, % 18.97/18.95 ! [V_w_2] : % 18.97/18.95 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 18.97/18.95 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 18.97/18.95 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 18.97/18.95 => 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)))) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_less__number__of__Suc,axiom, % 18.97/18.95 ! [V_n_2,V_v_2] : % 18.97/18.95 ( 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))) % 18.97/18.95 <=> 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)))) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_less__Suc__number__of,axiom, % 18.97/18.95 ! [V_v_2,V_n_2] : % 18.97/18.95 ( 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))) % 18.97/18.95 <=> 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))))) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_le__number__of__Suc,axiom, % 18.97/18.95 ! [V_n_2,V_v_2] : % 18.97/18.95 ( 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))) % 18.97/18.95 <=> 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)))) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_le__Suc__number__of,axiom, % 18.97/18.95 ! [V_v_2,V_n_2] : % 18.97/18.95 ( 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))) % 18.97/18.95 <=> 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))))) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_subtract__code__numeral__code,axiom, % 18.97/18.95 ! [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)) ). % 18.97/18.95 % 18.97/18.95 fof(fact_power__number__of__odd,axiom, % 18.97/18.95 ! [V_z_2,V_w_2,T_b] : % 18.97/18.95 ( class_Int_Onumber__ring(T_b) % 18.97/18.95 => ( ( 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))) % 18.97/18.95 => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_b,T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_b),c_Groups_Otimes__class_Otimes(T_b)),hAPP(c_Groups_Otimes__class_Otimes(T_b),V_z_2))),c_COMBI(T_b))) ) % 18.97/18.95 & ( ~ 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))) % 18.97/18.95 => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = c_Groups_Oone__class_Oone(T_b) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_zpower__number__of__odd,axiom, % 18.97/18.95 ! [V_z_2,V_w_2] : % 18.97/18.95 ( ( 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))) % 18.97/18.95 => 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))) ) % 18.97/18.95 & ( ~ 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))) % 18.97/18.95 => 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) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_negDivAlg_Osimps,axiom, % 18.97/18.95 ! [V_b,V_a] : % 18.97/18.95 ( ( ( 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_a),V_b))) % 18.97/18.95 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 18.97/18.95 => 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)) ) % 18.97/18.95 & ( ~ ( 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_a),V_b))) % 18.97/18.95 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 18.97/18.95 => 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))) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_power__number__of__odd__number__of,axiom, % 18.97/18.95 ! [V_v_2,V_w_2,T_b] : % 18.97/18.95 ( class_Int_Onumber__ring(T_b) % 18.97/18.95 => ( ( 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))) % 18.97/18.95 => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_b,T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_b),c_Groups_Otimes__class_Otimes(T_b)),hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)))),c_COMBI(T_b))) ) % 18.97/18.95 & ( ~ 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))) % 18.97/18.95 => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = c_Groups_Oone__class_Oone(T_b) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_code__numeral_Orecs_I1_J,axiom, % 18.97/18.95 ! [V_f2_2,V_f1_2,T_b] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(T_b,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = V_f1_2 ). % 18.97/18.95 % 18.97/18.95 fof(fact_negDivAlg__eqn__number__of,axiom, % 18.97/18.95 ! [V_w,V_v] : % 18.97/18.95 ( 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))) % 18.97/18.95 => ( ( 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(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))) % 18.97/18.95 => 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))) ) % 18.97/18.95 & ( ~ 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(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))) % 18.97/18.95 => 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)))) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_negDivAlg__eqn,axiom, % 18.97/18.95 ! [V_a,V_b] : % 18.97/18.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 18.97/18.95 => ( ( 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_a),V_b))) % 18.97/18.95 => 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)) ) % 18.97/18.95 & ( ~ 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_a),V_b))) % 18.97/18.95 => 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))) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_norm__frac_Osimps,axiom, % 18.97/18.95 ! [V_a_2,V_b_2] : % 18.97/18.95 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 18.97/18.95 => 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)) ) % 18.97/18.95 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 18.97/18.95 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 18.97/18.95 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 18.97/18.95 => 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)) ) % 18.97/18.95 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 18.97/18.95 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 18.97/18.95 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,V_a_2),V_b_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b_2))) ) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_nat__case__add__eq__if,axiom, % 18.97/18.95 ! [V_n_2,V_v_2,V_f_2,V_a_2,T_b] : c_Nat_Onat_Onat__case(T_b,V_a_2,V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),V_n_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(T_b,V_a_2,V_f_2,V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),V_f_2),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))) ). % 18.97/18.95 % 18.97/18.95 fof(fact_posDivAlg__eqn__1__number__of,axiom, % 18.97/18.95 ! [V_w] : % 18.97/18.95 ( 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))) % 18.97/18.95 => ( ( 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))) % 18.97/18.95 => 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)) ) % 18.97/18.95 & ( ~ 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))) % 18.97/18.95 => 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)))) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_posDivAlg_Osimps,axiom, % 18.97/18.95 ! [V_b,V_a] : % 18.97/18.95 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 18.97/18.95 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 18.97/18.95 => 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) ) % 18.97/18.95 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 18.97/18.95 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 18.97/18.95 => 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))) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_adjust__def,axiom, % 18.97/18.95 ! [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))))))) ). % 18.97/18.95 % 18.97/18.95 fof(fact_nat__case__0,axiom, % 18.97/18.95 ! [V_f2_2,V_f1_2,T_b] : c_Nat_Onat_Onat__case(T_b,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_f1_2 ). % 18.97/18.95 % 18.97/18.95 fof(fact_nat__case__Suc,axiom, % 18.97/18.95 ! [V_nat_2,V_f2_2,V_f1_2,T_b] : c_Nat_Onat_Onat__case(T_b,V_f1_2,V_f2_2,hAPP(c_Nat_OSuc,V_nat_2)) = hAPP(V_f2_2,V_nat_2) ). % 18.97/18.95 % 18.97/18.95 fof(fact_posDivAlg__0,axiom, % 18.97/18.95 ! [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)) ). % 18.97/18.95 % 18.97/18.95 fof(fact_less__eq__nat_Osimps_I2_J,axiom, % 18.97/18.95 ! [V_n_2,V_m_2] : % 18.97/18.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2)) % 18.97/18.95 <=> 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)) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_diff__Suc,axiom, % 18.97/18.95 ! [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)) ). % 18.97/18.95 % 18.97/18.95 fof(fact_posDivAlg__div__mod,axiom, % 18.97/18.95 ! [V_l,V_k] : % 18.97/18.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 18.97/18.95 => c_Divides_OposDivAlg(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l)) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_nat__case__number__of,axiom, % 18.97/18.95 ! [V_v_2,V_f_2,V_a_2,T_b] : c_Nat_Onat_Onat__case(T_b,V_a_2,V_f_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),c_Nat__Numeral_Oneg)),V_a_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),V_f_2),c_Int_Onat))) ). % 18.97/18.95 % 18.97/18.95 fof(fact_posDivAlg__eqn,axiom, % 18.97/18.95 ! [V_a,V_b] : % 18.97/18.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 18.97/18.95 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 18.97/18.95 => 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) ) % 18.97/18.95 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 18.97/18.95 => 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))) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_posDivAlg__eqn__number__of,axiom, % 18.97/18.95 ! [V_w,V_v] : % 18.97/18.95 ( 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))) % 18.97/18.95 => ( ( 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))) % 18.97/18.95 => 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)) ) % 18.97/18.95 & ( ~ 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))) % 18.97/18.95 => 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)))) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_of__int__num,axiom, % 18.97/18.95 ! [V_k_2,T_b] : % 18.97/18.95 ( class_Rings_Oring__1(T_b) % 18.97/18.95 => ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 18.97/18.95 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = c_Groups_Ozero__class_Ozero(T_b) ) % 18.97/18.95 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 18.97/18.95 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 18.97/18.95 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k_2))) ) % 18.97/18.95 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 18.97/18.95 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(T_b,T_b)),tc_fun(tc_Int_Oint,T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),T_b),tc_fun(tc_fun(tc_Int_Oint,tc_fun(T_b,T_b)),tc_fun(tc_Int_Oint,T_b)),tc_Int_Oint),c_COMBB(tc_fun(T_b,T_b),T_b,tc_Int_Oint)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_fun(T_b,T_b),T_b),tc_Int_Oint),c_HOL_OLet(T_b,T_b)),c_Int_Oring__1__class_Oof__int(T_b)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(T_b,T_b),tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,T_b)),tc_Int_Oint),c_COMBS(T_b,T_b,T_b)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(T_b,T_b),tc_fun(T_b,tc_fun(T_b,T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_fun(T_b,T_b))),tc_Int_Oint),c_COMBB(T_b,tc_fun(T_b,T_b),T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),c_Groups_Oplus__class_Oplus(T_b)),c_COMBI(T_b))))),hAPP(hAPP(c_COMBC(T_b,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_b),c_Groups_Oplus__class_Oplus(T_b)),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),c_Groups_Oplus__class_Oplus(T_b)),c_COMBI(T_b)))),c_Groups_Oone__class_Oone(T_b))))),c_Divides_Odivmod__int(V_k_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) ) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_nat__rec__add__eq__if,axiom, % 18.97/18.95 ! [V_n_2,V_v_2,V_f_2,V_a_2,T_b] : hAPP(c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),V_n_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2),V_n_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_b,T_b),tc_Int_Oint),V_f_2),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),V_n_2))))) ). % 18.97/18.95 % 18.97/18.95 fof(fact_MGT__def,axiom, % 18.97/18.95 ! [V_c_2] : c_Hoare__Mirabelle_OMGT(V_c_2) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal),V_c_2),c_Natural_Oevalc(V_c_2)) ). % 18.97/18.95 % 18.97/18.95 fof(fact_divmod__nat__rel__mult2__eq,axiom, % 18.97/18.95 ! [V_c,V_r,V_q,V_b,V_a] : % 18.97/18.95 ( 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))) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_b)) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 18.97/18.95 => hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_q),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_q,V_c))),V_r)))) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_divmod__nat__rel__mult1__eq,axiom, % 18.97/18.95 ! [V_a,V_r,V_q,V_c,V_b] : % 18.97/18.95 ( 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))) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 18.97/18.95 => hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_b),V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_q)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_r)),V_c))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_r),V_c)))) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_divmod__nat__rel__unique,axiom, % 18.97/18.95 ! [V_qr_H,V_qr,V_n,V_m] : % 18.97/18.95 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr)) % 18.97/18.95 => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr_H)) % 18.97/18.95 => V_qr = V_qr_H ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_nat__rec__0,axiom, % 18.97/18.95 ! [V_f2_2,V_f1_2,T_b] : hAPP(c_Nat_Onat_Onat__rec(T_b,V_f1_2,V_f2_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_f1_2 ). % 18.97/18.95 % 18.97/18.95 fof(fact_nat__rec__Suc,axiom, % 18.97/18.95 ! [V_nat_2,V_f2_2,V_f1_2,T_b] : hAPP(c_Nat_Onat_Onat__rec(T_b,V_f1_2,V_f2_2),hAPP(c_Nat_OSuc,V_nat_2)) = hAPP(hAPP(V_f2_2,V_nat_2),hAPP(c_Nat_Onat_Onat__rec(T_b,V_f1_2,V_f2_2),V_nat_2)) ). % 18.97/18.95 % 18.97/18.95 fof(fact_divmod__nat__rel__divmod__nat,axiom, % 18.97/18.95 ! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),c_Divides_Odivmod__nat(V_m,V_n))) ). % 18.97/18.95 % 18.97/18.95 fof(fact_divmod__nat__eq,axiom, % 18.97/18.95 ! [V_qr,V_n,V_m] : % 18.97/18.95 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr)) % 18.97/18.95 => c_Divides_Odivmod__nat(V_m,V_n) = V_qr ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_mod__eq,axiom, % 18.97/18.95 ! [V_r,V_q,V_n,V_m] : % 18.97/18.95 ( 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))) % 18.97/18.95 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_r ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_div__eq,axiom, % 18.97/18.95 ! [V_r,V_q,V_n,V_m] : % 18.97/18.95 ( 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))) % 18.97/18.95 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = V_q ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_divmod__nat__rel,axiom, % 18.97/18.95 ! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)))) ). % 18.97/18.95 % 18.97/18.95 fof(fact_divmod__int__mod__div,axiom, % 18.97/18.95 ! [V_q,V_p] : c_Divides_Odivmod__int(V_p,V_q) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_p),V_q)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_p,V_q)) ). % 18.97/18.95 % 18.97/18.95 fof(fact_divmod__nat__rel__add1__eq,axiom, % 18.97/18.95 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] : % 18.97/18.95 ( 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))) % 18.97/18.95 => ( 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))) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 18.97/18.95 => hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a),V_b),V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_aq),V_bq)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_ar),V_br)),V_c))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_ar),V_br),V_c)))) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_nat__rec__number__of,axiom, % 18.97/18.95 ! [V_v_2,V_f_2,V_a_2,T_b] : hAPP(c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),c_Nat__Numeral_Oneg)),V_a_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_b,T_b),tc_Int_Oint),V_f_2),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2)),c_Int_Onat)))) ). % 18.97/18.95 % 18.97/18.95 fof(fact_Nitpick_OFrac__def,axiom, % 18.97/18.95 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)))) ). % 18.97/18.95 % 18.97/18.95 fof(fact_divmod__int__def,axiom, % 18.97/18.95 ! [V_b,V_a] : % 18.97/18.95 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 18.97/18.95 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 18.97/18.95 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OposDivAlg(V_a,V_b) ) % 18.97/18.95 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 18.97/18.95 => ( ( V_a = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 18.97/18.95 => 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)) ) % 18.97/18.95 & ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 18.97/18.95 => 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))) ) ) ) ) ) % 18.97/18.95 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 18.97/18.95 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 18.97/18.95 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OnegDivAlg(V_a,V_b) ) % 18.97/18.95 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 18.97/18.95 => 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))) ) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_divmod__int__pdivmod,axiom, % 18.97/18.95 ! [V_l_2,V_k_2] : % 18.97/18.95 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 18.97/18.95 => 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)) ) % 18.97/18.95 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 18.97/18.95 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 18.97/18.95 => 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) ) % 18.97/18.95 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 18.97/18.95 => 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)))) ) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_divmod__int__code,axiom, % 18.97/18.95 ! [V_l_2,V_k_2] : % 18.97/18.95 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 18.97/18.95 => 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)) ) % 18.97/18.95 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 18.97/18.95 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 18.97/18.95 => 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) ) % 18.97/18.95 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 18.97/18.95 => 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)))) ) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_negDivAlg_Opsimps,axiom, % 18.97/18.95 ! [V_b_2,V_a_2] : % 18.97/18.95 ( 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))) % 18.97/18.95 => ( ( ( 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_a_2),V_b_2))) % 18.97/18.95 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 18.97/18.95 => 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)) ) % 18.97/18.95 & ( ~ ( 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_a_2),V_b_2))) % 18.97/18.95 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 18.97/18.95 => 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))) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_accp__subset,axiom, % 18.97/18.95 ! [V_R2_2,V_R1_2,T_b] : % 18.97/18.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),V_R1_2),V_R2_2)) % 18.97/18.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Oaccp(T_b,V_R2_2)),c_Wellfounded_Oaccp(T_b,V_R1_2))) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_negateSnd__def,axiom, % 18.97/18.95 c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)) ). % 18.97/18.95 % 18.97/18.95 fof(fact_accp__downward,axiom, % 18.97/18.95 ! [V_a_2,V_b_2,V_r_2,T_b] : % 18.97/18.95 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_b_2)) % 18.97/18.95 => ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 18.97/18.95 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2)) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_accp_Oequations,axiom, % 18.97/18.95 ! [V_a_2,V_r_2,T_b] : % 18.97/18.95 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2)) % 18.97/18.95 <=> ! [B_x] : % 18.97/18.95 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2)) % 18.97/18.95 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_accp_Osimps,axiom, % 18.97/18.95 ! [V_a_2,V_r_2,T_b] : % 18.97/18.95 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2)) % 18.97/18.95 <=> ! [B_x] : % 18.97/18.95 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2)) % 18.97/18.95 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_negateSnd__eq,axiom, % 18.97/18.95 ! [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)) ). % 18.97/18.95 % 18.97/18.95 fof(fact_pdivmod__def,axiom, % 18.97/18.95 ! [V_l,V_k] : c_Divides_Opdivmod(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_k)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_k),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l))) ). % 18.97/18.95 % 18.97/18.95 fof(fact_pdivmod__posDivAlg,axiom, % 18.97/18.95 ! [V_k,V_l] : % 18.97/18.95 ( ( V_l = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 18.97/18.95 => 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)) ) % 18.97/18.95 & ( V_l != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 18.97/18.95 => 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)) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_posDivAlg_Opsimps,axiom, % 18.97/18.95 ! [V_b_2,V_a_2] : % 18.97/18.95 ( 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))) % 18.97/18.95 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2)) % 18.97/18.95 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 18.97/18.95 => 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) ) % 18.97/18.95 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2)) % 18.97/18.95 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 18.97/18.95 => 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))) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_norm__frac_Opsimps,axiom, % 18.97/18.95 ! [V_b_2,V_a_2] : % 18.97/18.95 ( 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))) % 18.97/18.95 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 18.97/18.95 => 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)) ) % 18.97/18.95 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 18.97/18.95 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 18.97/18.95 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 18.97/18.95 => 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)) ) % 18.97/18.95 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 18.97/18.95 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 18.97/18.95 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,V_a_2),V_b_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b_2))) ) ) ) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_prod__caseI,axiom, % 18.97/18.95 ! [T_c,T_b,V_b_2,V_a_2,V_f1_2] : % 18.97/18.95 ( hBOOL(hAPP(hAPP(V_f1_2,V_a_2),V_b_2)) % 18.97/18.95 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_f1_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_splitI,axiom, % 18.97/18.95 ! [T_c,T_b,V_b_2,V_a_2,V_f_2] : % 18.97/18.95 ( hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) % 18.97/18.95 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_negDivAlg_Opinduct,axiom, % 18.97/18.95 ! [V_Pa_2,V_a1_2,V_a0_2] : % 18.97/18.95 ( 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))) % 18.97/18.95 => ( ! [B_a,B_b] : % 18.97/18.95 ( 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))) % 18.97/18.95 => ( ( ~ ( 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),B_a),B_b))) % 18.97/18.95 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 18.97/18.95 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B_b))) ) % 18.97/18.95 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) ) % 18.97/18.95 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_Pair__inject,axiom, % 18.97/18.95 ! [V_b_H,V_a_H,V_b,V_a,T_b,T_a] : % 18.97/18.95 ( 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) % 18.97/18.95 => ~ ( V_a = V_a_H % 18.97/18.95 => V_b != V_b_H ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_Pair__eq,axiom, % 18.97/18.95 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] : % 18.97/18.95 ( hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_H_2),V_b_H_2) % 18.97/18.95 <=> ( V_a_2 = V_a_H_2 % 18.97/18.95 & V_b_2 = V_b_H_2 ) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_split__paired__All,axiom, % 18.97/18.95 ! [T_c,T_b,V_Pa_2] : % 18.97/18.95 ( ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 18.97/18.95 <=> ! [B_a,B_b] : hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b))) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_split__weak__cong,axiom, % 18.97/18.95 ! [V_c_2,T_d,T_c,T_b,V_q_2,V_p_2] : % 18.97/18.95 ( V_p_2 = V_q_2 % 18.97/18.95 => hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_c_2),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_c_2),V_q_2) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_split__conv,axiom, % 18.97/18.95 ! [V_b_2,V_a_2,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_f_2,V_a_2),V_b_2) ). % 18.97/18.95 % 18.97/18.95 fof(fact_prod_Osimps_I2_J,axiom, % 18.97/18.95 ! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f1_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2) ). % 18.97/18.95 % 18.97/18.95 fof(fact_splitD,axiom, % 18.97/18.95 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] : % 18.97/18.95 ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) % 18.97/18.95 => hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) ) ). % 18.97/18.95 % 18.97/18.95 fof(fact_apsnd__conv,axiom, % 18.97/18.95 ! [V_y_2,V_x_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),V_x_2),V_y_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),hAPP(V_f_2,V_y_2)) ). % 18.97/18.95 % 18.97/18.95 fof(fact_split__eta,axiom, % 18.97/18.95 ! [V_f_2,T_d,T_c,T_b] : hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,T_d),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),T_d,T_c),V_f_2)),c_Product__Type_OPair(T_b,T_c))) = V_f_2 ). % 18.97/18.95 % 18.97/18.95 fof(fact_split__twice,axiom, % 18.97/18.95 ! [V_p_2,V_g_2,T_f,T_e,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_e,T_f,tc_prod(T_c,T_d)),V_g_2),V_p_2)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_e,T_f,T_b),hAPP(hAPP(c_COMBB(tc_fun(T_f,tc_prod(T_c,T_d)),tc_fun(T_f,T_b),T_e),hAPP(c_COMBB(tc_prod(T_c,T_d),T_b,T_f),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2))),V_g_2)),V_p_2) ). % 18.97/18.95 % 18.97/18.95 fof(fact_div__mod__code__numeral__def,axiom, % 18.97/18.95 ! [V_m,V_n] : c_Code__Numeral_Odiv__mod__code__numeral(V_n,V_m) = hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_n),V_m)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,V_n,V_m)) ). % 18.97/18.95 % 18.97/18.95 fof(fact_posDivAlg_Opinduct,axiom, % 18.97/18.95 ! [V_Pa_2,V_a1_2,V_a0_2] : % 18.97/18.95 ( 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))) % 18.97/18.95 => ( ! [B_a,B_b] : % 18.97/18.95 ( 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))) % 18.97/18.95 => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_a),B_b)) % 18.97/18.95 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 18.97/18.95 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B_b))) ) % 18.97/18.95 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) ) % 18.97/18.95 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ). % 18.97/18.95 % 19.07/18.95 fof(fact_nat__gcd_Opsimps,axiom, % 19.07/18.95 ! [V_y_2,V_x_2] : % 19.07/18.95 ( 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))) % 19.07/18.95 => ( ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 19.07/18.95 => c_Nitpick_Onat__gcd(V_x_2,V_y_2) = V_x_2 ) % 19.07/18.95 & ( V_y_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 19.07/18.95 => 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)) ) ) ) ). % 19.07/18.95 % 19.07/18.95 fof(fact_zmult2__lemma,axiom, % 19.07/18.95 ! [V_c,V_r,V_q,V_b,V_a] : % 19.07/18.95 ( 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))) % 19.07/18.95 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 19.07/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 19.07/18.95 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_q),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r)))) ) ) ) ). % 19.07/18.95 % 19.07/18.95 fof(fact_mod__pos__neg__1__number__of,axiom, % 19.07/18.95 ! [V_w] : % 19.07/18.95 ( 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))) % 19.07/18.95 => 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))))) ) ). % 19.07/18.95 % 19.07/18.95 fof(fact_splitD_H,axiom, % 19.07/18.95 ! [V_c_2,V_b_2,V_a_2,V_R_2,T_d,T_c,T_b] : % 19.07/18.95 ( hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_d,tc_HOL_Obool)),V_R_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_c_2)) % 19.07/18.95 => hBOOL(hAPP(hAPP(hAPP(V_R_2,V_a_2),V_b_2),V_c_2)) ) ). % 19.07/18.95 % 19.07/18.95 fof(fact_snd__eqD,axiom, % 19.07/18.95 ! [V_a,V_y,V_x,T_a,T_b] : % 19.07/18.95 ( 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 % 19.07/18.95 => V_y = V_a ) ). % 19.07/18.95 % 19.07/18.95 fof(fact_snd__conv,axiom, % 19.07/18.95 ! [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 ). % 19.07/18.95 % 19.07/18.95 fof(fact_apsnd__eq__conv,axiom, % 19.07/18.95 ! [V_g_2,V_x_2,V_f_2,T_b,T_c,T_d] : % 19.07/18.95 ( hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),V_x_2) = hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_g_2),V_x_2) % 19.07/18.95 <=> hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_b,T_d),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_b,T_d),V_x_2)) ) ). % 19.07/18.95 % 19.07/18.95 fof(fact_snd__apsnd,axiom, % 19.07/18.95 ! [V_x_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(c_Product__Type_Oapsnd(T_d,T_b,T_c,V_f_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_c,T_d),V_x_2)) ). % 19.07/18.95 % 19.07/18.95 fof(fact_snd__def,axiom, % 19.07/18.95 ! [V_p_2,T_b,T_c] : hAPP(c_Product__Type_Osnd(T_c,T_b),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,T_b),hAPP(c_COMBK(tc_fun(T_b,T_b),T_c),c_COMBI(T_b))),V_p_2) ). % 19.07/18.95 % 19.07/18.95 fof(fact_mod__int__def,axiom, % 19.07/18.95 ! [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)) ). % 19.07/18.95 % 19.07/18.95 fof(fact_divmod__int__rel__0,axiom, % 19.07/18.95 ! [V_b] : % 19.07/18.95 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 19.07/18.95 => 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)))) ) ). % 19.07/18.95 % 19.07/18.95 fof(fact_self__remainder,axiom, % 19.07/18.95 ! [V_r,V_q,V_a] : % 19.07/18.95 ( 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))) % 19.07/18.95 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 19.07/18.95 => V_r = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 19.07/18.95 % 19.07/18.95 fof(fact_unique__quotient,axiom, % 19.07/18.95 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] : % 19.07/18.95 ( 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))) % 19.07/18.95 => ( 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))) % 19.07/18.95 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 19.07/18.95 => V_q = V_q_H ) ) ) ). % 19.07/18.95 % 19.07/18.95 fof(fact_unique__remainder,axiom, % 19.07/18.95 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] : % 19.07/18.95 ( 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))) % 19.07/18.95 => ( 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))) % 19.07/18.95 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 19.07/18.95 => V_r = V_r_H ) ) ) ). % 19.07/18.95 % 19.07/18.95 fof(fact_divmod__int__rel__neg,axiom, % 19.07/18.95 ! [V_qr,V_b,V_a] : % 19.07/18.95 ( 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)) % 19.07/18.95 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(c_Divides_OnegateSnd,V_qr))) ) ). % 19.07/18.95 % 19.07/18.95 fof(fact_divmod__int__correct,axiom, % 19.07/18.95 ! [V_a,V_b] : % 19.07/18.95 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 19.07/18.95 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_Odivmod__int(V_a,V_b))) ) ). % 19.07/18.95 % 19.07/18.95 fof(fact_self__quotient,axiom, % 19.07/18.95 ! [V_r,V_q,V_a] : % 19.07/18.95 ( 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))) % 19.07/18.95 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 19.07/18.95 => V_q = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ). % 19.07/18.95 % 19.07/18.95 fof(fact_divmod__int__rel__mod,axiom, % 19.07/18.95 ! [V_r,V_q,V_b,V_a] : % 19.07/18.95 ( 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))) % 19.07/18.95 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 19.07/18.95 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_r ) ) ). % 19.07/18.95 % 19.07/18.95 fof(fact_divmod__int__rel__div,axiom, % 19.07/18.95 ! [V_r,V_q,V_b,V_a] : % 19.07/18.95 ( 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))) % 19.07/18.95 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 19.07/18.95 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = V_q ) ) ). % 19.07/18.95 % 19.07/18.95 fof(fact_negDivAlg__correct,axiom, % 19.07/18.95 ! [V_b,V_a] : % 19.07/18.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 19.07/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 19.07/18.95 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OnegDivAlg(V_a,V_b))) ) ) ). % 19.07/18.95 % 19.07/18.95 fof(fact_mod__neg__pos,axiom, % 19.07/18.95 ! [V_b,V_a] : % 19.07/18.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 19.07/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 19.07/18.95 => 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)) ) ) ). % 19.07/18.95 % 19.07/18.95 fof(fact_divmod__int__rel__div__mod,axiom, % 19.07/18.95 ! [V_a,V_b] : % 19.07/18.95 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 19.07/18.95 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)))) ) ). % 19.07/18.95 % 19.07/18.95 fof(fact_posDivAlg__correct,axiom, % 19.07/18.95 ! [V_b,V_a] : % 19.07/18.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 19.07/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 19.07/18.95 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OposDivAlg(V_a,V_b))) ) ) ). % 19.07/18.95 % 19.07/18.95 fof(fact_mod__pos__pos,axiom, % 19.07/18.95 ! [V_b,V_a] : % 19.07/18.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 19.07/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 19.07/18.95 => 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)) ) ) ). % 19.07/18.95 % 19.07/18.95 fof(fact_mod__pos__pos__1__number__of,axiom, % 19.07/18.95 ! [V_w] : % 19.07/18.95 ( 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))) % 19.07/18.95 => 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))) ) ). % 19.07/18.95 % 19.07/18.95 fof(fact_zadd1__lemma,axiom, % 19.07/18.95 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] : % 19.07/18.95 ( 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))) % 19.07/18.95 => ( 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))) % 19.07/18.95 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 19.07/18.95 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b),V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_aq),V_bq)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_ar),V_br)),V_c))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_ar),V_br),V_c)))) ) ) ) ). % 19.07/18.95 % 19.07/18.95 fof(fact_zminus1__lemma,axiom, % 19.07/18.95 ! [V_r_2,V_q_2,V_b_2,V_a_2] : % 19.07/18.95 ( 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))) % 19.07/18.95 => 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))))) ) ). % 19.07/18.95 % 19.07/18.95 fof(fact_mod__pos__neg,axiom, % 19.07/18.95 ! [V_b,V_a] : % 19.07/18.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 19.07/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 19.07/18.95 => 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)))) ) ) ). % 19.07/18.95 % 19.07/18.95 fof(fact_divmod__nat__if,axiom, % 19.07/18.95 ! [V_m_2,V_n_2] : % 19.07/18.95 ( ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 19.07/18.95 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) % 19.07/18.95 => 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) ) % 19.07/18.95 & ( ~ ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 19.07/18.95 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) % 19.07/18.95 => 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)) ) ) ). % 19.07/18.95 % 19.07/18.95 fof(fact_divmod__int__relI,axiom, % 19.07/18.95 ! [V_r,V_q,V_b,V_a] : % 19.07/18.95 ( 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) % 19.07/18.95 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 19.07/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 19.07/18.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) ) ) % 19.07/18.95 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 19.07/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 19.07/18.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) % 19.07/18.95 => 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))) ) ) ). % 19.07/18.95 % 19.07/18.95 fof(fact_mod__neg__neg,axiom, % 19.07/18.95 ! [V_b,V_a] : % 19.07/18.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 19.07/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 19.07/18.95 => 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)))) ) ) ). % 19.07/18.95 % 19.07/18.95 fof(fact_zmult1__lemma,axiom, % 19.07/18.95 ! [V_a,V_r,V_q,V_c,V_b] : % 19.07/18.95 ( 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))) % 19.07/18.95 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 19.07/18.95 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_r)),V_c))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_r),V_c)))) ) ) ). % 19.07/18.95 % 19.07/18.95 fof(fact_divmod__int__rel__def,axiom, % 19.07/18.95 ! [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))))))) ). % 19.07/18.95 % 19.07/18.95 fof(fact_norm__frac_Opinduct,axiom, % 19.07/18.95 ! [V_Pa_2,V_a1_2,V_a0_2] : % 19.07/18.95 ( 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))) % 19.07/18.95 => ( ! [B_a,B_b] : % 19.07/18.95 ( 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))) % 19.07/18.95 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 19.07/18.95 => hBOOL(hAPP(hAPP(V_Pa_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B_a)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B_b))) ) % 19.07/18.95 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) ) % 19.07/18.95 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ). % 19.07/18.95 % 19.07/18.95 fof(fact_equalityI,axiom, % 19.07/18.95 ! [V_B_2,V_A_2,T_b] : % 19.07/18.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 19.07/18.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 19.07/18.95 => V_A_2 = V_B_2 ) ) ). % 19.07/18.95 % 19.07/18.95 fof(fact_div__pos__neg__1__number__of,axiom, % 19.07/18.95 ! [V_w] : % 19.07/18.95 ( 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))) % 19.07/18.96 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))))) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_nat__gcd_Opinduct,axiom, % 19.07/18.96 ! [V_Pa_2,V_a1_2,V_a0_2] : % 19.07/18.96 ( 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))) % 19.07/18.96 => ( ! [B_x,B_y] : % 19.07/18.96 ( 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))) % 19.07/18.96 => ( ( B_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 19.07/18.96 => hBOOL(hAPP(hAPP(V_Pa_2,B_y),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B_x,B_y))) ) % 19.07/18.96 => hBOOL(hAPP(hAPP(V_Pa_2,B_x),B_y)) ) ) % 19.07/18.96 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_div__neg__neg,axiom, % 19.07/18.96 ! [V_b,V_a] : % 19.07/18.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 19.07/18.96 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)))) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_fst__conv,axiom, % 19.07/18.96 ! [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 ). % 19.07/18.96 % 19.07/18.96 fof(fact_fst__eqD,axiom, % 19.07/18.96 ! [V_a,V_y,V_x,T_b,T_a] : % 19.07/18.96 ( 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 % 19.07/18.96 => V_x = V_a ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_Pair__fst__snd__eq,axiom, % 19.07/18.96 ! [T_c,T_b,V_t_2,V_s_2] : % 19.07/18.96 ( V_s_2 = V_t_2 % 19.07/18.96 <=> ( hAPP(c_Product__Type_Ofst(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Ofst(T_b,T_c),V_t_2) % 19.07/18.96 & hAPP(c_Product__Type_Osnd(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Osnd(T_b,T_c),V_t_2) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_prod__eqI,axiom, % 19.07/18.96 ! [V_q,V_p,T_b,T_a] : % 19.07/18.96 ( hAPP(c_Product__Type_Ofst(T_a,T_b),V_p) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_q) % 19.07/18.96 => ( hAPP(c_Product__Type_Osnd(T_a,T_b),V_p) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_q) % 19.07/18.96 => V_p = V_q ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_fst__apsnd,axiom, % 19.07/18.96 ! [V_x_2,V_f_2,T_d,T_c,T_b] : hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),V_x_2)) = hAPP(c_Product__Type_Ofst(T_b,T_d),V_x_2) ). % 19.07/18.96 % 19.07/18.96 fof(fact_fst__def,axiom, % 19.07/18.96 ! [V_p_2,T_c,T_b] : hAPP(c_Product__Type_Ofst(T_b,T_c),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_b),c_COMBK(T_b,T_c)),V_p_2) ). % 19.07/18.96 % 19.07/18.96 fof(fact_pair__collapse,axiom, % 19.07/18.96 ! [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 ). % 19.07/18.96 % 19.07/18.96 fof(fact_surjective__pairing,axiom, % 19.07/18.96 ! [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)) ). % 19.07/18.96 % 19.07/18.96 fof(fact_prod__case__beta,axiom, % 19.07/18.96 ! [V_p_2,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2),V_p_2) = hAPP(hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_p_2)),hAPP(c_Product__Type_Osnd(T_c,T_d),V_p_2)) ). % 19.07/18.96 % 19.07/18.96 fof(fact_div__int__def,axiom, % 19.07/18.96 ! [V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(V_a,V_b)) ). % 19.07/18.96 % 19.07/18.96 fof(fact_mod__nat__def,axiom, % 19.07/18.96 ! [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)) ). % 19.07/18.96 % 19.07/18.96 fof(fact_split__comp__eq,axiom, % 19.07/18.96 ! [V_g_2,V_f_2,T_e,T_d,T_c,T_b] : hAPP(hAPP(c_COMBS(tc_prod(T_b,T_c),T_c,T_d),hAPP(hAPP(c_COMBB(T_e,tc_fun(T_c,T_d),tc_prod(T_b,T_c)),V_f_2),hAPP(hAPP(c_COMBB(T_b,T_e,tc_prod(T_b,T_c)),V_g_2),c_Product__Type_Ofst(T_b,T_c)))),c_Product__Type_Osnd(T_b,T_c)) = hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),hAPP(hAPP(c_COMBB(T_e,tc_fun(T_c,T_d),T_b),V_f_2),V_g_2)) ). % 19.07/18.96 % 19.07/18.96 fof(fact_split__beta,axiom, % 19.07/18.96 ! [V_z_2,V_Pa_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_Pa_2),V_z_2) = hAPP(hAPP(V_Pa_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_z_2)),hAPP(c_Product__Type_Osnd(T_c,T_d),V_z_2)) ). % 19.07/18.96 % 19.07/18.96 fof(fact_split__def,axiom, % 19.07/18.96 ! [V_p_2,V_c_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_c_2),V_p_2) = hAPP(hAPP(V_c_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_p_2)),hAPP(c_Product__Type_Osnd(T_c,T_d),V_p_2)) ). % 19.07/18.96 % 19.07/18.96 fof(fact_Diff__subset,axiom, % 19.07/18.96 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_A_2)) ). % 19.07/18.96 % 19.07/18.96 fof(fact_Diff__mono,axiom, % 19.07/18.96 ! [V_B_2,V_D_2,V_C_2,V_A_2,T_b] : % 19.07/18.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_D_2),V_B_2)) % 19.07/18.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2))) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_double__diff,axiom, % 19.07/18.96 ! [V_C_2,V_B_2,V_A_2,T_b] : % 19.07/18.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 19.07/18.96 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) = V_A_2 ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_Compl__subset__Compl__iff,axiom, % 19.07/18.96 ! [V_B_2,V_A_2,T_b] : % 19.07/18.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2))) % 19.07/18.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_Compl__anti__mono,axiom, % 19.07/18.96 ! [V_B_2,V_A_2,T_b] : % 19.07/18.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 19.07/18.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_subset__refl,axiom, % 19.07/18.96 ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2)) ). % 19.07/18.96 % 19.07/18.96 fof(fact_set__eq__subset,axiom, % 19.07/18.96 ! [T_b,V_B_2,V_A_2] : % 19.07/18.96 ( V_A_2 = V_B_2 % 19.07/18.96 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 19.07/18.96 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_equalityD1,axiom, % 19.07/18.96 ! [T_b,V_B_2,V_A_2] : % 19.07/18.96 ( V_A_2 = V_B_2 % 19.07/18.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_equalityD2,axiom, % 19.07/18.96 ! [T_b,V_B_2,V_A_2] : % 19.07/18.96 ( V_A_2 = V_B_2 % 19.07/18.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_subset__trans,axiom, % 19.07/18.96 ! [V_C_2,V_B_2,V_A_2,T_b] : % 19.07/18.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 19.07/18.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_equalityE,axiom, % 19.07/18.96 ! [T_b,V_B_2,V_A_2] : % 19.07/18.96 ( V_A_2 = V_B_2 % 19.07/18.96 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 19.07/18.96 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_psubset__eq,axiom, % 19.07/18.96 ! [V_B_2,V_A_2,T_b] : % 19.07/18.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 19.07/18.96 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 19.07/18.96 & V_A_2 != V_B_2 ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_subset__iff__psubset__eq,axiom, % 19.07/18.96 ! [V_B_2,V_A_2,T_b] : % 19.07/18.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 19.07/18.96 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 19.07/18.96 | V_A_2 = V_B_2 ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_psubset__imp__subset,axiom, % 19.07/18.96 ! [V_B_2,V_A_2,T_b] : % 19.07/18.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 19.07/18.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_psubset__subset__trans,axiom, % 19.07/18.96 ! [V_C_2,V_B_2,V_A_2,T_b] : % 19.07/18.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 19.07/18.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_subset__psubset__trans,axiom, % 19.07/18.96 ! [V_C_2,V_B_2,V_A_2,T_b] : % 19.07/18.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 19.07/18.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_div__neg__pos,axiom, % 19.07/18.96 ! [V_b,V_a] : % 19.07/18.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 19.07/18.96 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(V_a,V_b)) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_div__pos__pos,axiom, % 19.07/18.96 ! [V_b,V_a] : % 19.07/18.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 19.07/18.96 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(V_a,V_b)) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_div__pos__pos__1__number__of,axiom, % 19.07/18.96 ! [V_w] : % 19.07/18.96 ( 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_w))) % 19.07/18.96 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_div__pos__neg,axiom, % 19.07/18.96 ! [V_b,V_a] : % 19.07/18.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 19.07/18.96 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)))) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_prod__size__simp,axiom, % 19.07/18.96 ! [V_p_2,V_g_2,V_f_2,T_c,T_b] : c_Product__Type_Oprod_Oprod__size(T_b,T_c,V_f_2,V_g_2,V_p_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_b,T_c),V_p_2))),hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_b,T_c),V_p_2)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 19.07/18.96 % 19.07/18.96 fof(fact_exI__realizer,axiom, % 19.07/18.96 ! [T_b,T_c,V_x_2,V_y_2,V_Pa_2] : % 19.07/18.96 ( hBOOL(hAPP(hAPP(V_Pa_2,V_y_2),V_x_2)) % 19.07/18.96 => hBOOL(hAPP(hAPP(V_Pa_2,hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2))),hAPP(c_Product__Type_Ofst(T_c,T_b),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2)))) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_conjI__realizer,axiom, % 19.07/18.96 ! [T_c,T_b,V_q_2,V_Qa_2,V_p_2,V_Pa_2] : % 19.07/18.96 ( hBOOL(hAPP(V_Pa_2,V_p_2)) % 19.07/18.96 => ( hBOOL(hAPP(V_Qa_2,V_q_2)) % 19.07/18.96 => ( hBOOL(hAPP(V_Pa_2,hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_p_2),V_q_2)))) % 19.07/18.96 & hBOOL(hAPP(V_Qa_2,hAPP(c_Product__Type_Osnd(T_b,T_c),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_p_2),V_q_2)))) ) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__Suc__number__of,axiom, % 19.07/18.96 ! [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)))) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__number__of__Suc,axiom, % 19.07/18.96 ! [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)))) ). % 19.07/18.96 % 19.07/18.96 fof(fact_double__complement,axiom, % 19.07/18.96 ! [V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = V_A_2 ). % 19.07/18.96 % 19.07/18.96 fof(fact_Compl__eq__Compl__iff,axiom, % 19.07/18.96 ! [V_B_2,V_A_2,T_b] : % 19.07/18.96 ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2) % 19.07/18.96 <=> V_A_2 = V_B_2 ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_Diff__idemp,axiom, % 19.07/18.96 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ). % 19.07/18.96 % 19.07/18.96 fof(fact_psubset__trans,axiom, % 19.07/18.96 ! [V_C_2,V_B_2,V_A_2,T_b] : % 19.07/18.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 19.07/18.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__max_Oinf__le1,axiom, % 19.07/18.96 ! [V_y,V_x,T_a] : % 19.07/18.96 ( class_Orderings_Olinorder(T_a) % 19.07/18.96 => 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)) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__max_Oinf__le2,axiom, % 19.07/18.96 ! [V_y,V_x,T_a] : % 19.07/18.96 ( class_Orderings_Olinorder(T_a) % 19.07/18.96 => 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)) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__max_Ole__iff__inf,axiom, % 19.07/18.96 ! [V_y_2,V_x_2,T_b] : % 19.07/18.96 ( class_Orderings_Olinorder(T_b) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 19.07/18.96 <=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2) = V_x_2 ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__max_Ole__inf__iff,axiom, % 19.07/18.96 ! [V_z_2,V_y_2,V_x_2,T_b] : % 19.07/18.96 ( class_Orderings_Olinorder(T_b) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_y_2),V_z_2))) % 19.07/18.96 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 19.07/18.96 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__max_Ole__infI1,axiom, % 19.07/18.96 ! [V_b,V_x,V_a,T_a] : % 19.07/18.96 ( class_Orderings_Olinorder(T_a) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 19.07/18.96 => 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)) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__max_Ole__infI2,axiom, % 19.07/18.96 ! [V_a,V_x,V_b,T_a] : % 19.07/18.96 ( class_Orderings_Olinorder(T_a) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 19.07/18.96 => 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)) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__max_Oinf__absorb1,axiom, % 19.07/18.96 ! [V_y,V_x,T_a] : % 19.07/18.96 ( class_Orderings_Olinorder(T_a) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 19.07/18.96 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_x ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__max_Oinf__absorb2,axiom, % 19.07/18.96 ! [V_x,V_y,T_a] : % 19.07/18.96 ( class_Orderings_Olinorder(T_a) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 19.07/18.96 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_y ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__max_Ole__infI,axiom, % 19.07/18.96 ! [V_b,V_a,V_x,T_a] : % 19.07/18.96 ( class_Orderings_Olinorder(T_a) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 19.07/18.96 => 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))) ) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__max_Oinf__greatest,axiom, % 19.07/18.96 ! [V_z,V_y,V_x,T_a] : % 19.07/18.96 ( class_Orderings_Olinorder(T_a) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) % 19.07/18.96 => 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))) ) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__max_Oinf__mono,axiom, % 19.07/18.96 ! [V_d,V_b,V_c,V_a,T_a] : % 19.07/18.96 ( class_Orderings_Olinorder(T_a) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 19.07/18.96 => 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))) ) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__max_Ole__infE,axiom, % 19.07/18.96 ! [V_b,V_a,V_x,T_a] : % 19.07/18.96 ( class_Orderings_Olinorder(T_a) % 19.07/18.96 => ( 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))) % 19.07/18.96 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 19.07/18.96 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__le__iff__disj,axiom, % 19.07/18.96 ! [V_z_2,V_y_2,V_x_2,T_b] : % 19.07/18.96 ( class_Orderings_Olinorder(T_b) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2)),V_z_2)) % 19.07/18.96 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) % 19.07/18.96 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__Suc__Suc,axiom, % 19.07/18.96 ! [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)) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__diff__distrib__left,axiom, % 19.07/18.96 ! [V_z,V_y,V_x,T_a] : % 19.07/18.96 ( class_Groups_Oordered__ab__group__add(T_a) % 19.07/18.96 => 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)) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__less__iff__disj,axiom, % 19.07/18.96 ! [V_z_2,V_y_2,V_x_2,T_b] : % 19.07/18.96 ( class_Orderings_Olinorder(T_b) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2)),V_z_2)) % 19.07/18.96 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2)) % 19.07/18.96 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2)) ) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__less__iff__conj,axiom, % 19.07/18.96 ! [V_y_2,V_x_2,V_z_2,T_b] : % 19.07/18.96 ( class_Orderings_Olinorder(T_b) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2))) % 19.07/18.96 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2)) % 19.07/18.96 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2)) ) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__max_Oless__infI1,axiom, % 19.07/18.96 ! [V_b,V_x,V_a,T_a] : % 19.07/18.96 ( class_Orderings_Olinorder(T_a) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x)) % 19.07/18.96 => 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)) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__max_Oless__infI2,axiom, % 19.07/18.96 ! [V_a,V_x,V_b,T_a] : % 19.07/18.96 ( class_Orderings_Olinorder(T_a) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x)) % 19.07/18.96 => 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)) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__max_Oinf__assoc,axiom, % 19.07/18.96 ! [V_z,V_y,V_x,T_a] : % 19.07/18.96 ( class_Orderings_Olinorder(T_a) % 19.07/18.96 => 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)) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__max_Oinf_Oassoc,axiom, % 19.07/18.96 ! [V_c,V_b,V_a,T_a] : % 19.07/18.96 ( class_Orderings_Olinorder(T_a) % 19.07/18.96 => 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)) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__max_Oinf__left__commute,axiom, % 19.07/18.96 ! [V_z,V_y,V_x,T_a] : % 19.07/18.96 ( class_Orderings_Olinorder(T_a) % 19.07/18.96 => 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)) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__max_Oinf_Oleft__commute,axiom, % 19.07/18.96 ! [V_c,V_a,V_b,T_a] : % 19.07/18.96 ( class_Orderings_Olinorder(T_a) % 19.07/18.96 => 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)) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__max_Oinf__left__idem,axiom, % 19.07/18.96 ! [V_y,V_x,T_a] : % 19.07/18.96 ( class_Orderings_Olinorder(T_a) % 19.07/18.96 => 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) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__max_Oinf_Oleft__idem,axiom, % 19.07/18.96 ! [V_b,V_a,T_a] : % 19.07/18.96 ( class_Orderings_Olinorder(T_a) % 19.07/18.96 => 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) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__max_Oinf__commute,axiom, % 19.07/18.96 ! [V_y,V_x,T_a] : % 19.07/18.96 ( class_Orderings_Olinorder(T_a) % 19.07/18.96 => 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) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__max_Oinf_Ocommute,axiom, % 19.07/18.96 ! [V_b,V_a,T_a] : % 19.07/18.96 ( class_Orderings_Olinorder(T_a) % 19.07/18.96 => 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) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__max_Oinf_Oidem,axiom, % 19.07/18.96 ! [V_a,T_a] : % 19.07/18.96 ( class_Orderings_Olinorder(T_a) % 19.07/18.96 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_a) = V_a ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__add__distrib__left,axiom, % 19.07/18.96 ! [V_z,V_y,V_x,T_a] : % 19.07/18.96 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 19.07/18.96 => 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)) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__0L,axiom, % 19.07/18.96 ! [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) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__0R,axiom, % 19.07/18.96 ! [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) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__diff,axiom, % 19.07/18.96 ! [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) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__number__of,axiom, % 19.07/18.96 ! [V_v,V_u,T_b] : % 19.07/18.96 ( ( class_Int_Onumber(T_b) % 19.07/18.96 & class_Orderings_Oord(T_b) ) % 19.07/18.96 => ( ( 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))) % 19.07/18.96 => 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) ) % 19.07/18.96 & ( ~ 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))) % 19.07/18.96 => 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) ) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_div__nat__def,axiom, % 19.07/18.96 ! [V_n,V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(V_m,V_n)) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__Suc1,axiom, % 19.07/18.96 ! [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) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__Suc2,axiom, % 19.07/18.96 ! [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) ). % 19.07/18.96 % 19.07/18.96 fof(fact_divmod__nat__rel__def,axiom, % 19.07/18.96 ! [V_qr_2,V_n_2,V_m_2] : % 19.07/18.96 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m_2,V_n_2),V_qr_2)) % 19.07/18.96 <=> ( 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)) % 19.07/18.96 & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 19.07/18.96 => hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 19.07/18.96 & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 19.07/18.96 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 19.07/18.96 => ( 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))) % 19.07/18.96 & 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)) ) ) % 19.07/18.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 19.07/18.96 => ( 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))) % 19.07/18.96 & 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))) ) ) ) ) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_range,axiom, % 19.07/18.96 ! [V_s,V_k] : % 19.07/18.96 ( 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)) % 19.07/18.96 => 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)) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__ord__min,axiom, % 19.07/18.96 ! [T_b] : % 19.07/18.96 ( class_Orderings_Oord(T_b) % 19.07/18.96 => c_Orderings_Oord__class_Omin(T_b) = c_Orderings_Oord_Omin(T_b,c_Orderings_Oord__class_Oless__eq(T_b)) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_prod_Orecs,axiom, % 19.07/18.96 ! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : c_Product__Type_Oprod_Oprod__rec(T_c,T_d,T_b,V_f1_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2) ). % 19.07/18.96 % 19.07/18.96 fof(fact_New__DSequence_Opos__not__seq__def,axiom, % 19.07/18.96 ! [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))) ). % 19.07/18.96 % 19.07/18.96 fof(fact_max__Suc__number__of,axiom, % 19.07/18.96 ! [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)))) ). % 19.07/18.96 % 19.07/18.96 fof(fact_max__less__iff__conj,axiom, % 19.07/18.96 ! [V_z_2,V_y_2,V_x_2,T_b] : % 19.07/18.96 ( class_Orderings_Olinorder(T_b) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2)),V_z_2)) % 19.07/18.96 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2)) % 19.07/18.96 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2)) ) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_less__max__iff__disj,axiom, % 19.07/18.96 ! [V_y_2,V_x_2,V_z_2,T_b] : % 19.07/18.96 ( class_Orderings_Olinorder(T_b) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2))) % 19.07/18.96 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2)) % 19.07/18.96 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2)) ) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__max_Oless__supI1,axiom, % 19.07/18.96 ! [V_b,V_a,V_x,T_a] : % 19.07/18.96 ( class_Orderings_Olinorder(T_a) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a)) % 19.07/18.96 => 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))) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__max_Oless__supI2,axiom, % 19.07/18.96 ! [V_a,V_b,V_x,T_a] : % 19.07/18.96 ( class_Orderings_Olinorder(T_a) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b)) % 19.07/18.96 => 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))) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__max_Oinf__sup__distrib2,axiom, % 19.07/18.96 ! [V_x,V_z,V_y,T_a] : % 19.07/18.96 ( class_Orderings_Olinorder(T_a) % 19.07/18.96 => 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)) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__max_Osup__inf__distrib2,axiom, % 19.07/18.96 ! [V_x,V_z,V_y,T_a] : % 19.07/18.96 ( class_Orderings_Olinorder(T_a) % 19.07/18.96 => 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)) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__max_Oinf__sup__distrib1,axiom, % 19.07/18.96 ! [V_z,V_y,V_x,T_a] : % 19.07/18.96 ( class_Orderings_Olinorder(T_a) % 19.07/18.96 => 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)) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__max_Osup__inf__distrib1,axiom, % 19.07/18.96 ! [V_z,V_y,V_x,T_a] : % 19.07/18.96 ( class_Orderings_Olinorder(T_a) % 19.07/18.96 => 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)) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__max_Oinf__sup__absorb,axiom, % 19.07/18.96 ! [V_y,V_x,T_a] : % 19.07/18.96 ( class_Orderings_Olinorder(T_a) % 19.07/18.96 => 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 ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__max_Osup__inf__absorb,axiom, % 19.07/18.96 ! [V_y,V_x,T_a] : % 19.07/18.96 ( class_Orderings_Olinorder(T_a) % 19.07/18.96 => 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 ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_max__diff__distrib__left,axiom, % 19.07/18.96 ! [V_z,V_y,V_x,T_a] : % 19.07/18.96 ( class_Groups_Oordered__ab__group__add(T_a) % 19.07/18.96 => 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)) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_max__0R,axiom, % 19.07/18.96 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_n ). % 19.07/18.96 % 19.07/18.96 fof(fact_max__0L,axiom, % 19.07/18.96 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ). % 19.07/18.96 % 19.07/18.96 fof(fact_max__add__distrib__left,axiom, % 19.07/18.96 ! [V_z,V_y,V_x,T_a] : % 19.07/18.96 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 19.07/18.96 => 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)) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__max_Osup_Oidem,axiom, % 19.07/18.96 ! [V_a,T_a] : % 19.07/18.96 ( class_Orderings_Olinorder(T_a) % 19.07/18.96 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_a) = V_a ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__max_Osup_Ocommute,axiom, % 19.07/18.96 ! [V_b,V_a,T_a] : % 19.07/18.96 ( class_Orderings_Olinorder(T_a) % 19.07/18.96 => 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) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__max_Osup__commute,axiom, % 19.07/18.96 ! [V_y,V_x,T_a] : % 19.07/18.96 ( class_Orderings_Olinorder(T_a) % 19.07/18.96 => 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) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__max_Osup_Oleft__idem,axiom, % 19.07/18.96 ! [V_b,V_a,T_a] : % 19.07/18.96 ( class_Orderings_Olinorder(T_a) % 19.07/18.96 => 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) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__max_Osup__left__idem,axiom, % 19.07/18.96 ! [V_y,V_x,T_a] : % 19.07/18.96 ( class_Orderings_Olinorder(T_a) % 19.07/18.96 => 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) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__max_Osup_Oleft__commute,axiom, % 19.07/18.96 ! [V_c,V_a,V_b,T_a] : % 19.07/18.96 ( class_Orderings_Olinorder(T_a) % 19.07/18.96 => 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)) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__max_Osup__left__commute,axiom, % 19.07/18.96 ! [V_z,V_y,V_x,T_a] : % 19.07/18.96 ( class_Orderings_Olinorder(T_a) % 19.07/18.96 => 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)) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__max_Osup_Oassoc,axiom, % 19.07/18.96 ! [V_c,V_b,V_a,T_a] : % 19.07/18.96 ( class_Orderings_Olinorder(T_a) % 19.07/18.96 => 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)) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__max_Osup__assoc,axiom, % 19.07/18.96 ! [V_z,V_y,V_x,T_a] : % 19.07/18.96 ( class_Orderings_Olinorder(T_a) % 19.07/18.96 => 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)) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_max__Suc__Suc,axiom, % 19.07/18.96 ! [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)) ). % 19.07/18.96 % 19.07/18.96 fof(fact_le__max__iff__disj,axiom, % 19.07/18.96 ! [V_y_2,V_x_2,V_z_2,T_b] : % 19.07/18.96 ( class_Orderings_Olinorder(T_b) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2))) % 19.07/18.96 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_x_2)) % 19.07/18.96 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_y_2)) ) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__max_Ole__supE,axiom, % 19.07/18.96 ! [V_x,V_b,V_a,T_a] : % 19.07/18.96 ( class_Orderings_Olinorder(T_a) % 19.07/18.96 => ( 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)) % 19.07/18.96 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 19.07/18.96 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__max_Osup__mono,axiom, % 19.07/18.96 ! [V_d,V_b,V_c,V_a,T_a] : % 19.07/18.96 ( class_Orderings_Olinorder(T_a) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 19.07/18.96 => 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))) ) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__max_Osup__least,axiom, % 19.07/18.96 ! [V_z,V_x,V_y,T_a] : % 19.07/18.96 ( class_Orderings_Olinorder(T_a) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) % 19.07/18.96 => 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)) ) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__max_Ole__supI,axiom, % 19.07/18.96 ! [V_b,V_x,V_a,T_a] : % 19.07/18.96 ( class_Orderings_Olinorder(T_a) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 19.07/18.96 => 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)) ) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__max_Osup__absorb1,axiom, % 19.07/18.96 ! [V_x,V_y,T_a] : % 19.07/18.96 ( class_Orderings_Olinorder(T_a) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 19.07/18.96 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_x ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__max_Osup__absorb2,axiom, % 19.07/18.96 ! [V_y,V_x,T_a] : % 19.07/18.96 ( class_Orderings_Olinorder(T_a) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 19.07/18.96 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_y ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__max_Ole__supI2,axiom, % 19.07/18.96 ! [V_a,V_b,V_x,T_a] : % 19.07/18.96 ( class_Orderings_Olinorder(T_a) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 19.07/18.96 => 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))) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__max_Ole__supI1,axiom, % 19.07/18.96 ! [V_b,V_a,V_x,T_a] : % 19.07/18.96 ( class_Orderings_Olinorder(T_a) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 19.07/18.96 => 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))) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__max_Ole__sup__iff,axiom, % 19.07/18.96 ! [V_z_2,V_y_2,V_x_2,T_b] : % 19.07/18.96 ( class_Orderings_Olinorder(T_b) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2)),V_z_2)) % 19.07/18.96 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) % 19.07/18.96 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__max_Ole__iff__sup,axiom, % 19.07/18.96 ! [V_y_2,V_x_2,T_b] : % 19.07/18.96 ( class_Orderings_Olinorder(T_b) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 19.07/18.96 <=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2) = V_y_2 ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_le__maxI2,axiom, % 19.07/18.96 ! [V_x,V_y,T_a] : % 19.07/18.96 ( class_Orderings_Olinorder(T_a) % 19.07/18.96 => 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))) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_le__maxI1,axiom, % 19.07/18.96 ! [V_y,V_x,T_a] : % 19.07/18.96 ( class_Orderings_Olinorder(T_a) % 19.07/18.96 => 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))) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_max__number__of,axiom, % 19.07/18.96 ! [V_v,V_u,T_b] : % 19.07/18.96 ( ( class_Int_Onumber(T_b) % 19.07/18.96 & class_Orderings_Oord(T_b) ) % 19.07/18.96 => ( ( 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))) % 19.07/18.96 => 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) ) % 19.07/18.96 & ( ~ 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))) % 19.07/18.96 => 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) ) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__max_Odistrib__sup__le,axiom, % 19.07/18.96 ! [V_z,V_y,V_x,T_a] : % 19.07/18.96 ( class_Orderings_Olinorder(T_a) % 19.07/18.96 => 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)))) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_min__max_Odistrib__inf__le,axiom, % 19.07/18.96 ! [V_z,V_y,V_x,T_a] : % 19.07/18.96 ( class_Orderings_Olinorder(T_a) % 19.07/18.96 => 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)))) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_minus__min__eq__max,axiom, % 19.07/18.96 ! [V_y,V_x,T_a] : % 19.07/18.96 ( class_Groups_Olinordered__ab__group__add(T_a) % 19.07/18.96 => 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)) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_minus__max__eq__min,axiom, % 19.07/18.96 ! [V_y,V_x,T_a] : % 19.07/18.96 ( class_Groups_Olinordered__ab__group__add(T_a) % 19.07/18.96 => 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)) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_nat__minus__add__max,axiom, % 19.07/18.96 ! [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) ). % 19.07/18.96 % 19.07/18.96 fof(fact_max__Suc2,axiom, % 19.07/18.96 ! [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) ). % 19.07/18.96 % 19.07/18.96 fof(fact_max__Suc1,axiom, % 19.07/18.96 ! [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) ). % 19.07/18.96 % 19.07/18.96 fof(fact_max__number__of__Suc,axiom, % 19.07/18.96 ! [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)))) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dual__min,axiom, % 19.07/18.96 ! [T_b] : % 19.07/18.96 ( class_Orderings_Olinorder(T_b) % 19.07/18.96 => c_Orderings_Oord_Omin(T_b,hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_b))) = c_Orderings_Oord__class_Omax(T_b) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_max__ord__max,axiom, % 19.07/18.96 ! [T_b] : % 19.07/18.96 ( class_Orderings_Oord(T_b) % 19.07/18.96 => c_Orderings_Oord__class_Omax(T_b) = c_Orderings_Oord_Omax(T_b,c_Orderings_Oord__class_Oless__eq(T_b)) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_apfst__apsnd,axiom, % 19.07/18.96 ! [V_x_2,V_g_2,T_e,V_f_2,T_c,T_b,T_d] : hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),hAPP(c_Product__Type_Oapsnd(T_e,T_c,T_d,V_g_2),V_x_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_e),V_x_2))),hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_d,T_e),V_x_2))) ). % 19.07/18.96 % 19.07/18.96 fof(fact_apsnd__apfst,axiom, % 19.07/18.96 ! [V_x_2,V_g_2,T_e,V_f_2,T_b,T_c,T_d] : hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(c_Product__Type_Oapfst(T_e,T_b,T_d,V_g_2),V_x_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_e,T_d),V_x_2))),hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_e,T_d),V_x_2))) ). % 19.07/18.96 % 19.07/18.96 fof(fact_code__numeral__decr,axiom, % 19.07/18.96 ! [V_k] : % 19.07/18.96 ( V_k != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 19.07/18.96 => 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))) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_code__numeral_Onat__of__inject,axiom, % 19.07/18.96 ! [V_y_2,V_x_2] : % 19.07/18.96 ( hAPP(c_Code__Numeral_Onat__of,V_x_2) = hAPP(c_Code__Numeral_Onat__of,V_y_2) % 19.07/18.96 <=> V_x_2 = V_y_2 ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_Code__Numeral_Onat__of__inject,axiom, % 19.07/18.96 ! [V_l_2,V_k_2] : % 19.07/18.96 ( hAPP(c_Code__Numeral_Onat__of,V_k_2) = hAPP(c_Code__Numeral_Onat__of,V_l_2) % 19.07/18.96 <=> V_k_2 = V_l_2 ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_nat__of__inverse,axiom, % 19.07/18.96 ! [V_x] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_x)) = V_x ). % 19.07/18.96 % 19.07/18.96 fof(fact_of__nat__nat__of,axiom, % 19.07/18.96 ! [V_k] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_k)) = V_k ). % 19.07/18.96 % 19.07/18.96 fof(fact_nat__of__of__nat,axiom, % 19.07/18.96 ! [V_n] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_n)) = V_n ). % 19.07/18.96 % 19.07/18.96 fof(fact_apfst__conv,axiom, % 19.07/18.96 ! [V_y_2,V_x_2,V_f_2,T_c,T_b,T_d] : hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_d,T_c),V_x_2),V_y_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,V_x_2)),V_y_2) ). % 19.07/18.96 % 19.07/18.96 fof(fact_apfst__eq__conv,axiom, % 19.07/18.96 ! [V_g_2,V_x_2,V_f_2,T_c,T_b,T_d] : % 19.07/18.96 ( hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),V_x_2) = hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_g_2),V_x_2) % 19.07/18.96 <=> hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_c),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_d,T_c),V_x_2)) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_fst__apfst,axiom, % 19.07/18.96 ! [V_x_2,V_f_2,T_d,T_c,T_b] : hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_c),V_x_2)) ). % 19.07/18.96 % 19.07/18.96 fof(fact_snd__apfst,axiom, % 19.07/18.96 ! [V_x_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(c_Product__Type_Oapfst(T_d,T_c,T_b,V_f_2),V_x_2)) = hAPP(c_Product__Type_Osnd(T_d,T_b),V_x_2) ). % 19.07/18.96 % 19.07/18.96 fof(fact_apsnd__apfst__commute,axiom, % 19.07/18.96 ! [V_p_2,V_g_2,T_e,V_f_2,T_b,T_c,T_d] : hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(c_Product__Type_Oapfst(T_e,T_b,T_d,V_g_2),V_p_2)) = hAPP(c_Product__Type_Oapfst(T_e,T_b,T_c,V_g_2),hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_e,V_f_2),V_p_2)) ). % 19.07/18.96 % 19.07/18.96 fof(fact_less__code__numeral__def,axiom, % 19.07/18.96 ! [V_m_2,V_n_2] : % 19.07/18.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2)) % 19.07/18.96 <=> 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))) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_nat__of__number,axiom, % 19.07/18.96 ! [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) ). % 19.07/18.96 % 19.07/18.96 fof(fact_less__eq__code__numeral__def,axiom, % 19.07/18.96 ! [V_m_2,V_n_2] : % 19.07/18.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2)) % 19.07/18.96 <=> 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))) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_nat__of__code,axiom, % 19.07/18.96 ! [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)) ). % 19.07/18.96 % 19.07/18.96 fof(fact_nat__of__aux__def,axiom, % 19.07/18.96 ! [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) ). % 19.07/18.96 % 19.07/18.96 fof(fact_Min_Oidem,axiom, % 19.07/18.96 ! [V_x,T_a] : % 19.07/18.96 ( class_Orderings_Olinorder(T_a) % 19.07/18.96 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_x) = V_x ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_Max_Oidem,axiom, % 19.07/18.96 ! [V_x,T_a] : % 19.07/18.96 ( class_Orderings_Olinorder(T_a) % 19.07/18.96 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_x) = V_x ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dual__max,axiom, % 19.07/18.96 ! [T_b] : % 19.07/18.96 ( class_Orderings_Olinorder(T_b) % 19.07/18.96 => c_Orderings_Oord_Omax(T_b,hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_b))) = c_Orderings_Oord__class_Omin(T_b) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_Suc__code__numeral__def,axiom, % 19.07/18.96 ! [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))) ). % 19.07/18.96 % 19.07/18.96 fof(fact_minus__code__numeral__def,axiom, % 19.07/18.96 ! [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))) ). % 19.07/18.96 % 19.07/18.96 fof(fact_plus__code__numeral__def,axiom, % 19.07/18.96 ! [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))) ). % 19.07/18.96 % 19.07/18.96 fof(fact_div__code__numeral__def,axiom, % 19.07/18.96 ! [V_m,V_n] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n)),hAPP(c_Code__Numeral_Onat__of,V_m))) ). % 19.07/18.96 % 19.07/18.96 fof(fact_times__code__numeral__def,axiom, % 19.07/18.96 ! [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))) ). % 19.07/18.96 % 19.07/18.96 fof(fact_mod__code__numeral__def,axiom, % 19.07/18.96 ! [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))) ). % 19.07/18.96 % 19.07/18.96 fof(fact_Nitpick_Ozero__frac__def,axiom, % 19.07/18.96 ! [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))) ). % 19.07/18.96 % 19.07/18.96 fof(fact_pos__not__random__dseq__def,axiom, % 19.07/18.96 ! [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)) ). % 19.07/18.96 % 19.07/18.96 fof(fact_surjective__sum,axiom, % 19.07/18.96 ! [V_f_2,T_c,T_d,T_b] : c_Sum__Type_Osum_Osum__case(T_b,T_d,T_c,hAPP(hAPP(c_COMBB(tc_sum(T_b,T_c),T_d,T_b),V_f_2),c_Sum__Type_OInl(T_b,T_c)),hAPP(hAPP(c_COMBB(tc_sum(T_b,T_c),T_d,T_c),V_f_2),c_Sum__Type_OInr(T_c,T_b))) = V_f_2 ). % 19.07/18.96 % 19.07/18.96 fof(fact_iterate_Osimps,axiom, % 19.07/18.96 ! [V_x_2,V_f_2,T_b,T_c,V_k_2] : % 19.07/18.96 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 19.07/18.96 => hAPP(c_Random_Oiterate(T_c,T_b,V_k_2,V_f_2),V_x_2) = hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2) ) % 19.07/18.96 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 19.07/18.96 => hAPP(c_Random_Oiterate(T_c,T_b,V_k_2,V_f_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_c,T_b,tc_prod(T_c,T_b)),hAPP(V_f_2,V_x_2)),c_Random_Oiterate(T_c,T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_k_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),V_f_2)) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_scomp__unfold,axiom, % 19.07/18.96 ! [V_x_2,V_g_2,V_f_2,T_b,T_e,T_d,T_c] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_c,T_d,T_e,T_b),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_d,T_e),hAPP(V_f_2,V_x_2))),hAPP(c_Product__Type_Osnd(T_d,T_e),hAPP(V_f_2,V_x_2))) ). % 19.07/18.96 % 19.07/18.96 fof(fact_scomp__scomp,axiom, % 19.07/18.96 ! [V_h_2,V_g_2,V_f_2,T_g,T_f,T_c,T_e,T_d,T_b] : hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_d,T_e,T_c),hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_f,T_g,tc_prod(T_d,T_e)),V_f_2),V_g_2)),V_h_2) = hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_f,T_g,T_c),V_f_2),hAPP(hAPP(c_COMBC(T_f,tc_fun(T_d,tc_fun(T_e,T_c)),tc_fun(T_g,T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_g,tc_prod(T_d,T_e)),tc_fun(tc_fun(T_d,tc_fun(T_e,T_c)),tc_fun(T_g,T_c)),T_f),c_Product__Type_Oscomp(T_g,T_d,T_e,T_c)),V_g_2)),V_h_2)) ). % 19.07/18.96 % 19.07/18.96 fof(fact_sum__case__KK,axiom, % 19.07/18.96 ! [V_x_2,V_a_2,T_d,T_b,T_c] : hAPP(c_Sum__Type_Osum_Osum__case(T_c,T_b,T_d,hAPP(c_COMBK(T_b,T_c),V_a_2),hAPP(c_COMBK(T_b,T_d),V_a_2)),V_x_2) = V_a_2 ). % 19.07/18.96 % 19.07/18.96 fof(fact_sum__case__weak__cong,axiom, % 19.07/18.96 ! [V_g_2,V_f_2,T_c,T_d,T_b,V_t_2,V_s_2] : % 19.07/18.96 ( V_s_2 = V_t_2 % 19.07/18.96 => hAPP(c_Sum__Type_Osum_Osum__case(T_b,T_d,T_c,V_f_2,V_g_2),V_s_2) = hAPP(c_Sum__Type_Osum_Osum__case(T_b,T_d,T_c,V_f_2,V_g_2),V_t_2) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_sum__case__inject,axiom, % 19.07/18.96 ! [V_g2_2,V_g1_2,V_f2_2,V_f1_2,T_c,T_d,T_b] : % 19.07/18.96 ( c_Sum__Type_Osum_Osum__case(T_b,T_d,T_c,V_f1_2,V_f2_2) = c_Sum__Type_Osum_Osum__case(T_b,T_d,T_c,V_g1_2,V_g2_2) % 19.07/18.96 => ~ ( V_f1_2 = V_g1_2 % 19.07/18.96 => V_f2_2 != V_g2_2 ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_scomp__Pair,axiom, % 19.07/18.96 ! [V_x_2,T_d,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_c,T_d,tc_prod(T_c,T_d)),V_x_2),c_Product__Type_OPair(T_c,T_d)) = V_x_2 ). % 19.07/18.96 % 19.07/18.96 fof(fact_Pair__scomp,axiom, % 19.07/18.96 ! [V_f_2,V_x_2,T_c,T_d,T_b] : hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_d,T_b,T_c),hAPP(c_Product__Type_OPair(T_d,T_b),V_x_2)),V_f_2) = hAPP(V_f_2,V_x_2) ). % 19.07/18.96 % 19.07/18.96 fof(fact_scomp__apply,axiom, % 19.07/18.96 ! [V_x_2,V_g_2,V_f_2,T_b,T_e,T_d,T_c] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_c,T_d,T_e,T_b),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_b),V_g_2),hAPP(V_f_2,V_x_2)) ). % 19.07/18.96 % 19.07/18.96 fof(fact_sum_Osimps_I6_J,axiom, % 19.07/18.96 ! [V_b_2,V_f2_2,V_f1_2,T_d,T_b,T_c] : hAPP(c_Sum__Type_Osum_Osum__case(T_c,T_b,T_d,V_f1_2,V_f2_2),hAPP(c_Sum__Type_OInr(T_d,T_c),V_b_2)) = hAPP(V_f2_2,V_b_2) ). % 19.07/18.96 % 19.07/18.96 fof(fact_sum_Osimps_I5_J,axiom, % 19.07/18.96 ! [V_a_2,V_f2_2,V_f1_2,T_d,T_b,T_c] : hAPP(c_Sum__Type_Osum_Osum__case(T_c,T_b,T_d,V_f1_2,V_f2_2),hAPP(c_Sum__Type_OInl(T_c,T_d),V_a_2)) = hAPP(V_f1_2,V_a_2) ). % 19.07/18.96 % 19.07/18.96 fof(fact_scomp__def,axiom, % 19.07/18.96 ! [V_x_2,V_g_2,V_f_2,T_b,T_e,T_d,T_c] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_c,T_d,T_e,T_b),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_b),V_g_2),hAPP(V_f_2,V_x_2)) ). % 19.07/18.96 % 19.07/18.96 fof(fact_Nitpick_Oone__frac__def,axiom, % 19.07/18.96 ! [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))) ). % 19.07/18.96 % 19.07/18.96 fof(fact_Nitpick_Onumber__of__frac__def,axiom, % 19.07/18.96 ! [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))) ). % 19.07/18.96 % 19.07/18.96 fof(fact_Nitpick_Ofrac__def,axiom, % 19.07/18.96 ! [V_b,V_a,T_a] : hAPP(hAPP(c_Nitpick_Ofrac(T_a),V_a),V_b) = c_Nitpick_OAbs__Frac(T_a,c_Nitpick_Onorm__frac(V_a,V_b)) ). % 19.07/18.96 % 19.07/18.96 fof(fact_internal__split__def,axiom, % 19.07/18.96 ! [T_d,T_c,T_b] : c_Product__Type_Ointernal__split(T_b,T_c,T_d) = c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d) ). % 19.07/18.96 % 19.07/18.96 fof(fact_transfer__morphism__int__nat,axiom, % 19.07/18.96 c_Nat__Transfer_Otransfer__morphism(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_COMBK(tc_HOL_Obool,tc_Nat_Onat),c_fTrue)) ). % 19.07/18.96 % 19.07/18.96 fof(fact_internal__split__conv,axiom, % 19.07/18.96 ! [V_b_2,V_a_2,V_c_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ointernal__split(T_c,T_d,T_b),V_c_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_c_2,V_a_2),V_b_2) ). % 19.07/18.96 % 19.07/18.96 fof(fact_Nitpick_Oplus__frac__def,axiom, % 19.07/18.96 ! [V_r_2,V_q_2,T_b] : c_Nitpick_Oplus__frac(T_b,V_q_2,V_r_2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(T_b),V_q_2),hAPP(c_Nitpick_Odenom(T_b),V_r_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,T_b),tc_Int_Oint),c_Nitpick_Ofrac(T_b)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),V_q_2))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(T_b),V_q_2))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),V_r_2))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(T_b),V_r_2)))))),c_COMBI(tc_Int_Oint))) ). % 19.07/18.96 % 19.07/18.96 fof(fact_New__DSequence_Oneg__decr__bind__def,axiom, % 19.07/18.96 ! [V_f_2,V_x_2,T_b,T_c,V_i_2] : % 19.07/18.96 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 19.07/18.96 => hAPP(c_New__DSequence_Oneg__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohit__bound(T_b) ) % 19.07/18.96 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 19.07/18.96 => hAPP(c_New__DSequence_Oneg__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohb__bind(T_c,T_b,hAPP(V_x_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b))),V_f_2),V_i_2)) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_New__DSequence_Opos__decr__bind__def,axiom, % 19.07/18.96 ! [V_f_2,V_x_2,T_b,T_c,V_i_2] : % 19.07/18.96 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 19.07/18.96 => hAPP(c_New__DSequence_Opos__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Oempty(T_b) ) % 19.07/18.96 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 19.07/18.96 => hAPP(c_New__DSequence_Opos__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Obind(T_c,T_b,hAPP(V_x_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b)),V_f_2),V_i_2)) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_rev__predicate2D,axiom, % 19.07/18.96 ! [V_Qa_2,T_c,T_b,V_y_2,V_x_2,V_Pa_2] : % 19.07/18.96 ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2)) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_Pa_2),V_Qa_2)) % 19.07/18.96 => hBOOL(hAPP(hAPP(V_Qa_2,V_x_2),V_y_2)) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_predicate2D,axiom, % 19.07/18.96 ! [V_y_2,V_x_2,V_Qa_2,V_Pa_2,T_c,T_b] : % 19.07/18.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_Pa_2),V_Qa_2)) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2)) % 19.07/18.96 => hBOOL(hAPP(hAPP(V_Qa_2,V_x_2),V_y_2)) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_rev__predicate1D,axiom, % 19.07/18.96 ! [V_Qa_2,T_b,V_x_2,V_Pa_2] : % 19.07/18.96 ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_Pa_2),V_Qa_2)) % 19.07/18.96 => hBOOL(hAPP(V_Qa_2,V_x_2)) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_predicate1D,axiom, % 19.07/18.96 ! [V_x_2,V_Qa_2,V_Pa_2,T_b] : % 19.07/18.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_Pa_2),V_Qa_2)) % 19.07/18.96 => ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 19.07/18.96 => hBOOL(hAPP(V_Qa_2,V_x_2)) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_Nitpick_Otimes__frac__def,axiom, % 19.07/18.96 ! [V_r,V_q,T_a] : c_Nitpick_Otimes__frac(T_a,V_q,V_r) = hAPP(hAPP(c_Nitpick_Ofrac(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_a),V_q)),hAPP(c_Nitpick_Onum(T_a),V_r))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Odenom(T_a),V_q)),hAPP(c_Nitpick_Odenom(T_a),V_r))) ). % 19.07/18.96 % 19.07/18.96 fof(fact_Nitpick_Oof__frac__def,axiom, % 19.07/18.96 ! [V_q,T_a,T_b] : % 19.07/18.96 ( ( class_Rings_Oinverse(T_b) % 19.07/18.96 & class_Rings_Oring__1(T_b) ) % 19.07/18.96 => c_Nitpick_Oof__frac(T_a,T_b,V_q) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(c_Nitpick_Onum(T_a),V_q))),hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(c_Nitpick_Odenom(T_a),V_q))) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_Nitpick_Oinverse__frac__def,axiom, % 19.07/18.96 ! [V_q,T_a] : c_Nitpick_Oinverse__frac(T_a,V_q) = hAPP(hAPP(c_Nitpick_Ofrac(T_a),hAPP(c_Nitpick_Odenom(T_a),V_q)),hAPP(c_Nitpick_Onum(T_a),V_q)) ). % 19.07/18.96 % 19.07/18.96 fof(fact_Nitpick_Ouminus__frac__def,axiom, % 19.07/18.96 ! [V_q,T_a] : c_Nitpick_Ouminus__frac(T_a,V_q) = c_Nitpick_OAbs__Frac(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_a),V_q))),hAPP(c_Nitpick_Odenom(T_a),V_q))) ). % 19.07/18.96 % 19.07/18.96 fof(fact_New__Random__Sequence_Opos__decr__bind__def,axiom, % 19.07/18.96 ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_b,T_c] : c_New__Random__Sequence_Opos__decr__bind(T_c,T_b,V_R_2,V_f_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__decr__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b)))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)) ). % 19.07/18.96 % 19.07/18.96 fof(fact_Nitpick_Oless__frac__def,axiom, % 19.07/18.96 ! [V_r_2,V_q_2,T_b] : % 19.07/18.96 ( c_Nitpick_Oless__frac(T_b,V_q_2,V_r_2) % 19.07/18.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),c_Nitpick_Oplus__frac(T_b,V_q_2,c_Nitpick_Ouminus__frac(T_b,V_r_2)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_Nitpick_Oless__eq__frac__def,axiom, % 19.07/18.96 ! [V_r_2,V_q_2,T_b] : % 19.07/18.96 ( c_Nitpick_Oless__eq__frac(T_b,V_q_2,V_r_2) % 19.07/18.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),c_Nitpick_Oplus__frac(T_b,V_q_2,c_Nitpick_Ouminus__frac(T_b,V_r_2)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_New__Random__Sequence_Oneg__decr__bind__def,axiom, % 19.07/18.96 ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_b,T_c] : c_New__Random__Sequence_Oneg__decr__bind(T_c,T_b,V_R_2,V_f_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Oneg__decr__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b))))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)) ). % 19.07/18.96 % 19.07/18.96 fof(fact_New__DSequence_Oneg__bind__def,axiom, % 19.07/18.96 ! [V_i_2,V_f_2,V_x_2,T_b,T_c] : hAPP(c_New__DSequence_Oneg__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohb__bind(T_c,T_b,hAPP(V_x_2,V_i_2),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b))),V_f_2),V_i_2)) ). % 19.07/18.96 % 19.07/18.96 fof(fact_New__DSequence_Opos__empty__def,axiom, % 19.07/18.96 ! [V_i_1,T_a] : hAPP(c_New__DSequence_Opos__empty(T_a),V_i_1) = c_Lazy__Sequence_Oempty(T_a) ). % 19.07/18.96 % 19.07/18.96 fof(fact_pos__empty__def,axiom, % 19.07/18.96 ! [V_seed_2,V_size_2,V_nrandom_2,T_b] : c_New__Random__Sequence_Opos__empty(T_b,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__empty(T_b) ). % 19.07/18.96 % 19.07/18.96 fof(fact_neg__bind__def,axiom, % 19.07/18.96 ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_b,T_c] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(T_c,T_b,V_R_2,V_f_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Oneg__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b))))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)) ). % 19.07/18.96 % 19.07/18.96 fof(fact_New__DSequence_Opos__bind__def,axiom, % 19.07/18.96 ! [V_i_2,V_f_2,V_x_2,T_b,T_c] : hAPP(c_New__DSequence_Opos__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Obind(T_c,T_b,hAPP(V_x_2,V_i_2),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b)),V_f_2),V_i_2)) ). % 19.07/18.96 % 19.07/18.96 fof(fact_The__split,axiom, % 19.07/18.96 ! [V_Pa_2,T_c,T_b] : c_HOL_OThe(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_Pa_2)) = c_HOL_OThe(tc_prod(T_b,T_c),hAPP(hAPP(c_COMBS(tc_prod(T_b,T_c),T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_HOL_Obool),tc_prod(T_b,T_c)),V_Pa_2),c_Product__Type_Ofst(T_b,T_c))),c_Product__Type_Osnd(T_b,T_c))) ). % 19.07/18.96 % 19.07/18.96 fof(fact_Random_Osimps,axiom, % 19.07/18.96 ! [V_size_2,V_g_2,T_b,V_nrandom_2] : % 19.07/18.96 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_nrandom_2),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) % 19.07/18.96 => c_Random__Sequence_ORandom(T_b,V_g_2,V_nrandom_2,V_size_2) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(T_b)) ) % 19.07/18.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_nrandom_2),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) % 19.07/18.96 => c_Random__Sequence_ORandom(T_b,V_g_2,V_nrandom_2,V_size_2) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm)),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(V_g_2,V_size_2)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random__Sequence_ORandom(T_b,V_g_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_nrandom_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),V_size_2))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b))))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b))))),c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b))))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Ounion(T_b)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Osingle(T_b)),c_Product__Type_Ofst(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))))))) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_The__split__eq,axiom, % 19.07/18.96 ! [V_y_2,V_x_2,T_c,T_b] : c_HOL_OThe(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_x_2)))),hAPP(c_fequal,V_y_2)))) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2) ). % 19.07/18.96 % 19.07/18.96 fof(fact_split__paired__The,axiom, % 19.07/18.96 ! [V_Pa_2,T_c,T_b] : c_HOL_OThe(tc_prod(T_b,T_c),V_Pa_2) = c_HOL_OThe(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_Pa_2)),c_Product__Type_OPair(T_b,T_c)))) ). % 19.07/18.96 % 19.07/18.96 fof(fact_divmod__nat__def,axiom, % 19.07/18.96 ! [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)) ). % 19.07/18.96 % 19.07/18.96 fof(fact_Random__Sequence_Oempty__def,axiom, % 19.07/18.96 ! [V_size_2,V_nrandom_2,T_b] : c_Random__Sequence_Oempty(T_b,V_nrandom_2,V_size_2) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(T_b)) ). % 19.07/18.96 % 19.07/18.96 fof(fact_Random__Sequence_Osingle__def,axiom, % 19.07/18.96 ! [V_size_2,V_nrandom_2,V_x_2,T_b] : hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(T_b),V_x_2),V_nrandom_2),V_size_2) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_DSequence_Osingle(T_b),V_x_2)) ). % 19.07/18.96 % 19.07/18.96 fof(fact_pos__bind__def,axiom, % 19.07/18.96 ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_b,T_c] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(T_c,T_b,V_R_2,V_f_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Opos__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b)))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)) ). % 19.07/18.96 % 19.07/18.96 fof(fact_the__sym__eq__trivial,axiom, % 19.07/18.96 ! [V_x_2,T_b] : c_HOL_OThe(T_b,hAPP(c_fequal,V_x_2)) = V_x_2 ). % 19.07/18.96 % 19.07/18.96 fof(fact_the__eq__trivial,axiom, % 19.07/18.96 ! [V_a_2,T_b] : c_HOL_OThe(T_b,hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2)) = V_a_2 ). % 19.07/18.96 % 19.07/18.96 fof(fact_exE__realizer,axiom, % 19.07/18.96 ! [T_d,V_f_2,V_Qa_2,V_p_2,T_b,T_c,V_Pa_2] : % 19.07/18.96 ( hBOOL(hAPP(hAPP(V_Pa_2,hAPP(c_Product__Type_Osnd(T_c,T_b),V_p_2)),hAPP(c_Product__Type_Ofst(T_c,T_b),V_p_2))) % 19.07/18.96 => ( ! [B_x,B_y] : % 19.07/18.96 ( hBOOL(hAPP(hAPP(V_Pa_2,B_y),B_x)) % 19.07/18.96 => hBOOL(hAPP(V_Qa_2,hAPP(hAPP(V_f_2,B_x),B_y))) ) % 19.07/18.96 => hBOOL(hAPP(V_Qa_2,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,T_d),V_f_2),V_p_2))) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_hoare__derivs_OCall,axiom, % 19.07/18.96 ! [V_a_2,V_X_2,V_s_H_2,V_Qa_2,V_pna_2,V_Pa_2,V_G_2,T_b] : % 19.07/18.96 ( 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),V_Pa_2),hAPP(c_Com_Ocom_OBODY,V_pna_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_b),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),V_Qa_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_b),tc_HOL_Obool)))) % 19.07/18.96 => 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(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_b),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_b,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_b),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),V_Pa_2)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),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_pna_2,V_a_2)),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_beyond__def,axiom, % 19.07/18.96 ! [V_l,V_k] : % 19.07/18.96 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) % 19.07/18.96 => c_Quickcheck_Obeyond(V_k,V_l) = V_l ) % 19.07/18.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) % 19.07/18.96 => c_Quickcheck_Obeyond(V_k,V_l) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_curry__def,axiom, % 19.07/18.96 ! [V_y_2,V_x_2,V_c_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ocurry(T_c,T_d,T_b,V_c_2),V_x_2),V_y_2) = hAPP(V_c_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)) ). % 19.07/18.96 % 19.07/18.96 fof(fact_power__dvd__imp__le,axiom, % 19.07/18.96 ! [V_n,V_m,V_i] : % 19.07/18.96 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n))) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_i)) % 19.07/18.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_curryI,axiom, % 19.07/18.96 ! [V_b_2,V_a_2,T_c,T_b,V_f_2] : % 19.07/18.96 ( hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) % 19.07/18.96 => hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2)) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd_Oorder__refl,axiom, % 19.07/18.96 ! [V_x] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_x)) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd__0__right,axiom, % 19.07/18.96 ! [V_a,T_a] : % 19.07/18.96 ( class_Rings_Ocomm__semiring__1(T_a) % 19.07/18.96 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_empty__subsetI,axiom, % 19.07/18.96 ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_A_2)) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd__1__left,axiom, % 19.07/18.96 ! [V_k] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k)) ). % 19.07/18.96 % 19.07/18.96 fof(fact_subset__empty,axiom, % 19.07/18.96 ! [V_A_2,T_b] : % 19.07/18.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) % 19.07/18.96 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_nat__dvd__1__iff__1,axiom, % 19.07/18.96 ! [V_m_2] : % 19.07/18.96 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))) % 19.07/18.96 <=> V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_insert__mono,axiom, % 19.07/18.96 ! [V_a_2,V_D_2,V_C_2,T_b] : % 19.07/18.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2)) % 19.07/18.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_C_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_D_2))) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_subset__insertI2,axiom, % 19.07/18.96 ! [V_b_2,V_B_2,V_A_2,T_b] : % 19.07/18.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 19.07/18.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_subset__insertI,axiom, % 19.07/18.96 ! [V_a_2,V_B_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2))) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd__diff__nat,axiom, % 19.07/18.96 ! [V_n,V_m,V_k] : % 19.07/18.96 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m)) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n)) % 19.07/18.96 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n))) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_singleton__inject,axiom, % 19.07/18.96 ! [V_b_2,V_a_2,T_b] : % 19.07/18.96 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) % 19.07/18.96 => V_a_2 = V_b_2 ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_insert__code,axiom, % 19.07/18.96 ! [V_x_2,V_A_2,V_y_2,T_b] : % 19.07/18.96 ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2),V_x_2)) % 19.07/18.96 <=> ( V_y_2 = V_x_2 % 19.07/18.96 | hBOOL(hAPP(V_A_2,V_x_2)) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_doubleton__eq__iff,axiom, % 19.07/18.96 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] : % 19.07/18.96 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(T_b),V_c_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_d_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) % 19.07/18.96 <=> ( ( V_a_2 = V_c_2 % 19.07/18.96 & V_b_2 = V_d_2 ) % 19.07/18.96 | ( V_a_2 = V_d_2 % 19.07/18.96 & V_b_2 = V_c_2 ) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_insert__commute,axiom, % 19.07/18.96 ! [V_A_2,V_y_2,V_x_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) ). % 19.07/18.96 % 19.07/18.96 fof(fact_insert__absorb2,axiom, % 19.07/18.96 ! [V_A_2,V_x_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2) ). % 19.07/18.96 % 19.07/18.96 fof(fact_insert__not__empty,axiom, % 19.07/18.96 ! [V_A_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 19.07/18.96 % 19.07/18.96 fof(fact_empty__not__insert,axiom, % 19.07/18.96 ! [V_A_2,V_a_2,T_b] : c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) ). % 19.07/18.96 % 19.07/18.96 fof(fact_subset__singletonD,axiom, % 19.07/18.96 ! [V_x_2,V_A_2,T_b] : % 19.07/18.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) % 19.07/18.96 => ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.96 | 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))) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_asm,axiom, % 19.07/18.96 ! [V_G_2,V_ts_2,T_b] : % 19.07/18.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_ts_2),V_G_2)) % 19.07/18.96 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_ts_2) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_weaken,axiom, % 19.07/18.96 ! [V_ts_2,V_ts_H_2,V_G_2,T_b] : % 19.07/18.96 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_ts_H_2) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_ts_2),V_ts_H_2)) % 19.07/18.96 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_ts_2) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_hoare__derivs_Oequations_I7_J,axiom, % 19.07/18.96 ! [V_a2_2,V_a1_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_a1_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_a2_2),c_Com_Ocom_OSKIP),V_a2_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ). % 19.07/18.96 % 19.07/18.96 fof(fact_hoare__derivs_OSkip,axiom, % 19.07/18.96 ! [V_Pa_2,V_G_2,T_b] : 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),V_Pa_2),c_Com_Ocom_OSKIP),V_Pa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ). % 19.07/18.96 % 19.07/18.96 fof(fact_Comp,axiom, % 19.07/18.96 ! [V_R_2,V_d_2,V_Qa_2,V_c_2,V_Pa_2,V_G_2,T_b] : % 19.07/18.96 ( 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),V_Pa_2),V_c_2),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) % 19.07/18.96 => ( 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),V_Qa_2),V_d_2),V_R_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) % 19.07/18.96 => 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),V_Pa_2),c_Com_Ocom_OSemi(V_c_2,V_d_2)),V_R_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_div__dvd__div,axiom, % 19.07/18.96 ! [V_c_2,V_b_2,V_a_2,T_b] : % 19.07/18.96 ( class_Divides_Osemiring__div(T_b) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2)) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_c_2)) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_b_2),V_a_2)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_c_2),V_a_2))) % 19.07/18.96 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_b_2),V_c_2)) ) ) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd__0__left,axiom, % 19.07/18.96 ! [V_a,T_a] : % 19.07/18.96 ( class_Rings_Ocomm__semiring__1(T_a) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 19.07/18.96 => V_a = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd__add,axiom, % 19.07/18.96 ! [V_c,V_b,V_a,T_a] : % 19.07/18.96 ( class_Rings_Ocomm__semiring__1(T_a) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b)) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)) % 19.07/18.96 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))) ) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_one__dvd,axiom, % 19.07/18.96 ! [V_a,T_a] : % 19.07/18.96 ( class_Rings_Ocomm__semiring__1(T_a) % 19.07/18.96 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd_Oless__asym,axiom, % 19.07/18.96 ! [V_y,V_x] : % 19.07/18.96 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) % 19.07/18.96 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) ) % 19.07/18.96 => ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) % 19.07/18.96 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd_Oless__trans,axiom, % 19.07/18.96 ! [V_z,V_y,V_x] : % 19.07/18.96 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) % 19.07/18.96 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) ) % 19.07/18.96 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z)) % 19.07/18.96 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_y)) ) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z)) % 19.07/18.96 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x)) ) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd_Oless__asym_H,axiom, % 19.07/18.96 ! [V_b,V_a] : % 19.07/18.96 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) % 19.07/18.96 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) ) % 19.07/18.96 => ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) % 19.07/18.96 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd_Oless__le__trans,axiom, % 19.07/18.96 ! [V_z,V_y,V_x] : % 19.07/18.96 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) % 19.07/18.96 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) ) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z)) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z)) % 19.07/18.96 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x)) ) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd_Oord__less__eq__trans,axiom, % 19.07/18.96 ! [V_c,V_b,V_a] : % 19.07/18.96 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) % 19.07/18.96 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) ) % 19.07/18.96 => ( V_b = V_c % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) % 19.07/18.96 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_a)) ) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd_Oless__imp__not__eq2,axiom, % 19.07/18.96 ! [V_y,V_x] : % 19.07/18.96 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) % 19.07/18.96 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) ) % 19.07/18.96 => V_y != V_x ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd_Oless__imp__not__eq,axiom, % 19.07/18.96 ! [V_y,V_x] : % 19.07/18.96 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) % 19.07/18.96 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) ) % 19.07/18.96 => V_x != V_y ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd_Oless__imp__not__less,axiom, % 19.07/18.96 ! [V_y,V_x] : % 19.07/18.96 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) % 19.07/18.96 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) ) % 19.07/18.96 => ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) % 19.07/18.96 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd_Oless__imp__le,axiom, % 19.07/18.96 ! [V_y,V_x] : % 19.07/18.96 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) % 19.07/18.96 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) ) % 19.07/18.96 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd_Oless__not__sym,axiom, % 19.07/18.96 ! [V_y,V_x] : % 19.07/18.96 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) % 19.07/18.96 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) ) % 19.07/18.96 => ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) % 19.07/18.96 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd_Oless__imp__neq,axiom, % 19.07/18.96 ! [V_y,V_x] : % 19.07/18.96 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) % 19.07/18.96 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) ) % 19.07/18.96 => V_x != V_y ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd_Ole__less__trans,axiom, % 19.07/18.96 ! [V_z,V_y,V_x] : % 19.07/18.96 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) % 19.07/18.96 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z)) % 19.07/18.96 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_y)) ) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z)) % 19.07/18.96 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x)) ) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd_Oord__eq__less__trans,axiom, % 19.07/18.96 ! [V_c,V_b,V_a] : % 19.07/18.96 ( V_a = V_b % 19.07/18.96 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_c)) % 19.07/18.96 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_b)) ) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) % 19.07/18.96 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_a)) ) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd_Oorder__trans,axiom, % 19.07/18.96 ! [V_z,V_y,V_x] : % 19.07/18.96 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z)) % 19.07/18.96 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z)) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd_Oantisym,axiom, % 19.07/18.96 ! [V_y,V_x] : % 19.07/18.96 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) % 19.07/18.96 => V_x = V_y ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd__antisym,axiom, % 19.07/18.96 ! [V_n,V_m] : % 19.07/18.96 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n)) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_n),V_m)) % 19.07/18.96 => V_m = V_n ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd_Oord__le__eq__trans,axiom, % 19.07/18.96 ! [V_c,V_b,V_a] : % 19.07/18.96 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) % 19.07/18.96 => ( V_b = V_c % 19.07/18.96 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd_Oord__eq__le__trans,axiom, % 19.07/18.96 ! [V_c,V_b,V_a] : % 19.07/18.96 ( V_a = V_b % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_c)) % 19.07/18.96 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd_Ole__neq__trans,axiom, % 19.07/18.96 ! [V_b,V_a] : % 19.07/18.96 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) % 19.07/18.96 => ( V_a != V_b % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) % 19.07/18.96 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) ) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd_Ole__imp__less__or__eq,axiom, % 19.07/18.96 ! [V_y,V_x] : % 19.07/18.96 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) % 19.07/18.96 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) % 19.07/18.96 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) ) % 19.07/18.96 | V_x = V_y ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd_Oantisym__conv,axiom, % 19.07/18.96 ! [V_x_2,V_y_2] : % 19.07/18.96 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) % 19.07/18.96 <=> V_x_2 = V_y_2 ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd_Oeq__refl,axiom, % 19.07/18.96 ! [V_y,V_x] : % 19.07/18.96 ( V_x = V_y % 19.07/18.96 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd_Oneq__le__trans,axiom, % 19.07/18.96 ! [V_b,V_a] : % 19.07/18.96 ( V_a != V_b % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) % 19.07/18.96 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) ) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd_Oless__le,axiom, % 19.07/18.96 ! [V_y_2,V_x_2] : % 19.07/18.96 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) % 19.07/18.96 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) ) % 19.07/18.96 <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) % 19.07/18.96 & V_x_2 != V_y_2 ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd_Ole__less,axiom, % 19.07/18.96 ! [V_y_2,V_x_2] : % 19.07/18.96 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) % 19.07/18.96 <=> ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) % 19.07/18.96 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) ) % 19.07/18.96 | V_x_2 = V_y_2 ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd_Oeq__iff,axiom, % 19.07/18.96 ! [V_y_2,V_x_2] : % 19.07/18.96 ( V_x_2 = V_y_2 % 19.07/18.96 <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) % 19.07/18.96 & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_empty,axiom, % 19.07/18.96 ! [V_G_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))) ). % 19.07/18.96 % 19.07/18.96 fof(fact_hoare__derivs_Oequations_I1_J,axiom, % 19.07/18.96 ! [V_a_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))) ). % 19.07/18.96 % 19.07/18.96 fof(fact_cut,axiom, % 19.07/18.96 ! [V_G_2,V_ts_2,V_G_H_2,T_b] : % 19.07/18.96 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_ts_2) % 19.07/18.96 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_G_H_2) % 19.07/18.96 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_ts_2) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_hoare__derivs_Oinsert,axiom, % 19.07/18.96 ! [V_ts_2,V_t_2,V_G_2,T_b] : % 19.07/18.96 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),V_t_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) % 19.07/18.96 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_ts_2) % 19.07/18.96 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),V_t_2),V_ts_2)) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd__trans,axiom, % 19.07/18.96 ! [V_c,V_b,V_a,T_a] : % 19.07/18.96 ( class_Rings_Ocomm__semiring__1(T_a) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b)) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_c)) % 19.07/18.96 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)) ) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd__refl,axiom, % 19.07/18.96 ! [V_a,T_a] : % 19.07/18.96 ( class_Rings_Ocomm__semiring__1(T_a) % 19.07/18.96 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_a)) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_bot__apply,axiom, % 19.07/18.96 ! [V_x_2,T_c,T_b] : % 19.07/18.96 ( class_Orderings_Obot(T_b) % 19.07/18.96 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd__power__same,axiom, % 19.07/18.96 ! [V_n,V_y,V_x,T_a] : % 19.07/18.96 ( class_Rings_Ocomm__semiring__1(T_a) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y)) % 19.07/18.96 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_n))) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd__mod__iff,axiom, % 19.07/18.96 ! [V_m_2,V_n_2,V_k_2,T_b] : % 19.07/18.96 ( class_Divides_Osemiring__div(T_b) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_n_2)) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),c_Divides_Odiv__class_Omod(T_b,V_m_2,V_n_2))) % 19.07/18.96 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_m_2)) ) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_mod__mod__cancel,axiom, % 19.07/18.96 ! [V_a,V_b,V_c,T_a] : % 19.07/18.96 ( class_Divides_Osemiring__div(T_a) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_b)) % 19.07/18.96 => c_Divides_Odiv__class_Omod(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,V_a,V_c) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd__mod,axiom, % 19.07/18.96 ! [V_n,V_m,V_k,T_a] : % 19.07/18.96 ( class_Divides_Osemiring__div(T_a) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_m)) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_n)) % 19.07/18.96 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),c_Divides_Odiv__class_Omod(T_a,V_m,V_n))) ) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd__mod__imp__dvd,axiom, % 19.07/18.96 ! [V_n,V_m,V_k,T_a] : % 19.07/18.96 ( class_Divides_Osemiring__div(T_a) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),c_Divides_Odiv__class_Omod(T_a,V_m,V_n))) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_n)) % 19.07/18.96 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_m)) ) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd__mult__right,axiom, % 19.07/18.96 ! [V_c,V_b,V_a,T_a] : % 19.07/18.96 ( class_Rings_Ocomm__semiring__1(T_a) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c)) % 19.07/18.96 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_c)) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd__mult__left,axiom, % 19.07/18.96 ! [V_c,V_b,V_a,T_a] : % 19.07/18.96 ( class_Rings_Ocomm__semiring__1(T_a) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c)) % 19.07/18.96 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvdI,axiom, % 19.07/18.96 ! [V_k,V_b,V_a,T_a] : % 19.07/18.96 ( class_Rings_Odvd(T_a) % 19.07/18.96 => ( V_a = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_k) % 19.07/18.96 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_a)) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_mult__dvd__mono,axiom, % 19.07/18.96 ! [V_d,V_c,V_b,V_a,T_a] : % 19.07/18.96 ( class_Rings_Ocomm__semiring__1(T_a) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b)) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_d)) % 19.07/18.96 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd__mult,axiom, % 19.07/18.96 ! [V_b,V_c,V_a,T_a] : % 19.07/18.96 ( class_Rings_Ocomm__semiring__1(T_a) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)) % 19.07/18.96 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd__mult2,axiom, % 19.07/18.96 ! [V_c,V_b,V_a,T_a] : % 19.07/18.96 ( class_Rings_Ocomm__semiring__1(T_a) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b)) % 19.07/18.96 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd__triv__right,axiom, % 19.07/18.96 ! [V_b,V_a,T_a] : % 19.07/18.96 ( class_Rings_Ocomm__semiring__1(T_a) % 19.07/18.96 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a))) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd__triv__left,axiom, % 19.07/18.96 ! [V_b,V_a,T_a] : % 19.07/18.96 ( class_Rings_Ocomm__semiring__1(T_a) % 19.07/18.96 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd__abs__iff,axiom, % 19.07/18.96 ! [V_k_2,V_m_2,T_b] : % 19.07/18.96 ( class_Rings_Olinordered__idom(T_b) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_k_2))) % 19.07/18.96 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),V_k_2)) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_abs__dvd__iff,axiom, % 19.07/18.96 ! [V_k_2,V_m_2,T_b] : % 19.07/18.96 ( class_Rings_Olinordered__idom(T_b) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_m_2)),V_k_2)) % 19.07/18.96 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),V_k_2)) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd__if__abs__eq,axiom, % 19.07/18.96 ! [V_k,V_l,T_a] : % 19.07/18.96 ( class_Rings_Olinordered__idom(T_a) % 19.07/18.96 => ( hAPP(c_Groups_Oabs__class_Oabs(T_a),V_l) = hAPP(c_Groups_Oabs__class_Oabs(T_a),V_k) % 19.07/18.96 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_l),V_k)) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd__reduce,axiom, % 19.07/18.96 ! [V_n_2,V_k_2] : % 19.07/18.96 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2))) % 19.07/18.96 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_n_2)) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd__diff,axiom, % 19.07/18.96 ! [V_z,V_y,V_x,T_a] : % 19.07/18.96 ( class_Rings_Ocomm__ring__1(T_a) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y)) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_z)) % 19.07/18.96 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_y),V_z))) ) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_minus__dvd__iff,axiom, % 19.07/18.96 ! [V_y_2,V_x_2,T_b] : % 19.07/18.96 ( class_Rings_Ocomm__ring__1(T_b) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)),V_y_2)) % 19.07/18.96 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),V_y_2)) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd__minus__iff,axiom, % 19.07/18.96 ! [V_y_2,V_x_2,T_b] : % 19.07/18.96 ( class_Rings_Ocomm__ring__1(T_b) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2))) % 19.07/18.96 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),V_y_2)) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_bot__fun__def,axiom, % 19.07/18.96 ! [V_x_2,T_c,T_b] : % 19.07/18.96 ( class_Orderings_Obot(T_b) % 19.07/18.96 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_insert__Diff__single,axiom, % 19.07/18.96 ! [V_A_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) ). % 19.07/18.96 % 19.07/18.96 fof(fact_Diff__insert2,axiom, % 19.07/18.96 ! [V_B_2,V_a_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2) ). % 19.07/18.96 % 19.07/18.96 fof(fact_Diff__insert,axiom, % 19.07/18.96 ! [V_B_2,V_a_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ). % 19.07/18.96 % 19.07/18.96 fof(fact_empty__Diff,axiom, % 19.07/18.96 ! [V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 19.07/18.96 % 19.07/18.96 fof(fact_Diff__empty,axiom, % 19.07/18.96 ! [V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_A_2 ). % 19.07/18.96 % 19.07/18.96 fof(fact_Diff__cancel,axiom, % 19.07/18.96 ! [V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 19.07/18.96 % 19.07/18.96 fof(fact_hoare__derivs_Oequations_I8_J,axiom, % 19.07/18.96 ! [V_a4_2,V_a3_2,V_a2_2,V_a1_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_a1_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_b),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),V_a2_2)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),V_a3_2)),V_a4_2))),c_Com_Ocom_OAss(V_a3_2,V_a4_2)),V_a2_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ). % 19.07/18.96 % 19.07/18.96 fof(fact_Ass,axiom, % 19.07/18.96 ! [V_a_2,V_X_2,V_Pa_2,V_G_2,T_b] : 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(hAPP(c_COMBC(T_b,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_b),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),V_Pa_2)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),V_X_2)),V_a_2))),c_Com_Ocom_OAss(V_X_2,V_a_2)),V_Pa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ). % 19.07/18.96 % 19.07/18.96 fof(fact_not__psubset__empty,axiom, % 19.07/18.96 ! [V_A_2,T_b] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ). % 19.07/18.96 % 19.07/18.96 fof(fact_bot__least,axiom, % 19.07/18.96 ! [V_x,T_a] : % 19.07/18.96 ( class_Orderings_Obot(T_a) % 19.07/18.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x)) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd__mult__cancel__left,axiom, % 19.07/18.96 ! [V_b_2,V_a_2,V_c_2,T_b] : % 19.07/18.96 ( class_Rings_Oidom(T_b) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2))) % 19.07/18.96 <=> ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b) % 19.07/18.96 | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2)) ) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd__mult__cancel__right,axiom, % 19.07/18.96 ! [V_b_2,V_c_2,V_a_2,T_b] : % 19.07/18.96 ( class_Rings_Oidom(T_b) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2))) % 19.07/18.96 <=> ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b) % 19.07/18.96 | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2)) ) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd__imp__mod__0,axiom, % 19.07/18.96 ! [V_b,V_a,T_a] : % 19.07/18.96 ( class_Divides_Osemiring__div(T_a) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b)) % 19.07/18.96 => c_Divides_Odiv__class_Omod(T_a,V_b,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd__eq__mod__eq__0,axiom, % 19.07/18.96 ! [V_b_2,V_a_2,T_b] : % 19.07/18.96 ( class_Divides_Osemiring__div(T_b) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2)) % 19.07/18.96 <=> c_Divides_Odiv__class_Omod(T_b,V_b_2,V_a_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_div__add,axiom, % 19.07/18.96 ! [V_y,V_x,V_z,T_a] : % 19.07/18.96 ( class_Divides_Osemiring__div(T_a) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_x)) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_y)) % 19.07/18.96 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_z)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_y),V_z)) ) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_div__mult__div__if__dvd,axiom, % 19.07/18.96 ! [V_w,V_z,V_x,V_y,T_a] : % 19.07/18.96 ( class_Divides_Osemiring__div(T_a) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x)) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_w)) % 19.07/18.96 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_y)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_w),V_z)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_w)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z)) ) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd__div__mult,axiom, % 19.07/18.96 ! [V_c,V_b,V_a,T_a] : % 19.07/18.96 ( class_Divides_Osemiring__div(T_a) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b)) % 19.07/18.96 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_b),V_a)),V_c) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)),V_a) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd__div__mult__self,axiom, % 19.07/18.96 ! [V_b,V_a,T_a] : % 19.07/18.96 ( class_Divides_Osemiring__div(T_a) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b)) % 19.07/18.96 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_b),V_a)),V_a) = V_b ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_div__mult__swap,axiom, % 19.07/18.96 ! [V_a,V_b,V_c,T_a] : % 19.07/18.96 ( class_Divides_Osemiring__div(T_a) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_b)) % 19.07/18.96 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd__mult__div__cancel,axiom, % 19.07/18.96 ! [V_b,V_a,T_a] : % 19.07/18.96 ( class_Divides_Osemiring__div(T_a) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b)) % 19.07/18.96 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_b),V_a)) = V_b ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd__neg__div,axiom, % 19.07/18.96 ! [V_x,V_y,T_a] : % 19.07/18.96 ( class_Divides_Oring__div(T_a) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x)) % 19.07/18.96 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),V_y) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_y)) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd__div__neg,axiom, % 19.07/18.96 ! [V_x,V_y,T_a] : % 19.07/18.96 ( class_Divides_Oring__div(T_a) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x)) % 19.07/18.96 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_y)) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_le__imp__power__dvd,axiom, % 19.07/18.96 ! [V_a,V_n,V_m,T_a] : % 19.07/18.96 ( class_Rings_Ocomm__semiring__1(T_a) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 19.07/18.96 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd__power__le,axiom, % 19.07/18.96 ! [V_m,V_n,V_y,V_x,T_a] : % 19.07/18.96 ( class_Rings_Ocomm__semiring__1(T_a) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y)) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 19.07/18.96 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_m))) ) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_power__le__dvd,axiom, % 19.07/18.96 ! [V_m,V_b,V_n,V_a,T_a] : % 19.07/18.96 ( class_Rings_Ocomm__semiring__1(T_a) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_b)) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 19.07/18.96 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),V_b)) ) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_beyond__zero,axiom, % 19.07/18.96 ! [V_k] : c_Quickcheck_Obeyond(V_k,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ). % 19.07/18.96 % 19.07/18.96 fof(fact_div__power,axiom, % 19.07/18.96 ! [V_n,V_x,V_y,T_a] : % 19.07/18.96 ( class_Divides_Osemiring__div(T_a) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x)) % 19.07/18.96 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_y)),V_n) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_n)) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd__1__iff__1,axiom, % 19.07/18.96 ! [V_m_2] : % 19.07/18.96 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) % 19.07/18.96 <=> V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_nat__dvd__not__less,axiom, % 19.07/18.96 ! [V_n,V_m] : % 19.07/18.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 19.07/18.96 => ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_n),V_m)) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_nat__mult__dvd__cancel__disj,axiom, % 19.07/18.96 ! [V_n_2,V_m_2,V_k_2] : % 19.07/18.96 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))) % 19.07/18.96 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 19.07/18.96 | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd__diffD,axiom, % 19.07/18.96 ! [V_n,V_m,V_k] : % 19.07/18.96 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n))) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n)) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 19.07/18.96 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m)) ) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd__diffD1,axiom, % 19.07/18.96 ! [V_n,V_m,V_k] : % 19.07/18.96 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n))) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m)) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 19.07/18.96 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n)) ) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_hoare__derivs_OLocal,axiom, % 19.07/18.96 ! [V_a_2,V_s_H_2,V_X_2,V_Qa_2,V_c_2,V_Pa_2,V_G_2,T_b] : % 19.07/18.96 ( 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),V_Pa_2),V_c_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_b),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),V_Qa_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_b),tc_HOL_Obool)))) % 19.07/18.96 => 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(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_b),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_b,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_b),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),V_Pa_2)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),c_Com_Ovname_OLoc(V_X_2))),V_a_2)))),c_Com_Ocom_OLocal(V_X_2,V_a_2,V_c_2)),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_curryE,axiom, % 19.07/18.96 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] : % 19.07/18.96 ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2)) % 19.07/18.96 => hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_curryD,axiom, % 19.07/18.96 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] : % 19.07/18.96 ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2)) % 19.07/18.96 => hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_subset__Compl__self__eq,axiom, % 19.07/18.96 ! [V_A_2,T_b] : % 19.07/18.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) % 19.07/18.96 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_unity__coeff__ex,axiom, % 19.07/18.96 ! [V_l_2,V_Pa_2,T_b] : % 19.07/18.96 ( ( class_Rings_Odvd(T_b) % 19.07/18.96 & class_Rings_Osemiring__0(T_b) ) % 19.07/18.96 => ( ? [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_l_2),B_x))) % 19.07/18.96 <=> ? [B_x] : % 19.07/18.96 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_l_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),c_Groups_Ozero__class_Ozero(T_b)))) % 19.07/18.96 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_curry__conv,axiom, % 19.07/18.96 ! [V_b_2,V_a_2,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ocurry(T_c,T_d,T_b,V_f_2),V_a_2),V_b_2) = hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) ). % 19.07/18.96 % 19.07/18.96 fof(fact_inf__period_I4_J,axiom, % 19.07/18.96 ! [V_t_2,V_D_2,V_d_2,T_b] : % 19.07/18.96 ( ( class_Rings_Ocomm__ring(T_b) % 19.07/18.96 & class_Rings_Odvd(T_b) ) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2)) % 19.07/18.96 => ! [B_x,B_k] : % 19.07/18.96 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),V_t_2))) % 19.07/18.96 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_k),V_D_2))),V_t_2))) ) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_inf__period_I3_J,axiom, % 19.07/18.96 ! [V_t_2,V_D_2,V_d_2,T_b] : % 19.07/18.96 ( ( class_Rings_Ocomm__ring(T_b) % 19.07/18.96 & class_Rings_Odvd(T_b) ) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2)) % 19.07/18.96 => ! [B_x,B_k] : % 19.07/18.96 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),V_t_2))) % 19.07/18.96 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_k),V_D_2))),V_t_2))) ) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd__eq__mod__eq__0__number__of,axiom, % 19.07/18.96 ! [V_y_2,V_x_2,T_b] : % 19.07/18.96 ( ( class_Divides_Osemiring__div(T_b) % 19.07/18.96 & class_Int_Onumber(T_b) ) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2))) % 19.07/18.96 <=> c_Divides_Odiv__class_Omod(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)) = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd__div__div__eq__mult,axiom, % 19.07/18.96 ! [V_d_2,V_b_2,V_c_2,V_a_2,T_b] : % 19.07/18.96 ( class_Divides_Osemiring__div(T_b) % 19.07/18.96 => ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b) % 19.07/18.96 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2)) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_c_2),V_d_2)) % 19.07/18.96 => ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_b_2),V_a_2) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_d_2),V_c_2) % 19.07/18.96 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2) ) ) ) ) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd__div__eq__mult,axiom, % 19.07/18.96 ! [V_c_2,V_b_2,V_a_2,T_b] : % 19.07/18.96 ( class_Divides_Osemiring__div(T_b) % 19.07/18.96 => ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2)) % 19.07/18.96 => ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_b_2),V_a_2) = V_c_2 % 19.07/18.96 <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2) ) ) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_curry__split,axiom, % 19.07/18.96 ! [V_f_2,T_d,T_c,T_b] : c_Product__Type_Ocurry(T_b,T_c,T_d,hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_f_2)) = V_f_2 ). % 19.07/18.96 % 19.07/18.96 fof(fact_split__curry,axiom, % 19.07/18.96 ! [V_f_2,T_d,T_c,T_b] : hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),c_Product__Type_Ocurry(T_b,T_c,T_d,V_f_2)) = V_f_2 ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd__imp__le,axiom, % 19.07/18.96 ! [V_n,V_k] : % 19.07/18.96 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n)) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 19.07/18.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd__mult__cancel,axiom, % 19.07/18.96 ! [V_n,V_m,V_k] : % 19.07/18.96 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n))) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 19.07/18.96 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n)) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_nat__mult__dvd__cancel1,axiom, % 19.07/18.96 ! [V_n_2,V_m_2,V_k_2] : % 19.07/18.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))) % 19.07/18.96 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd__power,axiom, % 19.07/18.96 ! [V_x,V_n,T_a] : % 19.07/18.96 ( class_Rings_Ocomm__semiring__1(T_a) % 19.07/18.96 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 19.07/18.96 | V_x = c_Groups_Oone__class_Oone(T_a) ) % 19.07/18.96 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n))) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd__mult__cancel1,axiom, % 19.07/18.96 ! [V_n_2,V_m_2] : % 19.07/18.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)),V_m_2)) % 19.07/18.96 <=> V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd__mult__cancel2,axiom, % 19.07/18.96 ! [V_n_2,V_m_2] : % 19.07/18.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_m_2)),V_m_2)) % 19.07/18.96 <=> V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_the__elem__def,axiom, % 19.07/18.96 ! [V_X_2,T_b] : c_Set_Othe__elem(T_b,V_X_2) = c_HOL_OThe(T_b,hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),hAPP(c_fequal,V_X_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) ). % 19.07/18.96 % 19.07/18.96 fof(fact_the__elem__eq,axiom, % 19.07/18.96 ! [V_x_2,T_b] : c_Set_Othe__elem(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ). % 19.07/18.96 % 19.07/18.96 fof(fact_Option_Oset_Osimps_I2_J,axiom, % 19.07/18.96 ! [V_x_2,T_b] : c_Option_Oset(T_b,hAPP(c_Option_Ooption_OSome(T_b),V_x_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd_Ostrict__monoD,axiom, % 19.07/18.96 ! [V_y_2,V_x_2,V_f_2,T_b] : % 19.07/18.96 ( class_Orderings_Oorder(T_b) % 19.07/18.96 => ( c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,T_b,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_f_2) % 19.07/18.96 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) % 19.07/18.96 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) ) % 19.07/18.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_dvd_OmonoD,axiom, % 19.07/18.96 ! [V_y_2,V_x_2,V_f_2,T_b] : % 19.07/18.96 ( class_Orderings_Oorder(T_b) % 19.07/18.96 => ( c_Orderings_Oorder_Omono(tc_Nat_Onat,T_b,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_f_2) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) % 19.07/18.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_zdvd__antisym__abs,axiom, % 19.07/18.96 ! [V_b,V_a] : % 19.07/18.96 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a),V_b)) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_b),V_a)) % 19.07/18.96 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_a) = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_b) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_zdvd__zmod,axiom, % 19.07/18.96 ! [V_n,V_m,V_f] : % 19.07/18.96 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_f),V_m)) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_f),V_n)) % 19.07/18.96 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_f),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n))) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_zdvd__zmod__imp__zdvd,axiom, % 19.07/18.96 ! [V_n,V_m,V_k] : % 19.07/18.96 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n))) % 19.07/18.96 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_n)) % 19.07/18.96 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_m)) ) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_uminus__dvd__conv_I1_J,axiom, % 19.07/18.96 ! [V_t_2,V_d_2] : % 19.07/18.96 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_t_2)) % 19.07/18.96 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_d_2)),V_t_2)) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_uminus__dvd__conv_I2_J,axiom, % 19.07/18.96 ! [V_t_2,V_d_2] : % 19.07/18.96 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_t_2)) % 19.07/18.96 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_t_2))) ) ). % 19.07/18.96 % 19.07/18.96 fof(fact_zdvd__zdiffD,axiom, % 19.07/18.96 ! [V_n,V_m,V_k] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_m),V_n))) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_n)) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_m)) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_bot__nat__def,axiom, % 19.07/18.97 c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 19.07/18.97 % 19.07/18.97 fof(fact_zdvd__antisym__nonneg,axiom, % 19.07/18.97 ! [V_n,V_m] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m)) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_n)) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m),V_n)) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n),V_m)) % 19.07/18.97 => V_m = V_n ) ) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_zdvd__not__zless,axiom, % 19.07/18.97 ! [V_n,V_m] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m)) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_m),V_n)) % 19.07/18.97 => ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n),V_m)) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_zdvd__mult__cancel,axiom, % 19.07/18.97 ! [V_n,V_m,V_k] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_n))) % 19.07/18.97 => ( V_k != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m),V_n)) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_zdvd__mono,axiom, % 19.07/18.97 ! [V_t_2,V_m_2,V_k_2] : % 19.07/18.97 ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m_2),V_t_2)) % 19.07/18.97 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_t_2))) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_zdvd__reduce,axiom, % 19.07/18.97 ! [V_m_2,V_n_2,V_k_2] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_n_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_m_2)))) % 19.07/18.97 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k_2),V_n_2)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_zdvd__period,axiom, % 19.07/18.97 ! [V_c_2,V_t_2,V_x_2,V_d_2,V_a_2] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a_2),V_d_2)) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),V_t_2))) % 19.07/18.97 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_c_2),V_d_2))),V_t_2))) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_transfer__int__nat__relations_I4_J,axiom, % 19.07/18.97 ! [V_y_2,V_x_2] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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))) % 19.07/18.97 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_zdvd__int,axiom, % 19.07/18.97 ! [V_y_2,V_x_2] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) % 19.07/18.97 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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))) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_zdvd__mult__div__cancel,axiom, % 19.07/18.97 ! [V_m,V_n] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n),V_m)) % 19.07/18.97 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_n),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_m),V_n)) = V_m ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_zmod__eq__dvd__iff,axiom, % 19.07/18.97 ! [V_y_2,V_n_2,V_x_2] : % 19.07/18.97 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x_2,V_n_2) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_y_2,V_n_2) % 19.07/18.97 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x_2),V_y_2))) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_zdvd1__eq,axiom, % 19.07/18.97 ! [V_x_2] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_x_2),c_Groups_Oone__class_Oone(tc_Int_Oint))) % 19.07/18.97 <=> hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_abs__div,axiom, % 19.07/18.97 ! [V_x,V_y] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_y),V_x)) % 19.07/18.97 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_y)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_dvd_Ostrict__mono__mono,axiom, % 19.07/18.97 ! [V_f_2,T_b] : % 19.07/18.97 ( class_Orderings_Oorder(T_b) % 19.07/18.97 => ( c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,T_b,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_f_2) % 19.07/18.97 => c_Orderings_Oorder_Omono(tc_Nat_Onat,T_b,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_f_2) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_zdvd__imp__le,axiom, % 19.07/18.97 ! [V_n,V_z] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_z),V_n)) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_n)) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_n)) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_zdvd__iff__zmod__eq__0__number__of,axiom, % 19.07/18.97 ! [V_y_2,V_x_2] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_y_2))) % 19.07/18.97 <=> c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_x_2)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_dvd__imp__le__int,axiom, % 19.07/18.97 ! [V_d,V_i] : % 19.07/18.97 ( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d),V_i)) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_d)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i))) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_transfer__nat__int__relations_I4_J,axiom, % 19.07/18.97 ! [V_y_2,V_x_2] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,V_x_2)),hAPP(c_Int_Onat,V_y_2))) % 19.07/18.97 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_zdvd__mult__cancel1,axiom, % 19.07/18.97 ! [V_n_2,V_m_2] : % 19.07/18.97 ( V_m_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2)),V_m_2)) % 19.07/18.97 <=> hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_int__dvd__iff,axiom, % 19.07/18.97 ! [V_z_2,V_m_2] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)),V_z_2)) % 19.07/18.97 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_z_2)))) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_dvd__int__iff,axiom, % 19.07/18.97 ! [V_m_2,V_z_2] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_z_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2))) % 19.07/18.97 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_z_2))),V_m_2)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Option_Oset_Osimps_I1_J,axiom, % 19.07/18.97 ! [T_b] : c_Option_Oset(T_b,c_Option_Ooption_ONone(T_b)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 19.07/18.97 % 19.07/18.97 fof(fact_set__empty__eq,axiom, % 19.07/18.97 ! [V_xo_2,T_b] : % 19.07/18.97 ( c_Option_Oset(T_b,V_xo_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.97 <=> V_xo_2 = c_Option_Ooption_ONone(T_b) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_nat__dvd__iff,axiom, % 19.07/18.97 ! [V_m_2,V_z_2] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,V_z_2)),V_m_2)) % 19.07/18.97 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_z_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2))) ) % 19.07/18.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 19.07/18.97 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_psubset__insert__iff,axiom, % 19.07/18.97 ! [V_B_2,V_x_2,V_A_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2))) % 19.07/18.97 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) % 19.07/18.97 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) % 19.07/18.97 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2)) ) % 19.07/18.97 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_dvd_Ostrict__monoI,axiom, % 19.07/18.97 ! [V_f_2,T_b] : % 19.07/18.97 ( class_Orderings_Oorder(T_b) % 19.07/18.97 => ( ! [B_x,B_y] : % 19.07/18.97 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),B_x),B_y)) % 19.07/18.97 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),B_y),B_x)) ) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),hAPP(V_f_2,B_y))) ) % 19.07/18.97 => c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,T_b,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_f_2) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_dvd_OmonoI,axiom, % 19.07/18.97 ! [V_f_2,T_b] : % 19.07/18.97 ( class_Orderings_Oorder(T_b) % 19.07/18.97 => ( ! [B_x,B_y] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),B_x),B_y)) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_x)),hAPP(V_f_2,B_y))) ) % 19.07/18.97 => c_Orderings_Oorder_Omono(tc_Nat_Onat,T_b,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_f_2) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_diff__single__insert,axiom, % 19.07/18.97 ! [V_B_2,V_x_2,V_A_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2)) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2))) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_equalityCE,axiom, % 19.07/18.97 ! [V_c_2,T_b,V_B_2,V_A_2] : % 19.07/18.97 ( V_A_2 = V_B_2 % 19.07/18.97 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) % 19.07/18.97 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) % 19.07/18.97 => ~ ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_emptyE,axiom, % 19.07/18.97 ! [V_a_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ). % 19.07/18.97 % 19.07/18.97 fof(fact_insertCI,axiom, % 19.07/18.97 ! [V_b_2,V_B_2,V_a_2,T_b] : % 19.07/18.97 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2)) % 19.07/18.97 => V_a_2 = V_b_2 ) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_insertE,axiom, % 19.07/18.97 ! [V_A_2,V_b_2,V_a_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2))) % 19.07/18.97 => ( V_a_2 != V_b_2 % 19.07/18.97 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_subsetD,axiom, % 19.07/18.97 ! [V_c_2,V_B_2,V_A_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_DiffI,axiom, % 19.07/18.97 ! [V_B_2,V_A_2,V_c_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) % 19.07/18.97 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_DiffE,axiom, % 19.07/18.97 ! [V_B_2,V_A_2,V_c_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 19.07/18.97 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_ComplI,axiom, % 19.07/18.97 ! [V_A_2,V_c_2,T_b] : % 19.07/18.97 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_mem__splitI,axiom, % 19.07/18.97 ! [T_d,T_c,V_b_2,V_a_2,V_c_2,V_z_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_c_2,V_a_2),V_b_2))) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_fun(T_b,tc_HOL_Obool)),V_c_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)))) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_insert__absorb,axiom, % 19.07/18.97 ! [V_A_2,V_a_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 19.07/18.97 => hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) = V_A_2 ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_insertI2,axiom, % 19.07/18.97 ! [V_b_2,V_B_2,V_a_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2)) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_equals0D,axiom, % 19.07/18.97 ! [V_a_2,T_b,V_A_2] : % 19.07/18.97 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.97 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_insert__ident,axiom, % 19.07/18.97 ! [V_B_2,V_A_2,V_x_2,T_b] : % 19.07/18.97 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.97 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) % 19.07/18.97 => ( hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2) % 19.07/18.97 <=> V_A_2 = V_B_2 ) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_insert__iff,axiom, % 19.07/18.97 ! [V_A_2,V_b_2,V_a_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2))) % 19.07/18.97 <=> ( V_a_2 = V_b_2 % 19.07/18.97 | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_empty__iff,axiom, % 19.07/18.97 ! [V_c_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ). % 19.07/18.97 % 19.07/18.97 fof(fact_ex__in__conv,axiom, % 19.07/18.97 ! [V_A_2,T_b] : % 19.07/18.97 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 19.07/18.97 <=> V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_all__not__in__conv,axiom, % 19.07/18.97 ! [V_A_2,T_b] : % 19.07/18.97 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 19.07/18.97 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_insertI1,axiom, % 19.07/18.97 ! [V_B_2,V_a_2,T_b] : hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2))) ). % 19.07/18.97 % 19.07/18.97 fof(fact_in__mono,axiom, % 19.07/18.97 ! [V_x_2,V_B_2,V_A_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_set__rev__mp,axiom, % 19.07/18.97 ! [V_B_2,V_A_2,V_x_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_set__mp,axiom, % 19.07/18.97 ! [V_x_2,V_B_2,V_A_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_ComplE,axiom, % 19.07/18.97 ! [V_A_2,V_c_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) % 19.07/18.97 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_ComplD,axiom, % 19.07/18.97 ! [V_A_2,V_c_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) % 19.07/18.97 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Compl__iff,axiom, % 19.07/18.97 ! [V_A_2,V_c_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) % 19.07/18.97 <=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_pred__equals__eq,axiom, % 19.07/18.97 ! [V_S_2,V_R_2,T_b] : % 19.07/18.97 ( hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2) = hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2) % 19.07/18.97 <=> V_R_2 = V_S_2 ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_eq__mem,axiom, % 19.07/18.97 ! [V_y_2,V_x_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_fequal,V_y_2))) % 19.07/18.97 <=> V_x_2 = V_y_2 ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_eq__mem__trans,axiom, % 19.07/18.97 ! [V_A_2,T_b,V_b_2,V_a_2] : % 19.07/18.97 ( V_a_2 = V_b_2 % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2)) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_eqelem__imp__iff,axiom, % 19.07/18.97 ! [V_A_2,T_b,V_y_2,V_x_2] : % 19.07/18.97 ( V_x_2 = V_y_2 % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.97 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_eqset__imp__iff,axiom, % 19.07/18.97 ! [V_x_2,T_b,V_B_2,V_A_2] : % 19.07/18.97 ( V_A_2 = V_B_2 % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.97 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_mem__def,axiom, % 19.07/18.97 ! [V_A_2,V_x_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.97 <=> hBOOL(hAPP(V_A_2,V_x_2)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_DiffD2,axiom, % 19.07/18.97 ! [V_B_2,V_A_2,V_c_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 19.07/18.97 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_DiffD1,axiom, % 19.07/18.97 ! [V_B_2,V_A_2,V_c_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Diff__iff,axiom, % 19.07/18.97 ! [V_B_2,V_A_2,V_c_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 19.07/18.97 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) % 19.07/18.97 & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_psubsetD,axiom, % 19.07/18.97 ! [V_c_2,V_B_2,V_A_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_bot__empty__eq,axiom, % 19.07/18.97 ! [V_x_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_x_2)) % 19.07/18.97 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_pred__equals__eq2,axiom, % 19.07/18.97 ! [V_S_2,V_R_2,T_c,T_b] : % 19.07/18.97 ( hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_R_2) = hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_S_2) % 19.07/18.97 <=> V_R_2 = V_S_2 ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_bot__empty__eq2,axiom, % 19.07/18.97 ! [V_y_2,V_x_2,T_c,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_x_2),V_y_2)) % 19.07/18.97 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)))) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_pred__subset__eq,axiom, % 19.07/18.97 ! [V_S_2,V_R_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2))) % 19.07/18.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_singletonE,axiom, % 19.07/18.97 ! [V_a_2,V_b_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) % 19.07/18.97 => V_b_2 = V_a_2 ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_singleton__iff,axiom, % 19.07/18.97 ! [V_a_2,V_b_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) % 19.07/18.97 <=> V_b_2 = V_a_2 ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_subset__insert,axiom, % 19.07/18.97 ! [V_B_2,V_A_2,V_x_2,T_b] : % 19.07/18.97 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2))) % 19.07/18.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_insert__subset,axiom, % 19.07/18.97 ! [V_B_2,V_A_2,V_x_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2)) % 19.07/18.97 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) % 19.07/18.97 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_insert__Diff1,axiom, % 19.07/18.97 ! [V_A_2,V_B_2,V_x_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) % 19.07/18.97 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_insert__Diff__if,axiom, % 19.07/18.97 ! [V_A_2,V_B_2,V_x_2,T_b] : % 19.07/18.97 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) % 19.07/18.97 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ) % 19.07/18.97 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) % 19.07/18.97 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_elem__set,axiom, % 19.07/18.97 ! [V_xo_2,V_x_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Option_Oset(T_b,V_xo_2))) % 19.07/18.97 <=> V_xo_2 = hAPP(c_Option_Ooption_OSome(T_b),V_x_2) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_pred__subset__eq2,axiom, % 19.07/18.97 ! [V_S_2,V_R_2,T_c,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_S_2))) % 19.07/18.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_R_2),V_S_2)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_insert__Diff,axiom, % 19.07/18.97 ! [V_A_2,V_a_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 19.07/18.97 => hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = V_A_2 ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Diff__insert__absorb,axiom, % 19.07/18.97 ! [V_A_2,V_x_2,T_b] : % 19.07/18.97 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.97 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_A_2 ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_subset__insert__iff,axiom, % 19.07/18.97 ! [V_B_2,V_x_2,V_A_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2))) % 19.07/18.97 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2)) ) % 19.07/18.97 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_in__rel__def,axiom, % 19.07/18.97 ! [V_y_2,V_x_2,V_R_2,T_c,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_b,T_c,V_R_2),V_x_2),V_y_2)) % 19.07/18.97 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),V_R_2)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_fold__graph_H_Ointros_I2_J,axiom, % 19.07/18.97 ! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.97 => ( c_Nitpick_Ofold__graph_H(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_y_2) % 19.07/18.97 => c_Nitpick_Ofold__graph_H(T_b,T_c,V_f_2,V_z_2,V_A_2,hAPP(hAPP(V_f_2,V_x_2),V_y_2)) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Nitpick_Orefl_H__def,axiom, % 19.07/18.97 ! [V_r_2,T_b] : % 19.07/18.97 ( c_Nitpick_Orefl_H(T_b,V_r_2) % 19.07/18.97 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_flat__lub__def,axiom, % 19.07/18.97 ! [V_b_2,V_A_2,T_b] : % 19.07/18.97 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) % 19.07/18.97 => c_Partial__Function_Oflat__lub(T_b,V_b_2,V_A_2) = V_b_2 ) % 19.07/18.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) % 19.07/18.97 => c_Partial__Function_Oflat__lub(T_b,V_b_2,V_A_2) = c_HOL_OThe(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_bot2E,axiom, % 19.07/18.97 ! [V_y_2,V_x_2,T_c,T_b] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_x_2),V_y_2)) ). % 19.07/18.97 % 19.07/18.97 fof(fact_less__by__empty,axiom, % 19.07/18.97 ! [V_B_2,T_b,V_A_2] : % 19.07/18.97 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_fold__graph_H_Oequations_I1_J,axiom, % 19.07/18.97 ! [V_a2_2,V_a1_2,T_c,T_b] : c_Nitpick_Ofold__graph_H(T_b,T_c,V_a1_2,V_a2_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_a2_2) ). % 19.07/18.97 % 19.07/18.97 fof(fact_fold__graph_H_Ointros_I1_J,axiom, % 19.07/18.97 ! [V_z_2,V_f_2,T_c,T_b] : c_Nitpick_Ofold__graph_H(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_z_2) ). % 19.07/18.97 % 19.07/18.97 fof(fact_in__measure,axiom, % 19.07/18.97 ! [V_f_2,V_y_2,V_x_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(c_Wellfounded_Omeasure(T_b),V_f_2))) % 19.07/18.97 <=> 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))) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_mlex__leq,axiom, % 19.07/18.97 ! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] : % 19.07/18.97 ( 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))) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_R_2)) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2))) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_mlex__less,axiom, % 19.07/18.97 ! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] : % 19.07/18.97 ( 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))) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2))) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Nats__number__of,axiom, % 19.07/18.97 ! [V_w_2,T_b] : % 19.07/18.97 ( class_Int_Onumber__ring(T_b) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_w_2)) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Nats__0,axiom, % 19.07/18.97 ! [T_b] : % 19.07/18.97 ( class_Rings_Osemiring__1(T_b) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Nats__add,axiom, % 19.07/18.97 ! [V_b_2,V_a_2,T_b] : % 19.07/18.97 ( class_Rings_Osemiring__1(T_b) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b))) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Nat_Osemiring__1__class_ONats(T_b))) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Nats__mult,axiom, % 19.07/18.97 ! [V_b_2,V_a_2,T_b] : % 19.07/18.97 ( class_Rings_Osemiring__1(T_b) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b))) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Nat_Osemiring__1__class_ONats(T_b))) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Nats__1,axiom, % 19.07/18.97 ! [T_b] : % 19.07/18.97 ( class_Rings_Osemiring__1(T_b) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_of__nat__in__Nats,axiom, % 19.07/18.97 ! [V_n_2,T_b] : % 19.07/18.97 ( class_Rings_Osemiring__1(T_b) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Ints__odd__less__0,axiom, % 19.07/18.97 ! [V_a_2,T_b] : % 19.07/18.97 ( class_Rings_Olinordered__idom(T_b) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2)),V_a_2)),c_Groups_Ozero__class_Ozero(T_b))) % 19.07/18.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_fold__graph_H_Oequations_I2_J,axiom, % 19.07/18.97 ! [V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_c,T_b] : % 19.07/18.97 ( c_Nitpick_Ofold__graph_H(T_b,T_c,V_a3_2,V_a4_2,V_a2_2,hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2)) % 19.07/18.97 <=> ( ( V_a2_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.97 & hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = V_a4_2 ) % 19.07/18.97 | ? [B_x,B_y] : % 19.07/18.97 ( hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = hAPP(hAPP(V_a3_2,B_x),B_y) % 19.07/18.97 & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a2_2)) % 19.07/18.97 & c_Nitpick_Ofold__graph_H(T_b,T_c,V_a3_2,V_a4_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_a2_2),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),B_y) ) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_in__lex__prod,axiom, % 19.07/18.97 ! [V_s_2,V_r_2,V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_H_2),V_b_H_2))),c_Wellfounded_Olex__prod(T_b,T_c,V_r_2,V_s_2))) % 19.07/18.97 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_H_2)),V_r_2)) % 19.07/18.97 | ( V_a_2 = V_a_H_2 % 19.07/18.97 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_b_2),V_b_H_2)),V_s_2)) ) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_pair__lessI2,axiom, % 19.07/18.97 ! [V_t_2,V_s_2,V_b_2,V_a_2] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2)) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s_2),V_t_2)) % 19.07/18.97 => 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)) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Ints__0,axiom, % 19.07/18.97 ! [T_b] : % 19.07/18.97 ( class_Rings_Oring__1(T_b) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Int_Oring__1__class_OInts(T_b))) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Ints__add,axiom, % 19.07/18.97 ! [V_b_2,V_a_2,T_b] : % 19.07/18.97 ( class_Rings_Oring__1(T_b) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b))) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Ints__mult,axiom, % 19.07/18.97 ! [V_b_2,V_a_2,T_b] : % 19.07/18.97 ( class_Rings_Oring__1(T_b) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b))) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Ints__diff,axiom, % 19.07/18.97 ! [V_b_2,V_a_2,T_b] : % 19.07/18.97 ( class_Rings_Oring__1(T_b) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b))) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Ints__number__of,axiom, % 19.07/18.97 ! [V_w_2,T_b] : % 19.07/18.97 ( class_Int_Onumber__ring(T_b) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Int_Oring__1__class_OInts(T_b))) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Ints__1,axiom, % 19.07/18.97 ! [T_b] : % 19.07/18.97 ( class_Rings_Oring__1(T_b) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Int_Oring__1__class_OInts(T_b))) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Ints__minus,axiom, % 19.07/18.97 ! [V_a_2,T_b] : % 19.07/18.97 ( class_Rings_Oring__1(T_b) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Ints__of__nat,axiom, % 19.07/18.97 ! [V_n_2,T_b] : % 19.07/18.97 ( class_Rings_Oring__1(T_b) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),c_Int_Oring__1__class_OInts(T_b))) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Ints__power,axiom, % 19.07/18.97 ! [V_n_2,V_a_2,T_b] : % 19.07/18.97 ( class_Rings_Oring__1(T_b) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Ints__of__int,axiom, % 19.07/18.97 ! [V_z_2,T_b] : % 19.07/18.97 ( class_Rings_Oring__1(T_b) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)),c_Int_Oring__1__class_OInts(T_b))) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Ints__double__eq__0__iff,axiom, % 19.07/18.97 ! [V_a_2,T_b] : % 19.07/18.97 ( class_Int_Oring__char__0(T_b) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) % 19.07/18.97 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b) % 19.07/18.97 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_pair__lessI1,axiom, % 19.07/18.97 ! [V_t_2,V_s_2,V_b_2,V_a_2] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) % 19.07/18.97 => 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)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Ints__odd__nonzero,axiom, % 19.07/18.97 ! [V_a_2,T_b] : % 19.07/18.97 ( class_Int_Oring__char__0(T_b) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) % 19.07/18.97 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2)),V_a_2) != c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_same__fstI,axiom, % 19.07/18.97 ! [T_b,V_R_2,V_y_2,V_y_H_2,T_c,V_x_2,V_Pa_2] : % 19.07/18.97 ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_y_H_2),V_y_2)),hAPP(V_R_2,V_x_2))) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_H_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2))),c_Recdef_Osame__fst(T_b,T_c,V_Pa_2,V_R_2))) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_pair__leqI2,axiom, % 19.07/18.97 ! [V_t_2,V_s_2,V_b_2,V_a_2] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2)) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_s_2),V_t_2)) % 19.07/18.97 => 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)) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_smin__insertI,axiom, % 19.07/18.97 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)) % 19.07/18.97 => ( 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)) % 19.07/18.97 => ( 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)) % 19.07/18.97 => 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)) ) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_smax__insertI,axiom, % 19.07/18.97 ! [V_X_2,V_x_2,V_Y_2,V_y_2] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_Y_2)) % 19.07/18.97 => ( 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)) % 19.07/18.97 => ( 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)) % 19.07/18.97 => 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)) ) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_smin__emptyI,axiom, % 19.07/18.97 ! [V_X_2] : % 19.07/18.97 ( V_X_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) % 19.07/18.97 => 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)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_pair__leqI1,axiom, % 19.07/18.97 ! [V_t_2,V_s_2,V_b_2,V_a_2] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) % 19.07/18.97 => 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)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_wmax__insertI,axiom, % 19.07/18.97 ! [V_XS_2,V_x_2,V_YS_2,V_y_2] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2)) % 19.07/18.97 => ( 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)) % 19.07/18.97 => ( 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)) % 19.07/18.97 => 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)) ) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_wmin__insertI,axiom, % 19.07/18.97 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)) % 19.07/18.97 => ( 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)) % 19.07/18.97 => ( 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)) % 19.07/18.97 => 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)) ) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_wmin__emptyI,axiom, % 19.07/18.97 ! [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)) ). % 19.07/18.97 % 19.07/18.97 fof(fact_min__strict__def,axiom, % 19.07/18.97 c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ). % 19.07/18.97 % 19.07/18.97 fof(fact_min__weak__def,axiom, % 19.07/18.97 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)))) ). % 19.07/18.97 % 19.07/18.97 fof(fact_min__rpair__set,axiom, % 19.07/18.97 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)) ). % 19.07/18.97 % 19.07/18.97 fof(fact_max__rpair__set,axiom, % 19.07/18.97 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)) ). % 19.07/18.97 % 19.07/18.97 fof(fact_less__than__iff,axiom, % 19.07/18.97 ! [V_y_2,V_x_2] : % 19.07/18.97 ( 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)) % 19.07/18.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_sup1CI,axiom, % 19.07/18.97 ! [T_b,V_A_2,V_x_2,V_B_2] : % 19.07/18.97 ( ( ~ hBOOL(hAPP(V_B_2,V_x_2)) % 19.07/18.97 => hBOOL(hAPP(V_A_2,V_x_2)) ) % 19.07/18.97 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_sup1E,axiom, % 19.07/18.97 ! [V_x_2,V_B_2,V_A_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) % 19.07/18.97 => ( ~ hBOOL(hAPP(V_A_2,V_x_2)) % 19.07/18.97 => hBOOL(hAPP(V_B_2,V_x_2)) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_UnE,axiom, % 19.07/18.97 ! [V_B_2,V_A_2,V_c_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 19.07/18.97 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_UnCI,axiom, % 19.07/18.97 ! [V_A_2,V_B_2,V_c_2,T_b] : % 19.07/18.97 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_sup__bot__left,axiom, % 19.07/18.97 ! [V_x,T_a] : % 19.07/18.97 ( class_Lattices_Obounded__lattice__bot(T_a) % 19.07/18.97 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = V_x ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_sup__bot__right,axiom, % 19.07/18.97 ! [V_x,T_a] : % 19.07/18.97 ( class_Lattices_Obounded__lattice__bot(T_a) % 19.07/18.97 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = V_x ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_sup__eq__bot__iff,axiom, % 19.07/18.97 ! [V_y_2,V_x_2,T_b] : % 19.07/18.97 ( class_Lattices_Obounded__lattice__bot(T_b) % 19.07/18.97 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = c_Orderings_Obot__class_Obot(T_b) % 19.07/18.97 <=> ( V_x_2 = c_Orderings_Obot__class_Obot(T_b) % 19.07/18.97 & V_y_2 = c_Orderings_Obot__class_Obot(T_b) ) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Un__empty__left,axiom, % 19.07/18.97 ! [V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = V_B_2 ). % 19.07/18.97 % 19.07/18.97 fof(fact_Un__empty__right,axiom, % 19.07/18.97 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_A_2 ). % 19.07/18.97 % 19.07/18.97 fof(fact_Un__empty,axiom, % 19.07/18.97 ! [V_B_2,V_A_2,T_b] : % 19.07/18.97 ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.97 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.97 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_inf__sup__ord_I3_J,axiom, % 19.07/18.97 ! [V_y,V_x,T_a] : % 19.07/18.97 ( class_Lattices_Olattice(T_a) % 19.07/18.97 => 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))) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_sup__ge1,axiom, % 19.07/18.97 ! [V_y,V_x,T_a] : % 19.07/18.97 ( class_Lattices_Osemilattice__sup(T_a) % 19.07/18.97 => 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))) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_inf__sup__ord_I4_J,axiom, % 19.07/18.97 ! [V_x,V_y,T_a] : % 19.07/18.97 ( class_Lattices_Olattice(T_a) % 19.07/18.97 => 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))) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_sup__ge2,axiom, % 19.07/18.97 ! [V_x,V_y,T_a] : % 19.07/18.97 ( class_Lattices_Osemilattice__sup(T_a) % 19.07/18.97 => 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))) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_le__iff__sup,axiom, % 19.07/18.97 ! [V_y_2,V_x_2,T_b] : % 19.07/18.97 ( class_Lattices_Osemilattice__sup(T_b) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 19.07/18.97 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = V_y_2 ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_le__sup__iff,axiom, % 19.07/18.97 ! [V_z_2,V_y_2,V_x_2,T_b] : % 19.07/18.97 ( class_Lattices_Osemilattice__sup(T_b) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2)),V_z_2)) % 19.07/18.97 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) % 19.07/18.97 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_le__supI1,axiom, % 19.07/18.97 ! [V_b,V_a,V_x,T_a] : % 19.07/18.97 ( class_Lattices_Osemilattice__sup(T_a) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 19.07/18.97 => 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))) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_le__supI2,axiom, % 19.07/18.97 ! [V_a,V_b,V_x,T_a] : % 19.07/18.97 ( class_Lattices_Osemilattice__sup(T_a) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 19.07/18.97 => 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))) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_sup__absorb2,axiom, % 19.07/18.97 ! [V_y,V_x,T_a] : % 19.07/18.97 ( class_Lattices_Osemilattice__sup(T_a) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 19.07/18.97 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_y ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_sup__absorb1,axiom, % 19.07/18.97 ! [V_x,V_y,T_a] : % 19.07/18.97 ( class_Lattices_Osemilattice__sup(T_a) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 19.07/18.97 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_x ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_le__supI,axiom, % 19.07/18.97 ! [V_b,V_x,V_a,T_a] : % 19.07/18.97 ( class_Lattices_Osemilattice__sup(T_a) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 19.07/18.97 => 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)) ) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_sup__least,axiom, % 19.07/18.97 ! [V_z,V_x,V_y,T_a] : % 19.07/18.97 ( class_Lattices_Osemilattice__sup(T_a) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) % 19.07/18.97 => 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)) ) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_sup__mono,axiom, % 19.07/18.97 ! [V_d,V_b,V_c,V_a,T_a] : % 19.07/18.97 ( class_Lattices_Osemilattice__sup(T_a) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 19.07/18.97 => 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))) ) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_le__supE,axiom, % 19.07/18.97 ! [V_x,V_b,V_a,T_a] : % 19.07/18.97 ( class_Lattices_Osemilattice__sup(T_a) % 19.07/18.97 => ( 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)) % 19.07/18.97 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 19.07/18.97 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Un__mono,axiom, % 19.07/18.97 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2)) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2))) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Un__least,axiom, % 19.07/18.97 ! [V_B_2,V_C_2,V_A_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2)) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Un__absorb2,axiom, % 19.07/18.97 ! [V_A_2,V_B_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 19.07/18.97 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Un__absorb1,axiom, % 19.07/18.97 ! [V_B_2,V_A_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 19.07/18.97 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_subset__Un__eq,axiom, % 19.07/18.97 ! [V_B_2,V_A_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 19.07/18.97 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Un__upper2,axiom, % 19.07/18.97 ! [V_A_2,V_B_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Un__upper1,axiom, % 19.07/18.97 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ). % 19.07/18.97 % 19.07/18.97 fof(fact_sup1I2,axiom, % 19.07/18.97 ! [V_A_2,T_b,V_x_2,V_B_2] : % 19.07/18.97 ( hBOOL(hAPP(V_B_2,V_x_2)) % 19.07/18.97 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_sup1I1,axiom, % 19.07/18.97 ! [V_B_2,T_b,V_x_2,V_A_2] : % 19.07/18.97 ( hBOOL(hAPP(V_A_2,V_x_2)) % 19.07/18.97 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_ball__Un,axiom, % 19.07/18.97 ! [V_Pa_2,V_B_2,V_A_2,T_b] : % 19.07/18.97 ( ! [B_x] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 19.07/18.97 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 19.07/18.97 <=> ( ! [B_x] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 19.07/18.97 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 19.07/18.97 & ! [B_x] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) % 19.07/18.97 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_bex__Un,axiom, % 19.07/18.97 ! [V_Pa_2,V_B_2,V_A_2,T_b] : % 19.07/18.97 ( ? [B_x] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 19.07/18.97 & hBOOL(hAPP(V_Pa_2,B_x)) ) % 19.07/18.97 <=> ( ? [B_x] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 19.07/18.97 & hBOOL(hAPP(V_Pa_2,B_x)) ) % 19.07/18.97 | ? [B_x] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) % 19.07/18.97 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Un__assoc,axiom, % 19.07/18.97 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Un__left__commute,axiom, % 19.07/18.97 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Un__left__absorb,axiom, % 19.07/18.97 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Un__commute,axiom, % 19.07/18.97 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Un__absorb,axiom, % 19.07/18.97 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2) = V_A_2 ). % 19.07/18.97 % 19.07/18.97 fof(fact_sup__apply,axiom, % 19.07/18.97 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] : % 19.07/18.97 ( class_Lattices_Olattice(T_b) % 19.07/18.97 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,T_b)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_sup__assoc,axiom, % 19.07/18.97 ! [V_z,V_y,V_x,T_a] : % 19.07/18.97 ( class_Lattices_Osemilattice__sup(T_a) % 19.07/18.97 => 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)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_inf__sup__aci_I6_J,axiom, % 19.07/18.97 ! [V_z,V_y,V_x,T_a] : % 19.07/18.97 ( class_Lattices_Olattice(T_a) % 19.07/18.97 => 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)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_sup_Oassoc,axiom, % 19.07/18.97 ! [V_c,V_b,V_a,T_a] : % 19.07/18.97 ( class_Lattices_Osemilattice__sup(T_a) % 19.07/18.97 => 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)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_sup__left__commute,axiom, % 19.07/18.97 ! [V_z,V_y,V_x,T_a] : % 19.07/18.97 ( class_Lattices_Osemilattice__sup(T_a) % 19.07/18.97 => 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)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_inf__sup__aci_I7_J,axiom, % 19.07/18.97 ! [V_z,V_y,V_x,T_a] : % 19.07/18.97 ( class_Lattices_Olattice(T_a) % 19.07/18.97 => 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)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_sup_Oleft__commute,axiom, % 19.07/18.97 ! [V_c,V_a,V_b,T_a] : % 19.07/18.97 ( class_Lattices_Osemilattice__sup(T_a) % 19.07/18.97 => 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)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_sup__left__idem,axiom, % 19.07/18.97 ! [V_y,V_x,T_a] : % 19.07/18.97 ( class_Lattices_Osemilattice__sup(T_a) % 19.07/18.97 => 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) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_inf__sup__aci_I8_J,axiom, % 19.07/18.97 ! [V_y,V_x,T_a] : % 19.07/18.97 ( class_Lattices_Olattice(T_a) % 19.07/18.97 => 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) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_sup_Oleft__idem,axiom, % 19.07/18.97 ! [V_b,V_a,T_a] : % 19.07/18.97 ( class_Lattices_Osemilattice__sup(T_a) % 19.07/18.97 => 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) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_sup__commute,axiom, % 19.07/18.97 ! [V_y,V_x,T_a] : % 19.07/18.97 ( class_Lattices_Osemilattice__sup(T_a) % 19.07/18.97 => 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) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_inf__sup__aci_I5_J,axiom, % 19.07/18.97 ! [V_y,V_x,T_a] : % 19.07/18.97 ( class_Lattices_Olattice(T_a) % 19.07/18.97 => 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) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_sup_Ocommute,axiom, % 19.07/18.97 ! [V_b,V_a,T_a] : % 19.07/18.97 ( class_Lattices_Osemilattice__sup(T_a) % 19.07/18.97 => 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) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_sup__idem,axiom, % 19.07/18.97 ! [V_x,T_a] : % 19.07/18.97 ( class_Lattices_Osemilattice__sup(T_a) % 19.07/18.97 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_sup_Oidem,axiom, % 19.07/18.97 ! [V_a,T_a] : % 19.07/18.97 ( class_Lattices_Osemilattice__sup(T_a) % 19.07/18.97 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_a) = V_a ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_less__supI2,axiom, % 19.07/18.97 ! [V_a,V_b,V_x,T_a] : % 19.07/18.97 ( class_Lattices_Osemilattice__sup(T_a) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b)) % 19.07/18.97 => 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))) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_less__supI1,axiom, % 19.07/18.97 ! [V_b,V_a,V_x,T_a] : % 19.07/18.97 ( class_Lattices_Osemilattice__sup(T_a) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a)) % 19.07/18.97 => 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))) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_sup__fun__def,axiom, % 19.07/18.97 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] : % 19.07/18.97 ( class_Lattices_Olattice(T_b) % 19.07/18.97 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,T_b)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Un__Diff,axiom, % 19.07/18.97 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Un__Diff__cancel2,axiom, % 19.07/18.97 ! [V_A_2,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Un__Diff__cancel,axiom, % 19.07/18.97 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Sup__fin_Oidem,axiom, % 19.07/18.97 ! [V_x,T_a] : % 19.07/18.97 ( class_Lattices_Olattice(T_a) % 19.07/18.97 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_sup__max,axiom, % 19.07/18.97 ! [T_b] : % 19.07/18.97 ( ( class_Lattices_Osemilattice__sup(T_b) % 19.07/18.97 & class_Orderings_Olinorder(T_b) ) % 19.07/18.97 => c_Lattices_Osemilattice__sup__class_Osup(T_b) = c_Orderings_Oord__class_Omax(T_b) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Un__insert__right,axiom, % 19.07/18.97 ! [V_B_2,V_a_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Un__insert__left,axiom, % 19.07/18.97 ! [V_C_2,V_B_2,V_a_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ). % 19.07/18.97 % 19.07/18.97 fof(fact_UnI2,axiom, % 19.07/18.97 ! [V_A_2,V_B_2,V_c_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_UnI1,axiom, % 19.07/18.97 ! [V_B_2,V_A_2,V_c_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Un__iff,axiom, % 19.07/18.97 ! [V_B_2,V_A_2,V_c_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 19.07/18.97 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) % 19.07/18.97 | hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_sup__Un__eq,axiom, % 19.07/18.97 ! [V_x_2,V_S_2,V_R_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)),V_x_2)) % 19.07/18.97 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2))) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_insert__is__Un,axiom, % 19.07/18.97 ! [V_A_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_A_2) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Diff__subset__conv,axiom, % 19.07/18.97 ! [V_C_2,V_B_2,V_A_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2)) % 19.07/18.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Diff__partition,axiom, % 19.07/18.97 ! [V_B_2,V_A_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 19.07/18.97 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) = V_B_2 ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Compl__Diff__eq,axiom, % 19.07/18.97 ! [V_B_2,V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2) ). % 19.07/18.97 % 19.07/18.97 fof(fact_pair__less__def,axiom, % 19.07/18.97 c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than) ). % 19.07/18.97 % 19.07/18.97 fof(fact_max__weak__def,axiom, % 19.07/18.97 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)))) ). % 19.07/18.97 % 19.07/18.97 fof(fact_mlex__prod__def,axiom, % 19.07/18.97 ! [V_R_2,V_f_2,T_b] : c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,T_b),T_b),c_Wellfounded_Olex__prod(tc_Nat_Onat,T_b,c_Wellfounded_Oless__than,V_R_2)),hAPP(hAPP(c_COMBS(T_b,T_b,tc_prod(tc_Nat_Onat,T_b)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_b,tc_prod(tc_Nat_Onat,T_b)),T_b),c_Product__Type_OPair(tc_Nat_Onat,T_b)),V_f_2)),c_COMBI(T_b))) ). % 19.07/18.97 % 19.07/18.97 fof(fact_intrel__iff,axiom, % 19.07/18.97 ! [V_v_2,V_u_2,V_y_2,V_x_2] : % 19.07/18.97 ( 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)) % 19.07/18.97 <=> 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) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_rp__inv__image__rp,axiom, % 19.07/18.97 ! [V_f_2,T_c,V_Pa_2,T_b] : % 19.07/18.97 ( c_FunDef_Oreduction__pair(T_b,V_Pa_2) % 19.07/18.97 => c_FunDef_Oreduction__pair(T_c,hAPP(hAPP(c_FunDef_Orp__inv__image(T_b,T_c),V_Pa_2),V_f_2)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_sup__nat__def,axiom, % 19.07/18.97 c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat) ). % 19.07/18.97 % 19.07/18.97 fof(fact_rp__inv__image__def,axiom, % 19.07/18.97 ! [T_c,T_b] : c_FunDef_Orp__inv__image(T_b,T_c) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))))),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_COMBS(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,T_b),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),tc_fun(T_c,T_b)),c_Product__Type_OPair(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),c_Relation_Oinv__image(T_b,T_c))))),c_Relation_Oinv__image(T_b,T_c))) ). % 19.07/18.97 % 19.07/18.97 fof(fact_sup__Un__eq2,axiom, % 19.07/18.97 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_S_2)),V_x_2),V_y_2)) % 19.07/18.97 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_R_2),V_S_2))) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_max__strict__def,axiom, % 19.07/18.97 c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ). % 19.07/18.97 % 19.07/18.97 fof(fact_max__ext__additive,axiom, % 19.07/18.97 ! [V_D_2,V_C_2,V_R_2,V_B_2,V_A_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),c_Wellfounded_Omax__ext(T_b,V_R_2))) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2)),c_Wellfounded_Omax__ext(T_b,V_R_2))) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))),c_Wellfounded_Omax__ext(T_b,V_R_2))) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_max__extp__max__ext__eq,axiom, % 19.07/18.97 ! [V_xa_2,V_x_2,V_R_2,T_b] : % 19.07/18.97 ( c_Wellfounded_Omax__extp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_R_2),V_x_2,V_xa_2) % 19.07/18.97 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_xa_2)),c_Wellfounded_Omax__ext(T_b,V_R_2))) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_in__inv__image,axiom, % 19.07/18.97 ! [V_f_2,V_r_2,T_c,V_y_2,V_x_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),V_r_2),V_f_2))) % 19.07/18.97 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))),V_r_2)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_hoare__derivs_OBody,axiom, % 19.07/18.97 ! [V_Procs_2,V_Qa_2,V_Pa_2,V_G_2,T_b] : % 19.07/18.97 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_G_2),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_b),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_b)),V_Pa_2)),c_Com_Ocom_OBODY)),V_Qa_2)),V_Procs_2)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_b),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_b)),V_Pa_2)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),V_Qa_2)),V_Procs_2)) % 19.07/18.97 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_b),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_b)),V_Pa_2)),c_Com_Ocom_OBODY)),V_Qa_2)),V_Procs_2)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_equiv__intrel__iff,axiom, % 19.07/18.97 ! [V_y_2,V_x_2] : % 19.07/18.97 ( 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)))) % 19.07/18.97 <=> 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)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_sup2CI,axiom, % 19.07/18.97 ! [T_c,T_b,V_A_2,V_y_2,V_x_2,V_B_2] : % 19.07/18.97 ( ( ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) % 19.07/18.97 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ) % 19.07/18.97 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_sup2E,axiom, % 19.07/18.97 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) % 19.07/18.97 => ( ~ hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 19.07/18.97 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_image__eqI,axiom, % 19.07/18.97 ! [T_b,V_A_2,T_c,V_x_2,V_f_2,V_b_2] : % 19.07/18.97 ( V_b_2 = hAPP(V_f_2,V_x_2) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_sup2I2,axiom, % 19.07/18.97 ! [V_A_2,T_c,T_b,V_y_2,V_x_2,V_B_2] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) % 19.07/18.97 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_sup2I1,axiom, % 19.07/18.97 ! [V_B_2,T_c,T_b,V_y_2,V_x_2,V_A_2] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 19.07/18.97 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_image__Un,axiom, % 19.07/18.97 ! [V_B_2,V_A_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2)) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Image__Un,axiom, % 19.07/18.97 ! [V_B_2,V_A_2,V_R_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_B_2)) ). % 19.07/18.97 % 19.07/18.97 fof(fact_image__mono,axiom, % 19.07/18.97 ! [V_f_2,T_c,V_B_2,V_A_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2))) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_subset__image__iff,axiom, % 19.07/18.97 ! [V_A_2,V_f_2,T_c,V_B_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) % 19.07/18.97 <=> ? [B_AA] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),B_AA),V_A_2)) % 19.07/18.97 & V_B_2 = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),B_AA) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_image__image,axiom, % 19.07/18.97 ! [V_A_2,V_g_2,T_d,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Oimage(T_d,T_c,V_g_2),V_A_2)) = hAPP(c_Set_Oimage(T_d,T_b,hAPP(hAPP(c_COMBB(T_c,T_b,T_d),V_f_2),V_g_2)),V_A_2) ). % 19.07/18.97 % 19.07/18.97 fof(fact_rev__image__eqI,axiom, % 19.07/18.97 ! [T_c,V_f_2,V_b_2,V_A_2,V_x_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.97 => ( V_b_2 = hAPP(V_f_2,V_x_2) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_imageI,axiom, % 19.07/18.97 ! [V_f_2,T_c,V_A_2,V_x_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_image__iff,axiom, % 19.07/18.97 ! [V_A_2,V_f_2,T_c,V_z_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) % 19.07/18.97 <=> ? [B_x] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 19.07/18.97 & V_z_2 = hAPP(V_f_2,B_x) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_image__insert,axiom, % 19.07/18.97 ! [V_B_2,V_a_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2)) ). % 19.07/18.97 % 19.07/18.97 fof(fact_image__is__empty,axiom, % 19.07/18.97 ! [V_A_2,V_f_2,T_b,T_c] : % 19.07/18.97 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.97 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_image__empty,axiom, % 19.07/18.97 ! [V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 19.07/18.97 % 19.07/18.97 fof(fact_empty__is__image,axiom, % 19.07/18.97 ! [V_A_2,V_f_2,T_c,T_b] : % 19.07/18.97 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) % 19.07/18.97 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Image__empty,axiom, % 19.07/18.97 ! [V_R_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_R_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Image__mono,axiom, % 19.07/18.97 ! [V_A_2,V_A_H_2,V_r_2,V_r_H_2,T_c,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_H_2),V_r_2)) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_H_2),V_A_2)) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_c,V_r_H_2),V_A_H_2)),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_A_2))) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Un__Image,axiom, % 19.07/18.97 ! [V_A_2,V_S_2,V_R_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_R_2),V_S_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_c,T_b,V_S_2),V_A_2)) ). % 19.07/18.97 % 19.07/18.97 fof(fact_insert__image,axiom, % 19.07/18.97 ! [V_f_2,T_c,V_A_2,V_x_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.97 => hAPP(hAPP(c_Set_Oinsert(T_c),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_image__diff__subset,axiom, % 19.07/18.97 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2))),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))) ). % 19.07/18.97 % 19.07/18.97 fof(fact_rev__ImageI,axiom, % 19.07/18.97 ! [V_r_2,V_b_2,T_c,V_A_2,V_a_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2)) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_A_2))) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Image__iff,axiom, % 19.07/18.97 ! [V_A_2,V_r_2,T_c,V_b_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2))) % 19.07/18.97 <=> ? [B_x] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 19.07/18.97 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),V_b_2)),V_r_2)) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_image__constant__conv,axiom, % 19.07/18.97 ! [V_c_2,T_c,T_b,V_A_2] : % 19.07/18.97 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.97 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_c_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) % 19.07/18.97 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.97 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_c_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_image__constant,axiom, % 19.07/18.97 ! [V_c_2,T_c,V_A_2,V_x_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.97 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_c_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Image__singleton__iff,axiom, % 19.07/18.97 ! [V_a_2,V_r_2,T_c,V_b_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))) % 19.07/18.97 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_a_2),V_b_2)),V_r_2)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_measure__def,axiom, % 19.07/18.97 ! [T_b] : c_Wellfounded_Omeasure(T_b) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,T_b),c_Wellfounded_Oless__than) ). % 19.07/18.97 % 19.07/18.97 fof(fact_of__int,axiom, % 19.07/18.97 ! [V_j_2,V_i_2,T_b] : % 19.07/18.97 ( class_Rings_Oring__1(T_b) % 19.07/18.97 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_i_2),V_j_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_i_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_j_2)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_One__int__def,axiom, % 19.07/18.97 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))))) ). % 19.07/18.97 % 19.07/18.97 fof(fact_mult,axiom, % 19.07/18.97 ! [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))))) ). % 19.07/18.97 % 19.07/18.97 fof(fact_le,axiom, % 19.07/18.97 ! [V_v_2,V_u_2,V_y_2,V_x_2] : % 19.07/18.97 ( 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))))))) % 19.07/18.97 <=> 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))) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_pair__imageI,axiom, % 19.07/18.97 ! [V_f_2,T_d,V_A_2,V_b_2,V_a_2,T_c,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_A_2)) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_member(T_d),hAPP(hAPP(V_f_2,V_a_2),V_b_2)),hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_d,hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_f_2)),V_A_2))) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J,axiom, % 19.07/18.97 ! [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))) ). % 19.07/18.97 % 19.07/18.97 fof(fact_transfer__nat__int__set__relations_I5_J,axiom, % 19.07/18.97 ! [V_B_2,V_A_2] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2)) % 19.07/18.97 <=> 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))) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_transfer__nat__int__set__relations_I3_J,axiom, % 19.07/18.97 ! [V_B_2,V_A_2] : % 19.07/18.97 ( V_A_2 = V_B_2 % 19.07/18.97 <=> 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) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_transfer__int__nat__set__return__embed,axiom, % 19.07/18.97 ! [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 ). % 19.07/18.97 % 19.07/18.97 fof(fact_transfer__nat__int__set__relations_I4_J,axiom, % 19.07/18.97 ! [V_B_2,V_A_2] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2)) % 19.07/18.97 <=> 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))) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_transfer__nat__int__set__relations_I2_J,axiom, % 19.07/18.97 ! [V_A_2,V_x_2] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),V_A_2)) % 19.07/18.97 <=> 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))) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I2_J,axiom, % 19.07/18.97 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))) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J,axiom, % 19.07/18.97 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))) ). % 19.07/18.97 % 19.07/18.97 fof(fact_minus,axiom, % 19.07/18.97 ! [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))))) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Zero__int__def,axiom, % 19.07/18.97 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))))) ). % 19.07/18.97 % 19.07/18.97 fof(fact_int__def,axiom, % 19.07/18.97 ! [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))))) ). % 19.07/18.97 % 19.07/18.97 fof(fact_add,axiom, % 19.07/18.97 ! [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))))) ). % 19.07/18.97 % 19.07/18.97 fof(fact_nat,axiom, % 19.07/18.97 ! [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) ). % 19.07/18.97 % 19.07/18.97 fof(fact_less,axiom, % 19.07/18.97 ! [V_v_2,V_u_2,V_y_2,V_x_2] : % 19.07/18.97 ( 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))))))) % 19.07/18.97 <=> 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))) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_irrefl__def,axiom, % 19.07/18.97 ! [V_r_2,T_b] : % 19.07/18.97 ( c_Relation_Oirrefl(T_b,V_r_2) % 19.07/18.97 <=> ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_eq__Abs__Integ,axiom, % 19.07/18.97 ! [V_z_2] : % 19.07/18.97 ~ ! [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))))) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Field__insert,axiom, % 19.07/18.97 ! [V_r_2,V_b_2,V_a_2,T_b] : hAPP(c_Relation_OField(T_b),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OField(T_b),V_r_2)) ). % 19.07/18.97 % 19.07/18.97 fof(fact_ImageE,axiom, % 19.07/18.97 ! [V_A_2,V_r_2,T_c,V_b_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2))) % 19.07/18.97 => ~ ! [B_x] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),V_b_2)),V_r_2)) % 19.07/18.97 => ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Field__empty,axiom, % 19.07/18.97 ! [T_b] : hAPP(c_Relation_OField(T_b),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 19.07/18.97 % 19.07/18.97 fof(fact_mono__Field,axiom, % 19.07/18.97 ! [V_s_2,V_r_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OField(T_b),V_r_2)),hAPP(c_Relation_OField(T_b),V_s_2))) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Field__Un,axiom, % 19.07/18.97 ! [V_s_2,V_r_2,T_b] : hAPP(c_Relation_OField(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OField(T_b),V_r_2)),hAPP(c_Relation_OField(T_b),V_s_2)) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J,axiom, % 19.07/18.97 ! [V_B_2,V_A_2] : % 19.07/18.97 ( c_Nat__Transfer_Onat__set(V_A_2) % 19.07/18.97 => ( c_Nat__Transfer_Onat__set(V_B_2) % 19.07/18.97 => 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))) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_transfer__int__nat__set__relations_I4_J,axiom, % 19.07/18.97 ! [V_B_2,V_A_2] : % 19.07/18.97 ( c_Nat__Transfer_Onat__set(V_A_2) % 19.07/18.97 => ( c_Nat__Transfer_Onat__set(V_B_2) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) % 19.07/18.97 <=> 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))) ) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_transfer__int__nat__set__relations_I5_J,axiom, % 19.07/18.97 ! [V_B_2,V_A_2] : % 19.07/18.97 ( c_Nat__Transfer_Onat__set(V_A_2) % 19.07/18.97 => ( c_Nat__Transfer_Onat__set(V_B_2) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) % 19.07/18.97 <=> 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))) ) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_transfer__int__nat__set__relations_I2_J,axiom, % 19.07/18.97 ! [V_A_2,V_x_2] : % 19.07/18.97 ( c_Nat__Transfer_Ois__nat(V_x_2) % 19.07/18.97 => ( c_Nat__Transfer_Onat__set(V_A_2) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) % 19.07/18.97 <=> 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))) ) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J,axiom, % 19.07/18.97 c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J,axiom, % 19.07/18.97 ! [V_B_2,V_A_2] : % 19.07/18.97 ( c_Nat__Transfer_Onat__set(V_A_2) % 19.07/18.97 => ( c_Nat__Transfer_Onat__set(V_B_2) % 19.07/18.97 => 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)) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_nat__set__def,axiom, % 19.07/18.97 ! [V_S_2] : % 19.07/18.97 ( c_Nat__Transfer_Onat__set(V_S_2) % 19.07/18.97 <=> ! [B_x] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),V_S_2)) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J,axiom, % 19.07/18.97 ! [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)) ). % 19.07/18.97 % 19.07/18.97 fof(fact_transfer__int__nat__set__relations_I3_J,axiom, % 19.07/18.97 ! [V_B_2,V_A_2] : % 19.07/18.97 ( c_Nat__Transfer_Onat__set(V_A_2) % 19.07/18.97 => ( c_Nat__Transfer_Onat__set(V_B_2) % 19.07/18.97 => ( V_A_2 = V_B_2 % 19.07/18.97 <=> 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) ) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J,axiom, % 19.07/18.97 ! [V_x_2,V_A_2] : % 19.07/18.97 ( c_Nat__Transfer_Onat__set(V_A_2) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) % 19.07/18.97 => c_Nat__Transfer_Ois__nat(V_x_2) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J,axiom, % 19.07/18.97 ! [V_x_2,V_A_2] : % 19.07/18.97 ( c_Nat__Transfer_Onat__set(V_A_2) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_transfer__nat__int__set__return__embed,axiom, % 19.07/18.97 ! [V_A_2] : % 19.07/18.97 ( c_Nat__Transfer_Onat__set(V_A_2) % 19.07/18.97 => 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 ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_subset__equiv__class,axiom, % 19.07/18.97 ! [V_a_2,V_b_2,V_r_2,V_A_2,T_b] : % 19.07/18.97 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2)) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_accp__acc__eq,axiom, % 19.07/18.97 ! [V_x_2,V_r_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2)),V_x_2)) % 19.07/18.97 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_wmax__emptyI,axiom, % 19.07/18.97 ! [V_X_2] : % 19.07/18.97 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_X_2)) % 19.07/18.97 => 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)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_smax__emptyI,axiom, % 19.07/18.97 ! [V_Y_2] : % 19.07/18.97 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_Y_2)) % 19.07/18.97 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) % 19.07/18.97 => 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)) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_finite__Field,axiom, % 19.07/18.97 ! [V_r_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) % 19.07/18.97 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_OField(T_b),V_r_2))) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_acc__subset,axiom, % 19.07/18.97 ! [V_R2_2,V_R1_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R1_2),V_R2_2)) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Oacc(T_b,V_R2_2)),c_Wellfounded_Oacc(T_b,V_R1_2))) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_equiv__class__self,axiom, % 19.07/18.97 ! [V_a_2,V_r_2,V_A_2,T_b] : % 19.07/18.97 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_acc__downward,axiom, % 19.07/18.97 ! [V_a_2,V_r_2,V_b_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2))) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_acc_Osimps,axiom, % 19.07/18.97 ! [V_r_2,V_a_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2))) % 19.07/18.97 <=> ! [B_x] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),V_a_2)),V_r_2)) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_equiv__class__eq,axiom, % 19.07/18.97 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_b] : % 19.07/18.97 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) % 19.07/18.97 => hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_equiv__class__eq__iff,axiom, % 19.07/18.97 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] : % 19.07/18.97 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) % 19.07/18.97 <=> ( hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) % 19.07/18.97 & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.97 & hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_eq__equiv__class__iff,axiom, % 19.07/18.97 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] : % 19.07/18.97 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 19.07/18.97 => ( hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) % 19.07/18.97 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) ) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_eq__equiv__class,axiom, % 19.07/18.97 ! [V_A_2,V_b_2,V_a_2,V_r_2,T_b] : % 19.07/18.97 ( hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) % 19.07/18.97 => ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2)) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_equiv__class__subset,axiom, % 19.07/18.97 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_b] : % 19.07/18.97 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_finite__Diff,axiom, % 19.07/18.97 ! [V_B_2,V_A_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.97 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_finite__imageI,axiom, % 19.07/18.97 ! [V_h_2,T_c,V_F_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 19.07/18.97 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_F_2))) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_finite_OinsertI,axiom, % 19.07/18.97 ! [V_a_2,V_A_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.97 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_finite_OemptyI,axiom, % 19.07/18.97 ! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ). % 19.07/18.97 % 19.07/18.97 fof(fact_transfer__nat__int__set__relations_I1_J,axiom, % 19.07/18.97 ! [V_A_2] : % 19.07/18.97 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_A_2)) % 19.07/18.97 <=> 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))) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_transfer__int__nat__set__relations_I1_J,axiom, % 19.07/18.97 ! [V_A_2] : % 19.07/18.97 ( c_Nat__Transfer_Onat__set(V_A_2) % 19.07/18.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),V_A_2)) % 19.07/18.97 <=> 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))) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_finite__code,axiom, % 19.07/18.97 ! [V_A_2,T_b] : % 19.07/18.97 ( class_Finite__Set_Ofinite(T_b) % 19.07/18.97 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_finite,axiom, % 19.07/18.97 ! [V_A_2,T_b] : % 19.07/18.97 ( class_Finite__Set_Ofinite(T_b) % 19.07/18.97 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_finite_Oequations_I1_J,axiom, % 19.07/18.97 ! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ). % 19.07/18.97 % 19.07/18.97 fof(fact_finite__insert,axiom, % 19.07/18.97 ! [V_A_2,V_a_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))) % 19.07/18.97 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_rev__finite__subset,axiom, % 19.07/18.97 ! [V_A_2,V_B_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 19.07/18.97 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_finite__subset,axiom, % 19.07/18.97 ! [V_B_2,V_A_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 19.07/18.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 19.07/18.97 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_finite__UnI,axiom, % 19.07/18.97 ! [V_G_2,V_F_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 19.07/18.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_G_2)) % 19.07/18.97 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_G_2))) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_finite__Un,axiom, % 19.07/18.97 ! [V_G_2,V_F_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_G_2))) % 19.07/18.97 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 19.07/18.97 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_G_2)) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_finite__Diff2,axiom, % 19.07/18.97 ! [V_A_2,V_B_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 19.07/18.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 19.07/18.97 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_finite__surj,axiom, % 19.07/18.97 ! [V_f_2,V_B_2,T_c,V_A_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) % 19.07/18.97 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_finite__Diff__insert,axiom, % 19.07/18.97 ! [V_B_2,V_a_2,V_A_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)))) % 19.07/18.97 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_in__finite__psubset,axiom, % 19.07/18.97 ! [V_B_2,V_A_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),c_Wellfounded_Ofinite__psubset(T_b))) % 19.07/18.97 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 19.07/18.97 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_folding__image__simple_Oremove,axiom, % 19.07/18.97 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 19.07/18.97 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 19.07/18.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 19.07/18.97 => hAPP(V_F_2,V_A_2) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))) ) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_folding__one_Oremove,axiom, % 19.07/18.97 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] : % 19.07/18.97 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 19.07/18.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.97 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.97 => hAPP(V_F_2,V_A_2) = V_x_2 ) % 19.07/18.97 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.97 => hAPP(V_F_2,V_A_2) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_eq__equiv__class__iff2,axiom, % 19.07/18.97 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] : % 19.07/18.97 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 19.07/18.97 => ( hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2) = hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2) % 19.07/18.97 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) ) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_quotient__empty,axiom, % 19.07/18.97 ! [V_r_2,T_b] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) ). % 19.07/18.97 % 19.07/18.97 fof(fact_quotient__is__empty2,axiom, % 19.07/18.97 ! [V_r_2,V_A_2,T_b] : % 19.07/18.97 ( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2) % 19.07/18.97 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_quotient__is__empty,axiom, % 19.07/18.97 ! [V_r_2,V_A_2,T_b] : % 19.07/18.97 ( hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) % 19.07/18.97 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_folding__image__simple_Oempty,axiom, % 19.07/18.97 ! [V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 19.07/18.97 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 19.07/18.97 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2 ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_folding__one_Osingleton,axiom, % 19.07/18.97 ! [V_x_2,V_F_2,V_f_2,T_b] : % 19.07/18.97 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 19.07/18.97 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_singleton__quotient,axiom, % 19.07/18.97 ! [V_r_2,V_x_2,T_b] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2) = hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) ). % 19.07/18.97 % 19.07/18.97 fof(fact_quotientI,axiom, % 19.07/18.97 ! [V_r_2,V_A_2,V_x_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_quotient__eq__iff,axiom, % 19.07/18.97 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] : % 19.07/18.97 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2)) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2)) % 19.07/18.97 => ( V_X_2 = V_Y_2 % 19.07/18.97 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) ) ) ) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_quotient__eqI,axiom, % 19.07/18.97 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] : % 19.07/18.97 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2)) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2)) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) % 19.07/18.97 => V_X_2 = V_Y_2 ) ) ) ) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_folding__image__simple_Oinsert,axiom, % 19.07/18.97 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 19.07/18.97 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 19.07/18.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 19.07/18.97 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 19.07/18.97 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,V_A_2)) ) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_folding__one_Oinsert,axiom, % 19.07/18.97 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] : % 19.07/18.97 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 19.07/18.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.97 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.97 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.97 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) ) ) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_folding__one_Oinsert__remove,axiom, % 19.07/18.97 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] : % 19.07/18.97 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 19.07/18.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.97 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.97 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 ) % 19.07/18.97 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.97 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_folding__image__simple_Oinsert__remove,axiom, % 19.07/18.97 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 19.07/18.97 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 19.07/18.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 19.07/18.97 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_finite__nat__set__iff__bounded__le,axiom, % 19.07/18.97 ! [V_N_2] : % 19.07/18.97 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2)) % 19.07/18.97 <=> ? [B_m] : % 19.07/18.97 ! [B_x] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_x),B_m)) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_finite__nat__set__iff__bounded,axiom, % 19.07/18.97 ! [V_N_2] : % 19.07/18.97 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2)) % 19.07/18.97 <=> ? [B_m] : % 19.07/18.97 ! [B_x] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_x),B_m)) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_equiv__class__nondisjoint,axiom, % 19.07/18.97 ! [V_b_2,V_a_2,V_x_2,V_r_2,V_A_2,T_b] : % 19.07/18.97 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Sup__fin_Oremove,axiom, % 19.07/18.97 ! [V_x_2,V_A_2,T_b] : % 19.07/18.97 ( class_Lattices_Olattice(T_b) % 19.07/18.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.97 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.97 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = V_x_2 ) % 19.07/18.97 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.97 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_inf1I,axiom, % 19.07/18.97 ! [T_b,V_B_2,V_x_2,V_A_2] : % 19.07/18.97 ( hBOOL(hAPP(V_A_2,V_x_2)) % 19.07/18.97 => ( hBOOL(hAPP(V_B_2,V_x_2)) % 19.07/18.97 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_inf1E,axiom, % 19.07/18.97 ! [V_x_2,V_B_2,V_A_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) % 19.07/18.97 => ~ ( hBOOL(hAPP(V_A_2,V_x_2)) % 19.07/18.97 => ~ hBOOL(hAPP(V_B_2,V_x_2)) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_IntE,axiom, % 19.07/18.97 ! [V_B_2,V_A_2,V_c_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 19.07/18.97 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) % 19.07/18.97 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_IntI,axiom, % 19.07/18.97 ! [V_B_2,V_A_2,V_c_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_finite__Int,axiom, % 19.07/18.97 ! [V_G_2,V_F_2,T_b] : % 19.07/18.97 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 19.07/18.97 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_G_2)) ) % 19.07/18.97 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_G_2))) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_inf__Sup__absorb,axiom, % 19.07/18.97 ! [V_a_2,V_A_2,T_b] : % 19.07/18.97 ( class_Lattices_Olattice(T_b) % 19.07/18.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 19.07/18.97 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = V_a_2 ) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_inf__Int__eq,axiom, % 19.07/18.97 ! [V_x_2,V_S_2,V_R_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)),V_x_2)) % 19.07/18.97 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2))) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Int__mono,axiom, % 19.07/18.97 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2)) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2))) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Int__greatest,axiom, % 19.07/18.97 ! [V_B_2,V_A_2,V_C_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Int__absorb1,axiom, % 19.07/18.97 ! [V_A_2,V_B_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 19.07/18.97 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Int__absorb2,axiom, % 19.07/18.97 ! [V_B_2,V_A_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 19.07/18.97 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Int__lower2,axiom, % 19.07/18.97 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_B_2)) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Int__lower1,axiom, % 19.07/18.97 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_A_2)) ). % 19.07/18.97 % 19.07/18.97 fof(fact_inf__sup__ord_I1_J,axiom, % 19.07/18.97 ! [V_y,V_x,T_a] : % 19.07/18.97 ( class_Lattices_Olattice(T_a) % 19.07/18.97 => 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)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_inf__le1,axiom, % 19.07/18.97 ! [V_y,V_x,T_a] : % 19.07/18.97 ( class_Lattices_Osemilattice__inf(T_a) % 19.07/18.97 => 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)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_inf__sup__ord_I2_J,axiom, % 19.07/18.97 ! [V_y,V_x,T_a] : % 19.07/18.97 ( class_Lattices_Olattice(T_a) % 19.07/18.97 => 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)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_inf__le2,axiom, % 19.07/18.97 ! [V_y,V_x,T_a] : % 19.07/18.97 ( class_Lattices_Osemilattice__inf(T_a) % 19.07/18.97 => 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)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_le__iff__inf,axiom, % 19.07/18.97 ! [V_y_2,V_x_2,T_b] : % 19.07/18.97 ( class_Lattices_Osemilattice__inf(T_b) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 19.07/18.97 <=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = V_x_2 ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_le__inf__iff,axiom, % 19.07/18.97 ! [V_z_2,V_y_2,V_x_2,T_b] : % 19.07/18.97 ( class_Lattices_Osemilattice__inf(T_b) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_y_2),V_z_2))) % 19.07/18.97 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 19.07/18.97 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_le__infI1,axiom, % 19.07/18.97 ! [V_b,V_x,V_a,T_a] : % 19.07/18.97 ( class_Lattices_Osemilattice__inf(T_a) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 19.07/18.97 => 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)) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_le__infI2,axiom, % 19.07/18.97 ! [V_a,V_x,V_b,T_a] : % 19.07/18.97 ( class_Lattices_Osemilattice__inf(T_a) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 19.07/18.97 => 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)) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_inf__absorb1,axiom, % 19.07/18.97 ! [V_y,V_x,T_a] : % 19.07/18.97 ( class_Lattices_Osemilattice__inf(T_a) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 19.07/18.97 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_x ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_inf__absorb2,axiom, % 19.07/18.97 ! [V_x,V_y,T_a] : % 19.07/18.97 ( class_Lattices_Osemilattice__inf(T_a) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 19.07/18.97 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_y ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_le__infI,axiom, % 19.07/18.97 ! [V_b,V_a,V_x,T_a] : % 19.07/18.97 ( class_Lattices_Osemilattice__inf(T_a) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 19.07/18.97 => 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))) ) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_inf__greatest,axiom, % 19.07/18.97 ! [V_z,V_y,V_x,T_a] : % 19.07/18.97 ( class_Lattices_Osemilattice__inf(T_a) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) % 19.07/18.97 => 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))) ) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_inf__mono,axiom, % 19.07/18.97 ! [V_d,V_b,V_c,V_a,T_a] : % 19.07/18.97 ( class_Lattices_Osemilattice__inf(T_a) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 19.07/18.97 => 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))) ) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_le__infE,axiom, % 19.07/18.97 ! [V_b,V_a,V_x,T_a] : % 19.07/18.97 ( class_Lattices_Osemilattice__inf(T_a) % 19.07/18.97 => ( 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))) % 19.07/18.97 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 19.07/18.97 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_less__infI2,axiom, % 19.07/18.97 ! [V_a,V_x,V_b,T_a] : % 19.07/18.97 ( class_Lattices_Osemilattice__inf(T_a) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x)) % 19.07/18.97 => 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)) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_less__infI1,axiom, % 19.07/18.97 ! [V_b,V_x,V_a,T_a] : % 19.07/18.97 ( class_Lattices_Osemilattice__inf(T_a) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x)) % 19.07/18.97 => 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)) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_insert__inter__insert,axiom, % 19.07/18.97 ! [V_B_2,V_A_2,V_a_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ). % 19.07/18.97 % 19.07/18.97 fof(fact_disjoint__iff__not__equal,axiom, % 19.07/18.97 ! [V_B_2,V_A_2,T_b] : % 19.07/18.97 ( 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)) % 19.07/18.97 <=> ! [B_x] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 19.07/18.97 => ! [B_xa] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_B_2)) % 19.07/18.97 => B_x != B_xa ) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Int__empty__right,axiom, % 19.07/18.97 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Int__empty__left,axiom, % 19.07/18.97 ! [V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 19.07/18.97 % 19.07/18.97 fof(fact_inf__bot__right,axiom, % 19.07/18.97 ! [V_x,T_a] : % 19.07/18.97 ( class_Lattices_Obounded__lattice__bot(T_a) % 19.07/18.97 => 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) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_inf__bot__left,axiom, % 19.07/18.97 ! [V_x,T_a] : % 19.07/18.97 ( class_Lattices_Obounded__lattice__bot(T_a) % 19.07/18.97 => 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) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Int__iff,axiom, % 19.07/18.97 ! [V_B_2,V_A_2,V_c_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 19.07/18.97 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) % 19.07/18.97 & hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_IntD1,axiom, % 19.07/18.97 ! [V_B_2,V_A_2,V_c_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_IntD2,axiom, % 19.07/18.97 ! [V_B_2,V_A_2,V_c_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 19.07/18.97 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_inf__sup__absorb,axiom, % 19.07/18.97 ! [V_y,V_x,T_a] : % 19.07/18.97 ( class_Lattices_Olattice(T_a) % 19.07/18.97 => 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 ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_sup__inf__absorb,axiom, % 19.07/18.97 ! [V_y,V_x,T_a] : % 19.07/18.97 ( class_Lattices_Olattice(T_a) % 19.07/18.97 => 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 ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_inf__sup__distrib1,axiom, % 19.07/18.97 ! [V_z,V_y,V_x,T_a] : % 19.07/18.97 ( class_Lattices_Odistrib__lattice(T_a) % 19.07/18.97 => 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)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_sup__inf__distrib1,axiom, % 19.07/18.97 ! [V_z,V_y,V_x,T_a] : % 19.07/18.97 ( class_Lattices_Odistrib__lattice(T_a) % 19.07/18.97 => 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)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_inf__sup__distrib2,axiom, % 19.07/18.97 ! [V_x,V_z,V_y,T_a] : % 19.07/18.97 ( class_Lattices_Odistrib__lattice(T_a) % 19.07/18.97 => 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)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_sup__inf__distrib2,axiom, % 19.07/18.97 ! [V_x,V_z,V_y,T_a] : % 19.07/18.97 ( class_Lattices_Odistrib__lattice(T_a) % 19.07/18.97 => 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)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Int__Un__distrib,axiom, % 19.07/18.97 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Un__Int__distrib,axiom, % 19.07/18.97 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Int__Un__distrib2,axiom, % 19.07/18.97 ! [V_A_2,V_C_2,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Un__Int__distrib2,axiom, % 19.07/18.97 ! [V_A_2,V_C_2,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Un__Int__crazy,axiom, % 19.07/18.97 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Inf__fin_Oidem,axiom, % 19.07/18.97 ! [V_x,T_a] : % 19.07/18.97 ( class_Lattices_Olattice(T_a) % 19.07/18.97 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Diff__Int__distrib,axiom, % 19.07/18.97 ! [V_B_2,V_A_2,V_C_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Int__Diff,axiom, % 19.07/18.97 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Diff__Int__distrib2,axiom, % 19.07/18.97 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Diff__Int2,axiom, % 19.07/18.97 ! [V_B_2,V_C_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),V_B_2) ). % 19.07/18.97 % 19.07/18.97 fof(fact_inf__fun__def,axiom, % 19.07/18.97 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] : % 19.07/18.97 ( class_Lattices_Olattice(T_b) % 19.07/18.97 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,T_b)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_inf_Oidem,axiom, % 19.07/18.97 ! [V_a,T_a] : % 19.07/18.97 ( class_Lattices_Osemilattice__inf(T_a) % 19.07/18.97 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_a) = V_a ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_inf__idem,axiom, % 19.07/18.97 ! [V_x,T_a] : % 19.07/18.97 ( class_Lattices_Osemilattice__inf(T_a) % 19.07/18.97 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_inf_Ocommute,axiom, % 19.07/18.97 ! [V_b,V_a,T_a] : % 19.07/18.97 ( class_Lattices_Osemilattice__inf(T_a) % 19.07/18.97 => 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) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_inf__sup__aci_I1_J,axiom, % 19.07/18.97 ! [V_y,V_x,T_a] : % 19.07/18.97 ( class_Lattices_Olattice(T_a) % 19.07/18.97 => 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) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_inf__commute,axiom, % 19.07/18.97 ! [V_y,V_x,T_a] : % 19.07/18.97 ( class_Lattices_Osemilattice__inf(T_a) % 19.07/18.97 => 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) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_inf_Oleft__idem,axiom, % 19.07/18.97 ! [V_b,V_a,T_a] : % 19.07/18.97 ( class_Lattices_Osemilattice__inf(T_a) % 19.07/18.97 => 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) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_inf__sup__aci_I4_J,axiom, % 19.07/18.97 ! [V_y,V_x,T_a] : % 19.07/18.97 ( class_Lattices_Olattice(T_a) % 19.07/18.97 => 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) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_inf__left__idem,axiom, % 19.07/18.97 ! [V_y,V_x,T_a] : % 19.07/18.97 ( class_Lattices_Osemilattice__inf(T_a) % 19.07/18.97 => 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) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_inf_Oleft__commute,axiom, % 19.07/18.97 ! [V_c,V_a,V_b,T_a] : % 19.07/18.97 ( class_Lattices_Osemilattice__inf(T_a) % 19.07/18.97 => 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)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_inf__sup__aci_I3_J,axiom, % 19.07/18.97 ! [V_z,V_y,V_x,T_a] : % 19.07/18.97 ( class_Lattices_Olattice(T_a) % 19.07/18.97 => 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)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_inf__left__commute,axiom, % 19.07/18.97 ! [V_z,V_y,V_x,T_a] : % 19.07/18.97 ( class_Lattices_Osemilattice__inf(T_a) % 19.07/18.97 => 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)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_inf_Oassoc,axiom, % 19.07/18.97 ! [V_c,V_b,V_a,T_a] : % 19.07/18.97 ( class_Lattices_Osemilattice__inf(T_a) % 19.07/18.97 => 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)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_inf__sup__aci_I2_J,axiom, % 19.07/18.97 ! [V_z,V_y,V_x,T_a] : % 19.07/18.97 ( class_Lattices_Olattice(T_a) % 19.07/18.97 => 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)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_inf__assoc,axiom, % 19.07/18.97 ! [V_z,V_y,V_x,T_a] : % 19.07/18.97 ( class_Lattices_Osemilattice__inf(T_a) % 19.07/18.97 => 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)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_inf__apply,axiom, % 19.07/18.97 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] : % 19.07/18.97 ( class_Lattices_Olattice(T_b) % 19.07/18.97 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,T_b)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Int__absorb,axiom, % 19.07/18.97 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2) = V_A_2 ). % 19.07/18.97 % 19.07/18.97 fof(fact_Int__commute,axiom, % 19.07/18.97 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Int__left__absorb,axiom, % 19.07/18.97 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Int__left__commute,axiom, % 19.07/18.97 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Int__assoc,axiom, % 19.07/18.97 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ). % 19.07/18.97 % 19.07/18.97 fof(fact_inf__min,axiom, % 19.07/18.97 ! [T_b] : % 19.07/18.97 ( ( class_Lattices_Osemilattice__inf(T_b) % 19.07/18.97 & class_Orderings_Olinorder(T_b) ) % 19.07/18.97 => c_Lattices_Osemilattice__inf__class_Oinf(T_b) = c_Orderings_Oord__class_Omin(T_b) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_inf1D1,axiom, % 19.07/18.97 ! [V_x_2,V_B_2,V_A_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) % 19.07/18.97 => hBOOL(hAPP(V_A_2,V_x_2)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_inf1D2,axiom, % 19.07/18.97 ! [V_x_2,V_B_2,V_A_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) % 19.07/18.97 => hBOOL(hAPP(V_B_2,V_x_2)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J,axiom, % 19.07/18.97 ! [V_B_2,V_A_2] : % 19.07/18.97 ( c_Nat__Transfer_Onat__set(V_A_2) % 19.07/18.97 => ( c_Nat__Transfer_Onat__set(V_B_2) % 19.07/18.97 => 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)) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_distrib__sup__le,axiom, % 19.07/18.97 ! [V_z,V_y,V_x,T_a] : % 19.07/18.97 ( class_Lattices_Olattice(T_a) % 19.07/18.97 => 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)))) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_distrib__inf__le,axiom, % 19.07/18.97 ! [V_z,V_y,V_x,T_a] : % 19.07/18.97 ( class_Lattices_Olattice(T_a) % 19.07/18.97 => 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)))) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_inf__compl__bot,axiom, % 19.07/18.97 ! [V_x,T_a] : % 19.07/18.97 ( class_Lattices_Oboolean__algebra(T_a) % 19.07/18.97 => 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) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_compl__inf__bot,axiom, % 19.07/18.97 ! [V_x,T_a] : % 19.07/18.97 ( class_Lattices_Oboolean__algebra(T_a) % 19.07/18.97 => 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) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_diff__eq,axiom, % 19.07/18.97 ! [V_y,V_x,T_a] : % 19.07/18.97 ( class_Lattices_Oboolean__algebra(T_a) % 19.07/18.97 => 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)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_compl__inf,axiom, % 19.07/18.97 ! [V_y,V_x,T_a] : % 19.07/18.97 ( class_Lattices_Oboolean__algebra(T_a) % 19.07/18.97 => 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)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_compl__sup,axiom, % 19.07/18.97 ! [V_y,V_x,T_a] : % 19.07/18.97 ( class_Lattices_Oboolean__algebra(T_a) % 19.07/18.97 => 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)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Int__insert__right,axiom, % 19.07/18.97 ! [V_B_2,V_A_2,V_a_2,T_b] : % 19.07/18.97 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 19.07/18.97 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) % 19.07/18.97 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 19.07/18.97 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Int__insert__left,axiom, % 19.07/18.97 ! [V_B_2,V_C_2,V_a_2,T_b] : % 19.07/18.97 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2)) % 19.07/18.97 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ) % 19.07/18.97 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2)) % 19.07/18.97 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Int__insert__right__if0,axiom, % 19.07/18.97 ! [V_B_2,V_A_2,V_a_2,T_b] : % 19.07/18.97 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 19.07/18.97 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Int__insert__left__if0,axiom, % 19.07/18.97 ! [V_B_2,V_C_2,V_a_2,T_b] : % 19.07/18.97 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2)) % 19.07/18.97 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Int__insert__right__if1,axiom, % 19.07/18.97 ! [V_B_2,V_A_2,V_a_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 19.07/18.97 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Int__insert__left__if1,axiom, % 19.07/18.97 ! [V_B_2,V_C_2,V_a_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2)) % 19.07/18.97 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Sup__fin_Ounion__disjoint,axiom, % 19.07/18.97 ! [V_B_2,V_A_2,T_b] : % 19.07/18.97 ( class_Lattices_Olattice(T_b) % 19.07/18.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.97 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 19.07/18.97 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.97 => ( 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)) % 19.07/18.97 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)) ) ) ) ) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Sup__fin_Ounion__inter,axiom, % 19.07/18.97 ! [V_B_2,V_A_2,T_b] : % 19.07/18.97 ( class_Lattices_Olattice(T_b) % 19.07/18.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 19.07/18.97 => ( 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)) % 19.07/18.97 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)) ) ) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_image__Int__subset,axiom, % 19.07/18.97 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2)))) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Diff__disjoint,axiom, % 19.07/18.97 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Diff__triv,axiom, % 19.07/18.97 ! [V_B_2,V_A_2,T_b] : % 19.07/18.97 ( 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)) % 19.07/18.97 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Un__Int__assoc__eq,axiom, % 19.07/18.97 ! [V_C_2,V_B_2,V_A_2,T_b] : % 19.07/18.97 ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 19.07/18.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Diff__Int,axiom, % 19.07/18.97 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Diff__Un,axiom, % 19.07/18.97 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Un__Diff__Int,axiom, % 19.07/18.97 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = V_A_2 ). % 19.07/18.97 % 19.07/18.97 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J,axiom, % 19.07/18.97 ! [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))) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Compl__disjoint,axiom, % 19.07/18.97 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Compl__disjoint2,axiom, % 19.07/18.97 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Image__Int__subset,axiom, % 19.07/18.97 ! [V_B_2,V_A_2,V_R_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_B_2)))) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Compl__Int,axiom, % 19.07/18.97 ! [V_B_2,V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Compl__Un,axiom, % 19.07/18.97 ! [V_B_2,V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Diff__eq,axiom, % 19.07/18.97 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Diff__Compl,axiom, % 19.07/18.97 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Sup__fin_Osingleton,axiom, % 19.07/18.97 ! [V_x_2,T_b] : % 19.07/18.97 ( class_Lattices_Olattice(T_b) % 19.07/18.97 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J,axiom, % 19.07/18.97 ! [V_B_2,V_A_2] : % 19.07/18.97 ( c_Nat__Transfer_Onat__set(V_A_2) % 19.07/18.97 => ( c_Nat__Transfer_Onat__set(V_B_2) % 19.07/18.97 => 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))) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_disjoint__eq__subset__Compl,axiom, % 19.07/18.97 ! [V_B_2,V_A_2,T_b] : % 19.07/18.97 ( 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)) % 19.07/18.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2))) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_quotient__disj,axiom, % 19.07/18.97 ! [V_Y_2,V_X_2,V_r_2,V_A_2,T_b] : % 19.07/18.97 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) % 19.07/18.97 => ( V_X_2 = V_Y_2 % 19.07/18.97 | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_Y_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_folding__image__simple_Ounion__inter,axiom, % 19.07/18.97 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 19.07/18.97 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 19.07/18.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 19.07/18.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 19.07/18.97 => hAPP(hAPP(V_f_2,hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Sup__fin_Oin__idem,axiom, % 19.07/18.97 ! [V_x_2,V_A_2,T_b] : % 19.07/18.97 ( class_Lattices_Olattice(T_b) % 19.07/18.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.97 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) ) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_folding__image__simple_Ounion__disjoint,axiom, % 19.07/18.97 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 19.07/18.97 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 19.07/18.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 19.07/18.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 19.07/18.97 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 19.07/18.97 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_folding__one_Ounion__disjoint,axiom, % 19.07/18.97 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] : % 19.07/18.97 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 19.07/18.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.97 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 19.07/18.97 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.97 => ( 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)) % 19.07/18.97 => 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)) ) ) ) ) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_folding__one_Ounion__inter,axiom, % 19.07/18.97 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] : % 19.07/18.97 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 19.07/18.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 19.07/18.97 => ( 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)) % 19.07/18.97 => 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)) ) ) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Sup__fin_Oinsert__idem,axiom, % 19.07/18.97 ! [V_x_2,V_A_2,T_b] : % 19.07/18.97 ( class_Lattices_Olattice(T_b) % 19.07/18.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.97 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.97 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) ) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Sup__fin_Osubset__idem,axiom, % 19.07/18.97 ! [V_B_2,V_A_2,T_b] : % 19.07/18.97 ( class_Lattices_Olattice(T_b) % 19.07/18.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.97 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 19.07/18.97 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) ) ) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Sup__fin_Ounion__idem,axiom, % 19.07/18.97 ! [V_B_2,V_A_2,T_b] : % 19.07/18.97 ( class_Lattices_Olattice(T_b) % 19.07/18.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.97 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 19.07/18.97 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.97 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)) ) ) ) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Sup__fin_Oinsert,axiom, % 19.07/18.97 ! [V_x_2,V_A_2,T_b] : % 19.07/18.97 ( class_Lattices_Olattice(T_b) % 19.07/18.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.97 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.97 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.97 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) ) ) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Sup__fin_Oinsert__remove,axiom, % 19.07/18.97 ! [V_x_2,V_A_2,T_b] : % 19.07/18.97 ( class_Lattices_Olattice(T_b) % 19.07/18.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.97 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.97 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 ) % 19.07/18.97 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.97 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_dvd_OgreaterThanLessThan__empty,axiom, % 19.07/18.97 ! [V_k_2,V_l_2] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2)) % 19.07/18.97 => c_SetInterval_Oord_OgreaterThanLessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_dvd_OgreaterThan__iff,axiom, % 19.07/18.97 ! [V_k_2,V_i_2] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_i_2),c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2))) % 19.07/18.97 <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2)) % 19.07/18.97 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2)) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_dvd_OlessThan__iff,axiom, % 19.07/18.97 ! [V_k_2,V_i_2] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_i_2),c_SetInterval_Oord_OlessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2))) % 19.07/18.97 <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2)) % 19.07/18.97 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2)) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_dvd_OatLeast__iff,axiom, % 19.07/18.97 ! [V_k_2,V_i_2] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_i_2),c_SetInterval_Oord_OatLeast(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2))) % 19.07/18.97 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_inf__nat__def,axiom, % 19.07/18.97 c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat) ). % 19.07/18.97 % 19.07/18.97 fof(fact_inf__Int__eq2,axiom, % 19.07/18.97 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_S_2)),V_x_2),V_y_2)) % 19.07/18.97 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_R_2),V_S_2))) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_ord_OatLeast__iff,axiom, % 19.07/18.97 ! [V_k_2,V_less__eq_2,V_i_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeast(T_b,V_less__eq_2,V_k_2))) % 19.07/18.97 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_ord_OlessThan__iff,axiom, % 19.07/18.97 ! [V_k_2,V_less_2,V_i_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OlessThan(T_b,V_less_2,V_k_2))) % 19.07/18.97 <=> hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_ord_OgreaterThan__iff,axiom, % 19.07/18.97 ! [V_k_2,V_less_2,V_i_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThan(T_b,V_less_2,V_k_2))) % 19.07/18.97 <=> hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_ord_OgreaterThanLessThan__iff,axiom, % 19.07/18.97 ! [V_u_2,V_l_2,V_less_2,V_i_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThanLessThan(T_b,V_less_2,V_l_2,V_u_2))) % 19.07/18.97 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) % 19.07/18.97 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_dvd_OatMost__iff,axiom, % 19.07/18.97 ! [V_k_2,V_i_2] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_i_2),c_SetInterval_Oord_OatMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2))) % 19.07/18.97 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2)) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_quotientE,axiom, % 19.07/18.97 ! [V_r_2,V_A_2,V_X_2,T_b] : % 19.07/18.97 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) % 19.07/18.97 => ~ ! [B_x] : % 19.07/18.97 ( V_X_2 = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) % 19.07/18.97 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ). % 19.07/18.97 % 19.07/18.97 fof(fact_Sup__fin_Oclosed,axiom, % 19.07/18.98 ! [V_A_2,T_b] : % 19.07/18.98 ( class_Lattices_Olattice(T_b) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) % 19.07/18.98 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),V_A_2)) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_ord_OatMost__iff,axiom, % 19.07/18.98 ! [V_k_2,V_less__eq_2,V_i_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatMost(T_b,V_less__eq_2,V_k_2))) % 19.07/18.98 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2)) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_inf2I,axiom, % 19.07/18.98 ! [T_c,T_b,V_B_2,V_y_2,V_x_2,V_A_2] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) % 19.07/18.98 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_inf2E,axiom, % 19.07/18.98 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) % 19.07/18.98 => ~ ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 19.07/18.98 => ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_inf2D1,axiom, % 19.07/18.98 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) % 19.07/18.98 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_inf2D2,axiom, % 19.07/18.98 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) % 19.07/18.98 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_ord_OgreaterThanAtMost__iff,axiom, % 19.07/18.98 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThanAtMost(T_b,V_less__eq_2,V_less_2,V_l_2,V_u_2))) % 19.07/18.98 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) % 19.07/18.98 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_ord_OatLeastLessThan__iff,axiom, % 19.07/18.98 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeastLessThan(T_b,V_less__eq_2,V_less_2,V_l_2,V_u_2))) % 19.07/18.98 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) % 19.07/18.98 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_ord_OatLeastAtMost__iff,axiom, % 19.07/18.98 ! [V_u_2,V_l_2,V_less__eq_2,V_i_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeastAtMost(T_b,V_less__eq_2,V_l_2,V_u_2))) % 19.07/18.98 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) % 19.07/18.98 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_dvd_OatLeastLessThan__empty__iff2,axiom, % 19.07/18.98 ! [V_b_2,V_a_2] : % 19.07/18.98 ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_a_2,V_b_2) % 19.07/18.98 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) % 19.07/18.98 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2)) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_dvd_OatLeastatMost__empty__iff2,axiom, % 19.07/18.98 ! [V_b_2,V_a_2] : % 19.07/18.98 ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) % 19.07/18.98 <=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_dvd_OatLeastatMost__empty__iff,axiom, % 19.07/18.98 ! [V_b_2,V_a_2] : % 19.07/18.98 ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) % 19.07/18.98 <=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_dvd_OatLeastatMost__empty,axiom, % 19.07/18.98 ! [V_a_2,V_b_2] : % 19.07/18.98 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2)) % 19.07/18.98 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) ) % 19.07/18.98 => c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_dvd_OatLeastAtMost__singleton_H,axiom, % 19.07/18.98 ! [V_b_2,V_a_2] : % 19.07/18.98 ( V_a_2 = V_b_2 % 19.07/18.98 => c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_dvd_OatLeastAtMost__singleton,axiom, % 19.07/18.98 ! [V_a_2] : c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_a_2) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ). % 19.07/18.98 % 19.07/18.98 fof(fact_dvd_OatLeastAtMost__singleton__iff,axiom, % 19.07/18.98 ! [V_c_2,V_b_2,V_a_2] : % 19.07/18.98 ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) % 19.07/18.98 <=> ( V_a_2 = V_b_2 % 19.07/18.98 & V_b_2 = V_c_2 ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_dvd_OatLeastatMost__subset__iff,axiom, % 19.07/18.98 ! [V_d_2,V_c_2,V_b_2,V_a_2] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2,V_d_2))) % 19.07/18.98 <=> ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) % 19.07/18.98 | ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2),V_a_2)) % 19.07/18.98 & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_d_2)) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_dvd_OatLeastatMost__psubset__iff,axiom, % 19.07/18.98 ! [V_d_2,V_c_2,V_b_2,V_a_2] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2,V_d_2))) % 19.07/18.98 <=> ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) % 19.07/18.98 | ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2),V_a_2)) % 19.07/18.98 & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_d_2)) % 19.07/18.98 & ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2),V_a_2)) % 19.07/18.98 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_c_2)) ) % 19.07/18.98 | ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_d_2)) % 19.07/18.98 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_d_2),V_b_2)) ) ) ) ) % 19.07/18.98 & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2),V_d_2)) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_dvd_OgreaterThanAtMost__empty,axiom, % 19.07/18.98 ! [V_k_2,V_l_2] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2)) % 19.07/18.98 => c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_dvd_OatLeastLessThan__empty,axiom, % 19.07/18.98 ! [V_a_2,V_b_2] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2)) % 19.07/18.98 => c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_dvd_OgreaterThanAtMost__empty__iff,axiom, % 19.07/18.98 ! [V_l_2,V_k_2] : % 19.07/18.98 ( c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) % 19.07/18.98 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_l_2)) % 19.07/18.98 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2)) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_dvd_OatLeastLessThan__empty__iff,axiom, % 19.07/18.98 ! [V_b_2,V_a_2] : % 19.07/18.98 ( c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) % 19.07/18.98 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) % 19.07/18.98 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2)) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_dvd_OgreaterThanAtMost__empty__iff2,axiom, % 19.07/18.98 ! [V_l_2,V_k_2] : % 19.07/18.98 ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2,V_l_2) % 19.07/18.98 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_l_2)) % 19.07/18.98 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2)) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Inf__fin_Oremove,axiom, % 19.07/18.98 ! [V_x_2,V_A_2,T_b] : % 19.07/18.98 ( class_Lattices_Olattice(T_b) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.98 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = V_x_2 ) % 19.07/18.98 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Max_Oremove,axiom, % 19.07/18.98 ! [V_x_2,V_A_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.98 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2 ) % 19.07/18.98 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Min_Oremove,axiom, % 19.07/18.98 ! [V_x_2,V_A_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.98 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2 ) % 19.07/18.98 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_min__max_OSup__fin_Oremove,axiom, % 19.07/18.98 ! [V_x_2,V_A_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.98 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = V_x_2 ) % 19.07/18.98 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_minus__Min__eq__Max,axiom, % 19.07/18.98 ! [V_S_2,T_b] : % 19.07/18.98 ( class_Groups_Olinordered__ab__group__add(T_b) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 19.07/18.98 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_S_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),V_S_2)) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_minus__Max__eq__Min,axiom, % 19.07/18.98 ! [V_S_2,T_b] : % 19.07/18.98 ( class_Groups_Olinordered__ab__group__add(T_b) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 19.07/18.98 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_S_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),V_S_2)) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Max_Osingleton,axiom, % 19.07/18.98 ! [V_x_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Min_Osingleton,axiom, % 19.07/18.98 ! [V_x_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Inf__fin_Osingleton,axiom, % 19.07/18.98 ! [V_x_2,T_b] : % 19.07/18.98 ( class_Lattices_Olattice(T_b) % 19.07/18.98 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_min__max_OSup__fin_Oin__idem,axiom, % 19.07/18.98 ! [V_x_2,V_A_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.98 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Min__le,axiom, % 19.07/18.98 ! [V_x_2,V_A_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_x_2)) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Max__ge,axiom, % 19.07/18.98 ! [V_x_2,V_A_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2))) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_min__max_OSup__fin_Osingleton,axiom, % 19.07/18.98 ! [V_x_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Max__in,axiom, % 19.07/18.98 ! [V_A_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2)) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Min__in,axiom, % 19.07/18.98 ! [V_A_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2)) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_sup__Inf__absorb,axiom, % 19.07/18.98 ! [V_a_2,V_A_2,T_b] : % 19.07/18.98 ( class_Lattices_Olattice(T_b) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 19.07/18.98 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) = V_a_2 ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Inf__fin_Oin__idem,axiom, % 19.07/18.98 ! [V_x_2,V_A_2,T_b] : % 19.07/18.98 ( class_Lattices_Olattice(T_b) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.98 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Min_Oin__idem,axiom, % 19.07/18.98 ! [V_x_2,V_A_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.98 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Max_Oin__idem,axiom, % 19.07/18.98 ! [V_x_2,V_A_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.98 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_min__max_OSup__fin_Oinsert__idem,axiom, % 19.07/18.98 ! [V_x_2,V_A_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_min__max_OSup__fin_Osubset__idem,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 19.07/18.98 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_min__max_Oinf__Sup__absorb,axiom, % 19.07/18.98 ! [V_a_2,V_A_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 19.07/18.98 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_a_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) = V_a_2 ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_min__max_OSup__fin_Ounion__idem,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 19.07/18.98 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)) ) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Max__mono,axiom, % 19.07/18.98 ! [V_N_2,V_M_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2)) % 19.07/18.98 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 19.07/18.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_M_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_N_2))) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Min__antimono,axiom, % 19.07/18.98 ! [V_N_2,V_M_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2)) % 19.07/18.98 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 19.07/18.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_N_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_M_2))) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Inf__fin_Oinsert__idem,axiom, % 19.07/18.98 ! [V_x_2,V_A_2,T_b] : % 19.07/18.98 ( class_Lattices_Olattice(T_b) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Min__insert,axiom, % 19.07/18.98 ! [V_x_2,V_A_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Max__insert,axiom, % 19.07/18.98 ! [V_x_2,V_A_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Inf__fin_Osubset__idem,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,T_b] : % 19.07/18.98 ( class_Lattices_Olattice(T_b) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 19.07/18.98 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Min_Osubset__idem,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 19.07/18.98 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_B_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Max_Osubset__idem,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 19.07/18.98 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_B_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Inf__fin_Ounion__idem,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,T_b] : % 19.07/18.98 ( class_Lattices_Olattice(T_b) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 19.07/18.98 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)) ) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Min__Un,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 19.07/18.98 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_B_2)) ) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Max__Un,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 19.07/18.98 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_B_2)) ) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Inf__le__Sup,axiom, % 19.07/18.98 ! [V_A_2,T_b] : % 19.07/18.98 ( class_Lattices_Olattice(T_b) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2))) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_min__max_OSup__fin_Oinsert,axiom, % 19.07/18.98 ! [V_x_2,V_A_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_min__max_OSup__fin_Oinsert__remove,axiom, % 19.07/18.98 ! [V_x_2,V_A_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 ) % 19.07/18.98 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_min__max_OSup__fin_Ounion__inter,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 19.07/18.98 => ( 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)) % 19.07/18.98 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_min__max_OSup__fin_Ounion__disjoint,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 19.07/18.98 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => ( 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)) % 19.07/18.98 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)) ) ) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Inf__fin_Oinsert,axiom, % 19.07/18.98 ! [V_x_2,V_A_2,T_b] : % 19.07/18.98 ( class_Lattices_Olattice(T_b) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Min_Oinsert,axiom, % 19.07/18.98 ! [V_x_2,V_A_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Max_Oinsert,axiom, % 19.07/18.98 ! [V_x_2,V_A_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Inf__fin_Oinsert__remove,axiom, % 19.07/18.98 ! [V_x_2,V_A_2,T_b] : % 19.07/18.98 ( class_Lattices_Olattice(T_b) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 ) % 19.07/18.98 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Min_Oinsert__remove,axiom, % 19.07/18.98 ! [V_x_2,V_A_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 ) % 19.07/18.98 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Inf__fin_Ounion__inter,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,T_b] : % 19.07/18.98 ( class_Lattices_Olattice(T_b) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 19.07/18.98 => ( 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)) % 19.07/18.98 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Inf__fin_Ounion__disjoint,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,T_b] : % 19.07/18.98 ( class_Lattices_Olattice(T_b) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 19.07/18.98 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => ( 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)) % 19.07/18.98 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)) ) ) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Max_Oinsert__remove,axiom, % 19.07/18.98 ! [V_x_2,V_A_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 ) % 19.07/18.98 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Min_Ounion__disjoint,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 19.07/18.98 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => ( 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)) % 19.07/18.98 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_B_2)) ) ) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Min_Ounion__inter,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 19.07/18.98 => ( 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)) % 19.07/18.98 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_B_2)) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Max_Ounion__inter,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 19.07/18.98 => ( 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)) % 19.07/18.98 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_B_2)) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Max_Ounion__disjoint,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 19.07/18.98 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => ( 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)) % 19.07/18.98 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_B_2)) ) ) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_min__max_OSup__fin_Oclosed,axiom, % 19.07/18.98 ! [V_A_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) % 19.07/18.98 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),V_A_2)) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Max_Oclosed,axiom, % 19.07/18.98 ! [V_A_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) % 19.07/18.98 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2)) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Min_Oclosed,axiom, % 19.07/18.98 ! [V_A_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) % 19.07/18.98 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2)) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Inf__fin_Oclosed,axiom, % 19.07/18.98 ! [V_A_2,T_b] : % 19.07/18.98 ( class_Lattices_Olattice(T_b) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) % 19.07/18.98 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),V_A_2)) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_min__max_OInf__le__Sup,axiom, % 19.07/18.98 ! [V_A_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2))) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_min__max_OInf__fin_Oremove,axiom, % 19.07/18.98 ! [V_x_2,V_A_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.98 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = V_x_2 ) % 19.07/18.98 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_folding__one_Oclosed,axiom, % 19.07/18.98 ! [V_A_2,V_F_2,V_f_2,T_b] : % 19.07/18.98 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(V_f_2,B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) % 19.07/18.98 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_F_2,V_A_2)),V_A_2)) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_min__max_OInf__fin_Oin__idem,axiom, % 19.07/18.98 ! [V_x_2,V_A_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.98 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_min__max_OInf__fin_Osingleton,axiom, % 19.07/18.98 ! [V_x_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_min__max_OInf__fin_Oinsert__idem,axiom, % 19.07/18.98 ! [V_x_2,V_A_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_min__max_OInf__fin_Osubset__idem,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 19.07/18.98 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_min__max_Osup__Inf__absorb,axiom, % 19.07/18.98 ! [V_a_2,V_A_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 19.07/18.98 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) = V_a_2 ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_min__max_OInf__fin_Ounion__idem,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 19.07/18.98 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)) ) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_min__max_OInf__fin_Oinsert,axiom, % 19.07/18.98 ! [V_x_2,V_A_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_min__max_OInf__fin_Oinsert__remove,axiom, % 19.07/18.98 ! [V_x_2,V_A_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 ) % 19.07/18.98 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_min__max_OInf__fin_Ounion__disjoint,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 19.07/18.98 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => ( 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)) % 19.07/18.98 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)) ) ) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_min__max_OInf__fin_Ounion__inter,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 19.07/18.98 => ( 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)) % 19.07/18.98 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_min__max_OInf__fin_Oclosed,axiom, % 19.07/18.98 ! [V_A_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) % 19.07/18.98 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),V_A_2)) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_card__Diff__singleton__if,axiom, % 19.07/18.98 ! [V_x_2,V_A_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.98 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) % 19.07/18.98 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.98 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_card__Diff__singleton,axiom, % 19.07/18.98 ! [V_x_2,V_A_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.98 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J,axiom, % 19.07/18.98 ! [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)) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J,axiom, % 19.07/18.98 ! [V_A_2] : % 19.07/18.98 ( c_Nat__Transfer_Onat__set(V_A_2) % 19.07/18.98 => 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)) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_card_Oempty,axiom, % 19.07/18.98 ! [T_b] : hAPP(c_Finite__Set_Ocard(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 19.07/18.98 % 19.07/18.98 fof(fact_card__infinite,axiom, % 19.07/18.98 ! [V_A_2,T_b] : % 19.07/18.98 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_card__eq__0__iff,axiom, % 19.07/18.98 ! [V_A_2,T_b] : % 19.07/18.98 ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 19.07/18.98 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_card__ge__0__finite,axiom, % 19.07/18.98 ! [V_A_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) % 19.07/18.98 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_card__insert__le,axiom, % 19.07/18.98 ! [V_x_2,V_A_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)))) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_card__seteq,axiom, % 19.07/18.98 ! [V_A_2,V_B_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) % 19.07/18.98 => V_A_2 = V_B_2 ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_card__mono,axiom, % 19.07/18.98 ! [V_A_2,V_B_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 19.07/18.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_card__image__le,axiom, % 19.07/18.98 ! [V_f_2,T_c,V_A_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_psubset__card__mono,axiom, % 19.07/18.98 ! [V_A_2,V_B_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 19.07/18.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_card__insert__if,axiom, % 19.07/18.98 ! [V_x_2,V_A_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.98 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ) % 19.07/18.98 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.98 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_b),V_A_2)) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_card__insert__disjoint,axiom, % 19.07/18.98 ! [V_x_2,V_A_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.98 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_b),V_A_2)) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_card__gt__0__iff,axiom, % 19.07/18.98 ! [V_A_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) % 19.07/18.98 <=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_card_Ounion__inter,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 19.07/18.98 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_card__Un__Int,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 19.07/18.98 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_card__Diff__subset,axiom, % 19.07/18.98 ! [V_A_2,V_B_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 19.07/18.98 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_card__Diff__subset__Int,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 19.07/18.98 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_diff__card__le__card__Diff,axiom, % 19.07/18.98 ! [V_A_2,V_B_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 19.07/18.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_card__psubset,axiom, % 19.07/18.98 ! [V_A_2,V_B_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))) % 19.07/18.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_card__insert,axiom, % 19.07/18.98 ! [V_x_2,V_A_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_card__Un__disjoint,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 19.07/18.98 => ( 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)) % 19.07/18.98 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_card__Diff1__le,axiom, % 19.07/18.98 ! [V_x_2,V_A_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_card_Oinsert,axiom, % 19.07/18.98 ! [V_x_2,V_A_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.98 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_card__Suc__Diff1,axiom, % 19.07/18.98 ! [V_x_2,V_A_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.98 => hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_card__Diff1__less,axiom, % 19.07/18.98 ! [V_x_2,V_A_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_card__Diff2__less,axiom, % 19.07/18.98 ! [V_y_2,V_x_2,V_A_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 19.07/18.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_card__Diff__insert,axiom, % 19.07/18.98 ! [V_B_2,V_a_2,V_A_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 19.07/18.98 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2)) % 19.07/18.98 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_card_Oinsert__remove,axiom, % 19.07/18.98 ! [V_x_2,V_A_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_card_Oremove,axiom, % 19.07/18.98 ! [V_x_2,V_A_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.98 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_card_Ounion__inter__neutral,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 19.07/18.98 => ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 19.07/18.98 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 19.07/18.98 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_card__Suc__eq,axiom, % 19.07/18.98 ! [V_k_2,V_A_2,T_b] : % 19.07/18.98 ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Nat_OSuc,V_k_2) % 19.07/18.98 <=> ? [B_b,B_B] : % 19.07/18.98 ( V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),B_b),B_B) % 19.07/18.98 & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_b),B_B)) % 19.07/18.98 & hAPP(c_Finite__Set_Ocard(T_b),B_B) = V_k_2 % 19.07/18.98 & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 19.07/18.98 => B_B = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_equiv__imp__dvd__card,axiom, % 19.07/18.98 ! [V_k_2,V_r_2,V_A_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 19.07/18.98 => ( ! [B_x] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) % 19.07/18.98 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(T_b),B_x))) ) % 19.07/18.98 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_card__greaterThanLessThan__int,axiom, % 19.07/18.98 ! [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)))) ). % 19.07/18.98 % 19.07/18.98 fof(fact_card__Plus__conv__if,axiom, % 19.07/18.98 ! [V_B_2,T_c,V_A_2,T_b] : % 19.07/18.98 ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) % 19.07/18.98 => hAPP(c_Finite__Set_Ocard(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2)) ) % 19.07/18.98 & ( ~ ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) % 19.07/18.98 => hAPP(c_Finite__Set_Ocard(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_setprod__gen__delta,axiom, % 19.07/18.98 ! [V_c_2,V_b_2,V_a_2,V_S_2,T_b,T_c] : % 19.07/18.98 ( class_Groups_Ocomm__monoid__mult(T_c) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 19.07/18.98 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 19.07/18.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),V_c_2)),V_S_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_b_2,V_a_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_S_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) % 19.07/18.98 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 19.07/18.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),V_c_2)),V_S_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_c_2),hAPP(c_Finite__Set_Ocard(T_b),V_S_2)) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_finite__greaterThanLessThan__int,axiom, % 19.07/18.98 ! [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))) ). % 19.07/18.98 % 19.07/18.98 fof(fact_InrI,axiom, % 19.07/18.98 ! [V_A_2,T_c,V_B_2,V_b_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_B_2)) % 19.07/18.98 => hBOOL(hAPP(hAPP(c_member(tc_sum(T_c,T_b)),hAPP(c_Sum__Type_OInr(T_b,T_c),V_b_2)),c_Sum__Type_OPlus(T_c,T_b,V_A_2,V_B_2))) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_InlI,axiom, % 19.07/18.98 ! [V_B_2,T_c,V_A_2,V_a_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 19.07/18.98 => hBOOL(hAPP(hAPP(c_member(tc_sum(T_b,T_c)),hAPP(c_Sum__Type_OInl(T_b,T_c),V_a_2)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2))) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_setprod__timesf,axiom, % 19.07/18.98 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] : % 19.07/18.98 ( class_Groups_Ocomm__monoid__mult(T_b) % 19.07/18.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_g_2),V_A_2)) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_of__nat__setprod,axiom, % 19.07/18.98 ! [V_A_2,V_f_2,T_c,T_b] : % 19.07/18.98 ( ( class_Groups_Ocomm__monoid__mult(T_b) % 19.07/18.98 & class_Rings_Osemiring__1(T_b) ) % 19.07/18.98 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,T_c),c_Nat_Osemiring__1__class_Oof__nat(T_b)),V_f_2)),V_A_2) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_int__setprod,axiom, % 19.07/18.98 ! [V_A_2,V_f_2,T_b] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2) ). % 19.07/18.98 % 19.07/18.98 fof(fact_transfer__nat__int__sum__prod2_I2_J,axiom, % 19.07/18.98 ! [V_A_2,V_f_2,T_b] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2)) ). % 19.07/18.98 % 19.07/18.98 fof(fact_of__int__setprod,axiom, % 19.07/18.98 ! [V_A_2,V_f_2,T_c,T_b] : % 19.07/18.98 ( ( class_Groups_Ocomm__monoid__mult(T_b) % 19.07/18.98 & class_Rings_Oring__1(T_b) ) % 19.07/18.98 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,tc_Int_Oint),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_b,T_c),c_Int_Oring__1__class_Oof__int(T_b)),V_f_2)),V_A_2) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_setprod__1,axiom, % 19.07/18.98 ! [V_A_2,T_c,T_b] : % 19.07/18.98 ( class_Groups_Ocomm__monoid__mult(T_b) % 19.07/18.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(c_COMBK(T_b,T_c),c_Groups_Oone__class_Oone(T_b))),V_A_2) = c_Groups_Oone__class_Oone(T_b) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_abs__setprod,axiom, % 19.07/18.98 ! [V_A_2,V_f_2,T_c,T_b] : % 19.07/18.98 ( class_Fields_Olinordered__field(T_b) % 19.07/18.98 => hAPP(c_Groups_Oabs__class_Oabs(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_transfer__nat__int__sum__prod_I2_J,axiom, % 19.07/18.98 ! [V_A_2,V_f_2,T_b] : % 19.07/18.98 ( ( class_Groups_Ocomm__monoid__add(T_b) % 19.07/18.98 & class_Groups_Ocomm__monoid__mult(T_b) ) % 19.07/18.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),V_f_2),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_setprod__zero__iff,axiom, % 19.07/18.98 ! [V_f_2,V_A_2,T_b,T_c] : % 19.07/18.98 ( ( class_Rings_Ocomm__semiring__1(T_c) % 19.07/18.98 & class_Rings_Ono__zero__divisors(T_c) ) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c) % 19.07/18.98 <=> ? [B_x] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 19.07/18.98 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_setprod__zero,axiom, % 19.07/18.98 ! [V_f_2,V_A_2,T_b,T_c] : % 19.07/18.98 ( class_Rings_Ocomm__semiring__1(T_c) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( ? [B_x] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 19.07/18.98 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) % 19.07/18.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_setprod__empty,axiom, % 19.07/18.98 ! [V_f_2,T_c,T_b] : % 19.07/18.98 ( class_Groups_Ocomm__monoid__mult(T_b) % 19.07/18.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(T_b) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_setprod_Oempty,axiom, % 19.07/18.98 ! [V_g_2,T_c,T_b] : % 19.07/18.98 ( class_Groups_Ocomm__monoid__mult(T_b) % 19.07/18.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_g_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(T_b) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_setprod__infinite,axiom, % 19.07/18.98 ! [V_f_2,V_A_2,T_b,T_c] : % 19.07/18.98 ( class_Groups_Ocomm__monoid__mult(T_c) % 19.07/18.98 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2) = c_Groups_Oone__class_Oone(T_c) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_setprod_Oinfinite,axiom, % 19.07/18.98 ! [V_g_2,V_A_2,T_b,T_c] : % 19.07/18.98 ( class_Groups_Ocomm__monoid__mult(T_c) % 19.07/18.98 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = c_Groups_Oone__class_Oone(T_c) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_setprod__eq__1__iff,axiom, % 19.07/18.98 ! [V_f_2,V_F_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 19.07/18.98 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_F_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 19.07/18.98 <=> ! [B_x] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2)) % 19.07/18.98 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Plus__eq__empty__conv,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,T_c,T_b] : % 19.07/18.98 ( c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(T_b,T_c),tc_HOL_Obool)) % 19.07/18.98 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_finite__PlusD_I2_J,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,T_c,T_b] : % 19.07/18.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2))) % 19.07/18.98 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_finite__PlusD_I1_J,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,T_c,T_b] : % 19.07/18.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2))) % 19.07/18.98 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_finite__Plus,axiom, % 19.07/18.98 ! [V_B_2,T_c,V_A_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 19.07/18.98 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2))) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_finite__Plus__iff,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,T_c,T_b] : % 19.07/18.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2))) % 19.07/18.98 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_transfer__int__nat__sum__prod_I2_J,axiom, % 19.07/18.98 ! [V_f_2,V_A_2,T_b] : % 19.07/18.98 ( ( class_Groups_Ocomm__monoid__add(T_b) % 19.07/18.98 & class_Groups_Ocomm__monoid__mult(T_b) ) % 19.07/18.98 => ( c_Nat__Transfer_Onat__set(V_A_2) % 19.07/18.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_b,tc_Nat_Onat),V_f_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_setprod_Odistrib,axiom, % 19.07/18.98 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] : % 19.07/18.98 ( class_Groups_Ocomm__monoid__mult(T_c) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Groups_Otimes__class_Otimes(T_c)),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_h_2),V_A_2)) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_setprod__dividef,axiom, % 19.07/18.98 ! [V_g_2,V_f_2,V_A_2,T_b,T_c] : % 19.07/18.98 ( class_Fields_Ofield__inverse__zero(T_c) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Rings_Oinverse__class_Odivide(T_c)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_dvd__setprod,axiom, % 19.07/18.98 ! [V_f_2,V_i_2,V_A_2,T_b,T_c] : % 19.07/18.98 ( class_Rings_Ocomm__semiring__1(T_c) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2)) % 19.07/18.98 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),hAPP(V_f_2,V_i_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2))) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_setprod__pos__nat__iff,axiom, % 19.07/18.98 ! [V_f_2,V_S_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_S_2))) % 19.07/18.98 <=> ! [B_x] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) % 19.07/18.98 => 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))) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_setprod__dvd__setprod__subset,axiom, % 19.07/18.98 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] : % 19.07/18.98 ( ( class_Groups_Ocomm__monoid__mult(T_c) % 19.07/18.98 & class_Rings_Odvd(T_c) ) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 19.07/18.98 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_B_2))) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_greaterThanLessThan__empty,axiom, % 19.07/18.98 ! [V_k_2,V_l_2,T_b] : % 19.07/18.98 ( class_Orderings_Oorder(T_b) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2)) % 19.07/18.98 => c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_image__uminus__greaterThanLessThan,axiom, % 19.07/18.98 ! [V_y_2,V_x_2,T_b] : % 19.07/18.98 ( class_Groups_Oordered__ab__group__add(T_b) % 19.07/18.98 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_x_2,V_y_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_setprod__delta_H,axiom, % 19.07/18.98 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] : % 19.07/18.98 ( class_Groups_Ocomm__monoid__mult(T_c) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 19.07/18.98 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 19.07/18.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = hAPP(V_b_2,V_a_2) ) % 19.07/18.98 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 19.07/18.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = c_Groups_Oone__class_Oone(T_c) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_setprod__delta,axiom, % 19.07/18.98 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] : % 19.07/18.98 ( class_Groups_Ocomm__monoid__mult(T_c) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 19.07/18.98 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 19.07/18.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = hAPP(V_b_2,V_a_2) ) % 19.07/18.98 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 19.07/18.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = c_Groups_Oone__class_Oone(T_c) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_setprod__constant,axiom, % 19.07/18.98 ! [V_y_2,V_A_2,T_b,T_c] : % 19.07/18.98 ( class_Groups_Ocomm__monoid__mult(T_c) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(c_COMBK(T_c,T_b),V_y_2)),V_A_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_y_2),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_setprod__insert,axiom, % 19.07/18.98 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] : % 19.07/18.98 ( class_Groups_Ocomm__monoid__mult(T_c) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 19.07/18.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_setprod_Oinsert,axiom, % 19.07/18.98 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] : % 19.07/18.98 ( class_Groups_Ocomm__monoid__mult(T_c) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_setprod_Ounion__inter,axiom, % 19.07/18.98 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 19.07/18.98 ( class_Groups_Ocomm__monoid__mult(T_c) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 19.07/18.98 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2)) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_setprod__Un__Int,axiom, % 19.07/18.98 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 19.07/18.98 ( class_Groups_Ocomm__monoid__mult(T_c) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 19.07/18.98 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2)) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Plus__def,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,T_c,T_b] : c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_sum(T_b,T_c),tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,tc_sum(T_b,T_c),c_Sum__Type_OInl(T_b,T_c)),V_A_2)),hAPP(c_Set_Oimage(T_c,tc_sum(T_b,T_c),c_Sum__Type_OInr(T_c,T_b)),V_B_2)) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Int__greaterThanLessThan,axiom, % 19.07/18.98 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_setprod_Oinsert__remove,axiom, % 19.07/18.98 ! [V_x_2,V_g_2,V_A_2,T_b,T_c] : % 19.07/18.98 ( class_Groups_Ocomm__monoid__mult(T_c) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_setprod_Ounion__disjoint,axiom, % 19.07/18.98 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 19.07/18.98 ( class_Groups_Ocomm__monoid__mult(T_c) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 19.07/18.98 => ( 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)) % 19.07/18.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2)) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_setprod__Un__disjoint,axiom, % 19.07/18.98 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 19.07/18.98 ( class_Groups_Ocomm__monoid__mult(T_c) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 19.07/18.98 => ( 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)) % 19.07/18.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2)) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_card__Plus,axiom, % 19.07/18.98 ! [V_B_2,T_c,V_A_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 19.07/18.98 => hAPP(c_Finite__Set_Ocard(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2)) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_setprod_Oremove,axiom, % 19.07/18.98 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] : % 19.07/18.98 ( class_Groups_Ocomm__monoid__mult(T_c) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_setprod__diff1,axiom, % 19.07/18.98 ! [V_a_2,V_f_2,V_A_2,T_b,T_c] : % 19.07/18.98 ( class_Fields_Ofield(T_c) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( hAPP(V_f_2,V_a_2) != c_Groups_Ozero__class_Ozero(T_c) % 19.07/18.98 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 19.07/18.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) ) % 19.07/18.98 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 19.07/18.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2) ) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_setprod__Un,axiom, % 19.07/18.98 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] : % 19.07/18.98 ( class_Fields_Ofield(T_c) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 19.07/18.98 => ( ! [B_x] : % 19.07/18.98 ( 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))) % 19.07/18.98 => hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_c) ) % 19.07/18.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_setprod_Ounion__inter__neutral,axiom, % 19.07/18.98 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 19.07/18.98 ( class_Groups_Ocomm__monoid__mult(T_c) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 19.07/18.98 => ( ! [B_x] : % 19.07/18.98 ( 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))) % 19.07/18.98 => hAPP(V_g_2,B_x) = c_Groups_Oone__class_Oone(T_c) ) % 19.07/18.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2)) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_setprod__Un__one,axiom, % 19.07/18.98 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] : % 19.07/18.98 ( class_Groups_Ocomm__monoid__mult(T_c) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 19.07/18.98 => ( ! [B_x] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))) % 19.07/18.98 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) ) % 19.07/18.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_S_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_T_2)) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_finite__greaterThanLessThan,axiom, % 19.07/18.98 ! [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))) ). % 19.07/18.98 % 19.07/18.98 fof(fact_card__greaterThanLessThan,axiom, % 19.07/18.98 ! [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)) ). % 19.07/18.98 % 19.07/18.98 fof(fact_transfer__int__nat__sum__prod2_I2_J,axiom, % 19.07/18.98 ! [V_f_2,V_A_2,T_b] : % 19.07/18.98 ( ! [B_x] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 19.07/18.98 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) ) % 19.07/18.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Int_Oint),V_f_2),V_A_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,T_b),c_Int_Onat),V_f_2)),V_A_2)) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_ivl__disj__un_I4_J,axiom, % 19.07/18.98 ! [V_u_2,V_l_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2)) % 19.07/18.98 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_quotient__def,axiom, % 19.07/18.98 ! [V_r_2,V_A_2,T_b] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),T_b),c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),c_Relation_OImage(T_b,T_b,V_r_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)))) ). % 19.07/18.98 % 19.07/18.98 fof(fact_finite__greaterThanAtMost,axiom, % 19.07/18.98 ! [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))) ). % 19.07/18.98 % 19.07/18.98 fof(fact_finite__greaterThanAtMost__int,axiom, % 19.07/18.98 ! [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))) ). % 19.07/18.98 % 19.07/18.98 fof(fact_SUP1__I,axiom, % 19.07/18.98 ! [T_c,V_b_2,V_B_2,V_A_2,V_a_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) % 19.07/18.98 => hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_finite__UN,axiom, % 19.07/18.98 ! [V_B_2,T_c,V_A_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) % 19.07/18.98 <=> ! [B_x] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 19.07/18.98 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Image__UN,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,T_d,V_r_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Relation_OImage(T_c,T_b,V_r_2)),V_B_2)) ). % 19.07/18.98 % 19.07/18.98 fof(fact_SUP1__iff,axiom, % 19.07/18.98 ! [V_b_2,V_B_2,V_A_2,T_c,T_b] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) % 19.07/18.98 <=> ? [B_x] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 19.07/18.98 & hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_greaterThanAtMost__empty,axiom, % 19.07/18.98 ! [V_k_2,V_l_2,T_b] : % 19.07/18.98 ( class_Orderings_Oorder(T_b) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2)) % 19.07/18.98 => c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_greaterThanAtMost__empty__iff2,axiom, % 19.07/18.98 ! [V_l_2,V_k_2,T_b] : % 19.07/18.98 ( class_Orderings_Oorder(T_b) % 19.07/18.98 => ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_k_2,V_l_2) % 19.07/18.98 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_greaterThanAtMost__empty__iff,axiom, % 19.07/18.98 ! [V_l_2,V_k_2,T_b] : % 19.07/18.98 ( class_Orderings_Oorder(T_b) % 19.07/18.98 => ( c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_ivl__disj__un_I20_J,axiom, % 19.07/18.98 ! [V_u_2,V_m_2,V_l_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2)) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2)) % 19.07/18.98 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_ivl__disj__int_I14_J,axiom, % 19.07/18.98 ! [V_u_2,V_m_2,V_l_2,T_b] : % 19.07/18.98 ( class_Orderings_Oorder(T_b) % 19.07/18.98 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_card__greaterThanAtMost,axiom, % 19.07/18.98 ! [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) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Image__eq__UN,axiom, % 19.07/18.98 ! [V_B_2,V_r_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Relation_OImage(T_c,T_b,V_r_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),c_Set_Oinsert(T_c)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Int__greaterThanAtMost,axiom, % 19.07/18.98 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_ivl__disj__int_I10_J,axiom, % 19.07/18.98 ! [V_u_2,V_m_2,V_l_2,T_b] : % 19.07/18.98 ( class_Orderings_Oorder(T_b) % 19.07/18.98 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_card__greaterThanAtMost__int,axiom, % 19.07/18.98 ! [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)) ). % 19.07/18.98 % 19.07/18.98 fof(fact_ivl__disj__un_I16_J,axiom, % 19.07/18.98 ! [V_u_2,V_m_2,V_l_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2)) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2)) % 19.07/18.98 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_UN__I,axiom, % 19.07/18.98 ! [V_B_2,V_b_2,T_c,V_A_2,V_a_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) % 19.07/18.98 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_image__eq__UN,axiom, % 19.07/18.98 ! [V_A_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Set_Oinsert(T_b)),V_f_2)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ). % 19.07/18.98 % 19.07/18.98 fof(fact_UN__equiv__class2,axiom, % 19.07/18.98 ! [V_a2_2,V_a1_2,V_f_2,T_d,V_r2_2,V_A2_2,T_c,V_r1_2,V_A1_2,T_b] : % 19.07/18.98 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2) % 19.07/18.98 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2) % 19.07/18.98 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a1_2),V_A1_2)) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a2_2),V_A2_2)) % 19.07/18.98 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r1_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_c,V_r2_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a2_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))),V_f_2)) = hAPP(hAPP(V_f_2,V_a1_2),V_a2_2) ) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_ball__UN,axiom, % 19.07/18.98 ! [V_Pa_2,V_B_2,V_A_2,T_c,T_b] : % 19.07/18.98 ( ! [B_x] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 19.07/18.98 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 19.07/18.98 <=> ! [B_x] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 19.07/18.98 => ! [B_xa] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(V_B_2,B_x))) % 19.07/18.98 => hBOOL(hAPP(V_Pa_2,B_xa)) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_SUP__commute,axiom, % 19.07/18.98 ! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] : % 19.07/18.98 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 19.07/18.98 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),T_b,T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,T_b),V_B_2)),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,T_b),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),T_b,T_d),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2)),hAPP(c_COMBC(T_c,T_d,T_b),V_f_2))) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_UN__UN__flatten,axiom, % 19.07/18.98 ! [V_C_2,V_B_2,V_A_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_d),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)) ). % 19.07/18.98 % 19.07/18.98 fof(fact_UN__simps_I9_J,axiom, % 19.07/18.98 ! [V_C_2,V_B_2,V_A_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_d),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)) ). % 19.07/18.98 % 19.07/18.98 fof(fact_UN__extend__simps_I9_J,axiom, % 19.07/18.98 ! [V_C_2,V_B_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) ). % 19.07/18.98 % 19.07/18.98 fof(fact_congruent2D,axiom, % 19.07/18.98 ! [V_z2_2,V_y2_2,V_z1_2,V_y1_2,V_f_2,V_r2_2,V_r1_2,T_d,T_c,T_b] : % 19.07/18.98 ( c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y1_2),V_z1_2)),V_r1_2)) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_y2_2),V_z2_2)),V_r2_2)) % 19.07/18.98 => hAPP(hAPP(V_f_2,V_y1_2),V_y2_2) = hAPP(hAPP(V_f_2,V_z1_2),V_z2_2) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_SUP__le__iff,axiom, % 19.07/18.98 ! [V_u_2,V_M_2,V_A_2,T_c,T_b] : % 19.07/18.98 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),V_M_2)),V_u_2)) % 19.07/18.98 <=> ! [B_x] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 19.07/18.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_M_2,B_x)),V_u_2)) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_less__SUP__iff,axiom, % 19.07/18.98 ! [V_f_2,V_A_2,T_c,V_a_2,T_b] : % 19.07/18.98 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 19.07/18.98 & class_Orderings_Olinorder(T_b) ) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),V_f_2))) % 19.07/18.98 <=> ? [B_x] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 19.07/18.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(V_f_2,B_x))) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_UN__iff,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,T_c,V_b_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 19.07/18.98 <=> ? [B_x] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 19.07/18.98 & hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x))) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_SUP__const,axiom, % 19.07/18.98 ! [V_M_2,T_b,V_A_2,T_c] : % 19.07/18.98 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 19.07/18.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),hAPP(c_COMBK(T_c,T_b),V_M_2)) = V_M_2 ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_UNION__empty__conv_I1_J,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,T_c,T_b] : % 19.07/18.98 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) % 19.07/18.98 <=> ! [B_x] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 19.07/18.98 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_UN__empty2,axiom, % 19.07/18.98 ! [V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 19.07/18.98 % 19.07/18.98 fof(fact_UN__constant,axiom, % 19.07/18.98 ! [V_c_2,T_c,T_b,V_A_2] : % 19.07/18.98 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_c_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) % 19.07/18.98 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_c_2)) = V_c_2 ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_UNION__empty__conv_I2_J,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,T_b,T_c] : % 19.07/18.98 ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 <=> ! [B_x] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 19.07/18.98 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_UN__subset__iff,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,V_I_2,T_c,T_b] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),V_B_2)) % 19.07/18.98 <=> ! [B_x] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2)) % 19.07/18.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_A_2,B_x)),V_B_2)) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_UN__simps_I10_J,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,V_f_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_b,tc_HOL_Obool),T_d),V_B_2),V_f_2)) ). % 19.07/18.98 % 19.07/18.98 fof(fact_image__UN,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,T_d,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Set_Oimage(T_c,T_b,V_f_2)),V_B_2)) ). % 19.07/18.98 % 19.07/18.98 fof(fact_UN__extend__simps_I10_J,axiom, % 19.07/18.98 ! [V_f_2,V_B_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),V_B_2) ). % 19.07/18.98 % 19.07/18.98 fof(fact_UN__Un__distrib,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,V_I_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_B_2)) ). % 19.07/18.98 % 19.07/18.98 fof(fact_UN__Un,axiom, % 19.07/18.98 ! [V_M_2,V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_M_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_M_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_M_2)) ). % 19.07/18.98 % 19.07/18.98 fof(fact_UN__simps_I5_J,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ). % 19.07/18.98 % 19.07/18.98 fof(fact_UN__simps_I4_J,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ). % 19.07/18.98 % 19.07/18.98 fof(fact_UN__extend__simps_I5_J,axiom, % 19.07/18.98 ! [V_B_2,V_C_2,T_c,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Int__UN__distrib,axiom, % 19.07/18.98 ! [V_A_2,V_I_2,T_c,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),V_A_2)) ). % 19.07/18.98 % 19.07/18.98 fof(fact_UN__extend__simps_I4_J,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,V_C_2,T_c,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Int__UN__distrib2,axiom, % 19.07/18.98 ! [V_B_2,V_J_2,T_d,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_J_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_J_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool))),T_c),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2))),V_B_2))) ). % 19.07/18.98 % 19.07/18.98 fof(fact_SUPR__apply,axiom, % 19.07/18.98 ! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] : % 19.07/18.98 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 19.07/18.98 => hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,T_b)),V_A_2),V_f_2),V_x_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),hAPP(hAPP(c_COMBC(T_c,T_d,T_b),V_f_2),V_x_2)) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_UN__simps_I6_J,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ). % 19.07/18.98 % 19.07/18.98 fof(fact_UN__extend__simps_I6_J,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,V_C_2,T_c,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) ). % 19.07/18.98 % 19.07/18.98 fof(fact_SUP__subset,axiom, % 19.07/18.98 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] : % 19.07/18.98 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 19.07/18.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_B_2),V_f_2))) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_le__SUPI,axiom, % 19.07/18.98 ! [V_M_2,V_A_2,V_i_2,T_b,T_c] : % 19.07/18.98 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2)) % 19.07/18.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_M_2,V_i_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),V_M_2))) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_UN__insert__distrib,axiom, % 19.07/18.98 ! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2)) % 19.07/18.98 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_UN__upper,axiom, % 19.07/18.98 ! [V_B_2,T_c,V_A_2,V_a_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 19.07/18.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_UN__absorb,axiom, % 19.07/18.98 ! [V_A_2,T_c,V_I_2,V_k_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2)) % 19.07/18.98 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_A_2,V_k_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_UN__extend__simps_I1_J,axiom, % 19.07/18.98 ! [V_B_2,V_a_2,T_c,T_b,V_C_2] : % 19.07/18.98 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) ) % 19.07/18.98 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_UN__singleton,axiom, % 19.07/18.98 ! [V_A_2,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_A_2 ). % 19.07/18.98 % 19.07/18.98 fof(fact_UN__simps_I1_J,axiom, % 19.07/18.98 ! [V_B_2,V_a_2,T_c,T_b,V_C_2] : % 19.07/18.98 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) % 19.07/18.98 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_UN__extend__simps_I2_J,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 19.07/18.98 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = V_B_2 ) % 19.07/18.98 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_UN__extend__simps_I3_J,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 19.07/18.98 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2 ) % 19.07/18.98 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_UN__simps_I2_J,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 19.07/18.98 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) % 19.07/18.98 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_UN__simps_I3_J,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 19.07/18.98 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) % 19.07/18.98 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_UN__insert,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,V_a_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ). % 19.07/18.98 % 19.07/18.98 fof(fact_congruent2__implies__congruent__UN,axiom, % 19.07/18.98 ! [V_a_2,V_f_2,T_d,V_r2_2,V_A2_2,T_c,V_r1_2,V_A1_2,T_b] : % 19.07/18.98 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2) % 19.07/18.98 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2) % 19.07/18.98 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A2_2)) % 19.07/18.98 => c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_d,tc_HOL_Obool),V_r1_2,hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_c,V_r2_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))),V_f_2)) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_minus__int__def,axiom, % 19.07/18.98 ! [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))))))) ). % 19.07/18.98 % 19.07/18.98 fof(fact_UN__equiv__class,axiom, % 19.07/18.98 ! [V_a_2,V_f_2,T_c,V_r_2,V_A_2,T_b] : % 19.07/18.98 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 19.07/18.98 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 19.07/18.98 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_f_2) = hAPP(V_f_2,V_a_2) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_SUP2__I,axiom, % 19.07/18.98 ! [T_d,T_c,V_c_2,V_b_2,V_B_2,V_A_2,V_a_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2)) % 19.07/18.98 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Rep__Integ__inject,axiom, % 19.07/18.98 ! [V_y_2,V_x_2] : % 19.07/18.98 ( hAPP(c_Int_ORep__Integ,V_x_2) = hAPP(c_Int_ORep__Integ,V_y_2) % 19.07/18.98 <=> V_x_2 = V_y_2 ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Rep__Integ__inverse,axiom, % 19.07/18.98 ! [V_x_2] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,V_x_2)) = V_x_2 ). % 19.07/18.98 % 19.07/18.98 fof(fact_congruentD,axiom, % 19.07/18.98 ! [V_z_2,V_y_2,V_f_2,V_r_2,T_c,T_b] : % 19.07/18.98 ( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),V_r_2)) % 19.07/18.98 => hAPP(V_f_2,V_y_2) = hAPP(V_f_2,V_z_2) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_nat__def,axiom, % 19.07/18.98 ! [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)))))) ). % 19.07/18.98 % 19.07/18.98 fof(fact_congruent2__implies__congruent,axiom, % 19.07/18.98 ! [V_a_2,V_f_2,V_r2_2,T_d,T_c,V_r1_2,V_A_2,T_b] : % 19.07/18.98 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r1_2) % 19.07/18.98 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 19.07/18.98 => c_Equiv__Relations_Ocongruent(T_c,T_d,V_r2_2,hAPP(V_f_2,V_a_2)) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_UN__equiv__class__inject,axiom, % 19.07/18.98 ! [V_Y_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] : % 19.07/18.98 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 19.07/18.98 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2) % 19.07/18.98 => ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_X_2),V_f_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_Y_2),V_f_2) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) % 19.07/18.98 => ( ! [B_x] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 19.07/18.98 => ! [B_y] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2)) % 19.07/18.98 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) % 19.07/18.98 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2)) ) ) ) % 19.07/18.98 => V_X_2 = V_Y_2 ) ) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_UN__equiv__class__type2,axiom, % 19.07/18.98 ! [V_B_2,V_X2_2,V_X1_2,V_f_2,T_d,V_r2_2,V_A2_2,T_c,V_r1_2,V_A1_2,T_b] : % 19.07/18.98 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2) % 19.07/18.98 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2) % 19.07/18.98 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X1_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A1_2),V_r1_2))) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_X2_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A2_2),V_r2_2))) % 19.07/18.98 => ( ! [B_x1] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x1),V_A1_2)) % 19.07/18.98 => ! [B_x2] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x2),V_A2_2)) % 19.07/18.98 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(V_f_2,B_x1),B_x2)),V_B_2)) ) ) % 19.07/18.98 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_d,tc_HOL_Obool)),V_X1_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_X2_2)),V_f_2))),V_B_2)) ) ) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_UN__equiv__class__type,axiom, % 19.07/18.98 ! [V_B_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] : % 19.07/18.98 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 19.07/18.98 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) % 19.07/18.98 => ( ! [B_x] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 19.07/18.98 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,B_x)),V_B_2)) ) % 19.07/18.98 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_X_2),V_f_2)),V_B_2)) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_SUP2__iff,axiom, % 19.07/18.98 ! [V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) % 19.07/18.98 <=> ? [B_x] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 19.07/18.98 & hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Id__on__def,axiom, % 19.07/18.98 ! [V_A_2,T_b] : c_Relation_OId__on(T_b,V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),T_b),c_Set_Oinsert(tc_prod(T_b,T_b))),hAPP(hAPP(c_COMBS(T_b,T_b,tc_prod(T_b,T_b)),c_Product__Type_OPair(T_b,T_b)),c_COMBI(T_b)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)))) ). % 19.07/18.98 % 19.07/18.98 fof(fact_fold__Un__disjoint,axiom, % 19.07/18.98 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 19.07/18.98 ( class_Groups_Ocomm__monoid__mult(T_c) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 19.07/18.98 => ( 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)) % 19.07/18.98 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_B_2)) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_min__max_OSup__fin_Ohom__commute,axiom, % 19.07/18.98 ! [V_N_2,V_h_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y)) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 19.07/18.98 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => hAPP(V_h_2,c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_N_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_fold__image__empty,axiom, % 19.07/18.98 ! [V_z_2,V_g_2,V_f_2,T_c,T_b] : hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2 ). % 19.07/18.98 % 19.07/18.98 fof(fact_Id__on__def_H,axiom, % 19.07/18.98 ! [V_A_2,T_b] : c_Relation_OId__on(T_b,V_A_2) = hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),c_fequal))),V_A_2)) ). % 19.07/18.98 % 19.07/18.98 fof(fact_folding__image__simple_Oeq__fold__g,axiom, % 19.07/18.98 ! [V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 19.07/18.98 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 19.07/18.98 => hAPP(V_F_2,V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),V_A_2) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Id__on__empty,axiom, % 19.07/18.98 ! [T_b] : c_Relation_OId__on(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Image__Id__on,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,T_b] : hAPP(c_Relation_OImage(T_b,T_b,c_Relation_OId__on(T_b,V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ). % 19.07/18.98 % 19.07/18.98 fof(fact_fold__image__distrib,axiom, % 19.07/18.98 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] : % 19.07/18.98 ( class_Groups_Ocomm__monoid__mult(T_c) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Groups_Otimes__class_Otimes(T_c)),V_g_2)),V_h_2)),c_Groups_Oone__class_Oone(T_c)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_h_2),c_Groups_Oone__class_Oone(T_c)),V_A_2)) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_fold__image__insert,axiom, % 19.07/18.98 ! [V_z_2,V_g_2,V_a_2,V_A_2,T_b,T_c] : % 19.07/18.98 ( class_Groups_Oab__semigroup__mult(T_c) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 19.07/18.98 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_a_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),V_z_2),V_A_2)) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_setprod_OF__eq,axiom, % 19.07/18.98 ! [V_g_2,V_A_2,T_b,T_c] : % 19.07/18.98 ( class_Groups_Ocomm__monoid__mult(T_c) % 19.07/18.98 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2) ) % 19.07/18.98 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = c_Groups_Oone__class_Oone(T_c) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_setprod_Oeq__fold,axiom, % 19.07/18.98 ! [V_g_2,V_A_2,T_b,T_c] : % 19.07/18.98 ( class_Groups_Ocomm__monoid__mult(T_c) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Id__on__iff,axiom, % 19.07/18.98 ! [V_A_2,V_y_2,V_x_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Relation_OId__on(T_b,V_A_2))) % 19.07/18.98 <=> ( V_x_2 = V_y_2 % 19.07/18.98 & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Id__on__eqI,axiom, % 19.07/18.98 ! [V_A_2,T_b,V_b_2,V_a_2] : % 19.07/18.98 ( V_a_2 = V_b_2 % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 19.07/18.98 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Relation_OId__on(T_b,V_A_2))) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_fold__image__Un__Int,axiom, % 19.07/18.98 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 19.07/18.98 ( class_Groups_Ocomm__monoid__mult(T_c) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 19.07/18.98 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_image__eq__fold__image,axiom, % 19.07/18.98 ! [V_f_2,T_c,V_A_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(T_c,tc_HOL_Obool),T_b,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Set_Oinsert(T_c)),V_f_2)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),V_A_2) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_card__def,axiom, % 19.07/18.98 ! [V_A_2,T_b] : % 19.07/18.98 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,T_b,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,T_b),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2) ) % 19.07/18.98 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_card_Oeq__fold__g,axiom, % 19.07/18.98 ! [V_A_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,T_b,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,T_b),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_comm__monoid__big_OF__eq,axiom, % 19.07/18.98 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] : % 19.07/18.98 ( c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2) % 19.07/18.98 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 19.07/18.98 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),V_A_2) ) % 19.07/18.98 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 19.07/18.98 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_fold__image__Un__one,axiom, % 19.07/18.98 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] : % 19.07/18.98 ( class_Groups_Ocomm__monoid__mult(T_c) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 19.07/18.98 => ( ! [B_x] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))) % 19.07/18.98 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) ) % 19.07/18.98 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_f_2),c_Groups_Oone__class_Oone(T_c)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_f_2),c_Groups_Oone__class_Oone(T_c)),V_S_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_f_2),c_Groups_Oone__class_Oone(T_c)),V_T_2)) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Id__onE,axiom, % 19.07/18.98 ! [V_A_2,V_c_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_c_2),c_Relation_OId__on(T_b,V_A_2))) % 19.07/18.98 => ~ ! [B_x] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 19.07/18.98 => V_c_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_comm__monoid__big_Oinfinite,axiom, % 19.07/18.98 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] : % 19.07/18.98 ( c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2) % 19.07/18.98 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 19.07/18.98 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_min__max_OInf__fin_Ohom__commute,axiom, % 19.07/18.98 ! [V_N_2,V_h_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y)) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 19.07/18.98 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => hAPP(V_h_2,c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_N_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Max_Ohom__commute,axiom, % 19.07/18.98 ! [V_N_2,V_h_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y)) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 19.07/18.98 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => hAPP(V_h_2,c_Big__Operators_Olinorder__class_OMax(T_b,V_N_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Min_Ohom__commute,axiom, % 19.07/18.98 ! [V_N_2,V_h_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y)) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 19.07/18.98 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => hAPP(V_h_2,c_Big__Operators_Olinorder__class_OMin(T_b,V_N_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Inf__fin_Ohom__commute,axiom, % 19.07/18.98 ! [V_N_2,V_h_2,T_b] : % 19.07/18.98 ( class_Lattices_Olattice(T_b) % 19.07/18.98 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),B_x),B_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y)) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 19.07/18.98 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => hAPP(V_h_2,c_Big__Operators_Olattice__class_OInf__fin(T_b,V_N_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Sup__fin_Ohom__commute,axiom, % 19.07/18.98 ! [V_N_2,V_h_2,T_b] : % 19.07/18.98 ( class_Lattices_Olattice(T_b) % 19.07/18.98 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),B_x),B_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y)) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 19.07/18.98 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => hAPP(V_h_2,c_Big__Operators_Olattice__class_OSup__fin(T_b,V_N_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_setprod__mono__one__right,axiom, % 19.07/18.98 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] : % 19.07/18.98 ( class_Groups_Ocomm__monoid__mult(T_c) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) % 19.07/18.98 => ( ! [B_x] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2))) % 19.07/18.98 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) ) % 19.07/18.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_T_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_S_2) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_setprod__mono__one__left,axiom, % 19.07/18.98 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] : % 19.07/18.98 ( class_Groups_Ocomm__monoid__mult(T_c) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) % 19.07/18.98 => ( ! [B_x] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2))) % 19.07/18.98 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) ) % 19.07/18.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_T_2) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_card__Pow,axiom, % 19.07/18.98 ! [V_A_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => hAPP(c_Finite__Set_Ocard(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_finite__empty__induct,axiom, % 19.07/18.98 ! [V_Pa_2,V_A_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( hBOOL(hAPP(V_Pa_2,V_A_2)) % 19.07/18.98 => ( ! [B_a,B_A] : % 19.07/18.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_A)) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) % 19.07/18.98 => ( hBOOL(hAPP(V_Pa_2,B_A)) % 19.07/18.98 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),B_A),hAPP(hAPP(c_Set_Oinsert(T_b),B_a),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) % 19.07/18.98 => hBOOL(hAPP(V_Pa_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_PowI,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 19.07/18.98 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2))) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Pow__not__empty,axiom, % 19.07/18.98 ! [V_A_2,T_b] : hAPP(c_Set_OPow(T_b),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) ). % 19.07/18.98 % 19.07/18.98 fof(fact_finite__Pow__iff,axiom, % 19.07/18.98 ! [V_A_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2))) % 19.07/18.98 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_image__Pow__surj,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,V_f_2,T_b,T_c] : % 19.07/18.98 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_B_2 % 19.07/18.98 => hAPP(c_Set_Oimage(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_c,T_b,V_f_2)),hAPP(c_Set_OPow(T_c),V_A_2)) = hAPP(c_Set_OPow(T_b),V_B_2) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Un__Pow__subset,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)),hAPP(c_Set_OPow(T_b),V_B_2))),hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Pow__top,axiom, % 19.07/18.98 ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_A_2))) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Pow__insert,axiom, % 19.07/18.98 ! [V_A_2,V_a_2,T_b] : hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)),hAPP(c_Set_Oimage(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oinsert(T_b),V_a_2)),hAPP(c_Set_OPow(T_b),V_A_2))) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Pow__Int__eq,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,T_b] : hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)),hAPP(c_Set_OPow(T_b),V_B_2)) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Pow__mono,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 19.07/18.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)),hAPP(c_Set_OPow(T_b),V_B_2))) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Pow__bottom,axiom, % 19.07/18.98 ! [V_B_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),hAPP(c_Set_OPow(T_b),V_B_2))) ). % 19.07/18.98 % 19.07/18.98 fof(fact_image__Pow__mono,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),V_B_2)) % 19.07/18.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_c,T_b,V_f_2)),hAPP(c_Set_OPow(T_c),V_A_2))),hAPP(c_Set_OPow(T_b),V_B_2))) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_PowD,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2))) % 19.07/18.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Pow__iff,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2))) % 19.07/18.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_UN__Pow__subset,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_c),c_Set_OPow(T_b)),V_B_2))),hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Pow__empty,axiom, % 19.07/18.98 ! [T_b] : hAPP(c_Set_OPow(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Powp__Pow__eq,axiom, % 19.07/18.98 ! [V_x_2,V_A_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(c_Predicate_OPowp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)),V_x_2)) % 19.07/18.98 <=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),hAPP(c_Set_OPow(T_b),V_A_2))) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_card__quotient__disjoint,axiom, % 19.07/18.98 ! [V_r_2,V_A_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( c_Fun_Oinj__on(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),T_b),c_Equiv__Relations_Oquotient(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_r_2),V_A_2) % 19.07/18.98 => hAPP(c_Finite__Set_Ocard(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_ivl__disj__un_I19_J,axiom, % 19.07/18.98 ! [V_u_2,V_m_2,V_l_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2)) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2)) % 19.07/18.98 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_finite__atLeastAtMost,axiom, % 19.07/18.98 ! [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))) ). % 19.07/18.98 % 19.07/18.98 fof(fact_finite__atLeastAtMost__int,axiom, % 19.07/18.98 ! [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))) ). % 19.07/18.98 % 19.07/18.98 fof(fact_image__Suc__atLeastAtMost,axiom, % 19.07/18.98 ! [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)) ). % 19.07/18.98 % 19.07/18.98 fof(fact_image__add__atLeastAtMost,axiom, % 19.07/18.98 ! [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)) ). % 19.07/18.98 % 19.07/18.98 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I2_J,axiom, % 19.07/18.98 ! [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))) ). % 19.07/18.98 % 19.07/18.98 fof(fact_finite__imageD,axiom, % 19.07/18.98 ! [V_A_2,V_f_2,T_c,T_b] : % 19.07/18.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) % 19.07/18.98 => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2) % 19.07/18.98 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_card__image,axiom, % 19.07/18.98 ! [V_A_2,V_f_2,T_c,T_b] : % 19.07/18.98 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 19.07/18.98 => hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_SetInterval_Otransfer__int__nat__set__functions,axiom, % 19.07/18.98 ! [V_n_2,V_m_2] : % 19.07/18.98 ( c_Nat__Transfer_Ois__nat(V_m_2) % 19.07/18.98 => ( c_Nat__Transfer_Ois__nat(V_n_2) % 19.07/18.98 => 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))) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_SetInterval_Otransfer__int__nat__set__function__closures,axiom, % 19.07/18.98 ! [V_y_2,V_x_2] : % 19.07/18.98 ( c_Nat__Transfer_Ois__nat(V_x_2) % 19.07/18.98 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_atLeastatMost__empty__iff,axiom, % 19.07/18.98 ! [V_b_2,V_a_2,T_b] : % 19.07/18.98 ( class_Orderings_Oorder(T_b) % 19.07/18.98 => ( c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_atLeastatMost__empty__iff2,axiom, % 19.07/18.98 ! [V_b_2,V_a_2,T_b] : % 19.07/18.98 ( class_Orderings_Oorder(T_b) % 19.07/18.98 => ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) % 19.07/18.98 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_atLeastatMost__empty,axiom, % 19.07/18.98 ! [V_a_2,V_b_2,T_b] : % 19.07/18.98 ( class_Orderings_Oorder(T_b) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) % 19.07/18.98 => c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_atLeastatMost__subset__iff,axiom, % 19.07/18.98 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] : % 19.07/18.98 ( class_Orderings_Oorder(T_b) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2))) % 19.07/18.98 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) % 19.07/18.98 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2)) % 19.07/18.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2)) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_atLeastAtMost__singleton,axiom, % 19.07/18.98 ! [V_a_2,T_b] : % 19.07/18.98 ( class_Orderings_Oorder(T_b) % 19.07/18.98 => c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_a_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_atLeastAtMost__singleton__iff,axiom, % 19.07/18.98 ! [V_c_2,V_b_2,V_a_2,T_b] : % 19.07/18.98 ( class_Orderings_Oorder(T_b) % 19.07/18.98 => ( c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) % 19.07/18.98 <=> ( V_a_2 = V_b_2 % 19.07/18.98 & V_b_2 = V_c_2 ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_atLeastAtMost__singleton_H,axiom, % 19.07/18.98 ! [V_b_2,V_a_2,T_b] : % 19.07/18.98 ( class_Orderings_Oorder(T_b) % 19.07/18.98 => ( V_a_2 = V_b_2 % 19.07/18.98 => c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_image__uminus__atLeastAtMost,axiom, % 19.07/18.98 ! [V_y_2,V_x_2,T_b] : % 19.07/18.98 ( class_Groups_Oordered__ab__group__add(T_b) % 19.07/18.98 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_x_2,V_y_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_atLeastSucAtMost__greaterThanAtMost,axiom, % 19.07/18.98 ! [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) ). % 19.07/18.98 % 19.07/18.98 fof(fact_finite__surj__inj,axiom, % 19.07/18.98 ! [V_f_2,V_A_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_Oimage(T_b,T_b,V_f_2),V_A_2))) % 19.07/18.98 => c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_endo__inj__surj,axiom, % 19.07/18.98 ! [V_f_2,V_A_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_b,V_f_2),V_A_2)),V_A_2)) % 19.07/18.98 => ( c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2) % 19.07/18.98 => hAPP(c_Set_Oimage(T_b,T_b,V_f_2),V_A_2) = V_A_2 ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_eq__card__imp__inj__on,axiom, % 19.07/18.98 ! [V_f_2,T_c,V_A_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) % 19.07/18.98 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_inj__on__iff__eq__card,axiom, % 19.07/18.98 ! [V_f_2,T_c,V_A_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 19.07/18.98 <=> hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_pigeonhole,axiom, % 19.07/18.98 ! [V_A_2,V_f_2,T_c,T_b] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))),hAPP(c_Finite__Set_Ocard(T_c),V_A_2))) % 19.07/18.98 => ~ c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_SetInterval_Otransfer__nat__int__set__function__closures,axiom, % 19.07/18.98 ! [V_y_2,V_x_2] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 19.07/18.98 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_card__atLeastAtMost,axiom, % 19.07/18.98 ! [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) ). % 19.07/18.98 % 19.07/18.98 fof(fact_atLeastAtMostSuc__conv,axiom, % 19.07/18.98 ! [V_n_2,V_m_2] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 19.07/18.98 => 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)) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Powp__mono,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 19.07/18.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(T_b,V_A_2)),c_Predicate_OPowp(T_b,V_B_2))) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom, % 19.07/18.98 ! [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) ). % 19.07/18.98 % 19.07/18.98 fof(fact_card__bij__eq,axiom, % 19.07/18.98 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b] : % 19.07/18.98 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_B_2)) % 19.07/18.98 => ( c_Fun_Oinj__on(T_c,T_b,V_g_2,V_B_2) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),V_B_2)),V_A_2)) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 19.07/18.98 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Int__atLeastAtMost,axiom, % 19.07/18.98 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_atLeastatMost__psubset__iff,axiom, % 19.07/18.98 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] : % 19.07/18.98 ( class_Orderings_Oorder(T_b) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2))) % 19.07/18.98 <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) % 19.07/18.98 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2)) % 19.07/18.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2)) % 19.07/18.98 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_a_2)) % 19.07/18.98 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_d_2)) ) ) ) % 19.07/18.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_d_2)) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_ivl__disj__un_I22_J,axiom, % 19.07/18.98 ! [V_u_2,V_m_2,V_l_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2)) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2)) % 19.07/18.98 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_ivl__disj__int_I16_J,axiom, % 19.07/18.98 ! [V_u_2,V_m_2,V_l_2,T_b] : % 19.07/18.98 ( class_Orderings_Oorder(T_b) % 19.07/18.98 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_ivl__disj__int_I13_J,axiom, % 19.07/18.98 ! [V_u_2,V_m_2,V_l_2,T_b] : % 19.07/18.98 ( class_Orderings_Oorder(T_b) % 19.07/18.98 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_ivl__disj__int_I12_J,axiom, % 19.07/18.98 ! [V_u_2,V_m_2,V_l_2,T_b] : % 19.07/18.98 ( class_Orderings_Oorder(T_b) % 19.07/18.98 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_simp__from__to,axiom, % 19.07/18.98 ! [V_i_2,V_j_2] : % 19.07/18.98 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2)) % 19.07/18.98 => 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)) ) % 19.07/18.98 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2)) % 19.07/18.98 => 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)) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_inj__on__iff__card__le,axiom, % 19.07/18.98 ! [V_B_2,T_c,V_A_2,T_b] : % 19.07/18.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 19.07/18.98 => ( ? [B_f] : % 19.07/18.98 ( c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2) % 19.07/18.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,B_f),V_A_2)),V_B_2)) ) % 19.07/18.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2))) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_card__inj__on__le,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 19.07/18.98 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_B_2)) % 19.07/18.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 19.07/18.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2))) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_quotient__diff1,axiom, % 19.07/18.98 ! [V_a_2,V_A_2,V_r_2,T_b] : % 19.07/18.98 ( c_Fun_Oinj__on(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),T_b),c_Equiv__Relations_Oquotient(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_r_2),V_A_2) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 19.07/18.98 => hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_r_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2)) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_card__atLeastAtMost__int,axiom, % 19.07/18.98 ! [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))) ). % 19.07/18.98 % 19.07/18.98 fof(fact_ivl__disj__un_I5_J,axiom, % 19.07/18.98 ! [V_u_2,V_l_2,T_b] : % 19.07/18.98 ( class_Orderings_Olinorder(T_b) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) % 19.07/18.98 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_inj__on__Un,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 19.07/18.98 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 19.07/18.98 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 19.07/18.98 & c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) % 19.07/18.98 & hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_inj__on__insert,axiom, % 19.07/18.98 ! [V_A_2,V_a_2,V_f_2,T_c,T_b] : % 19.07/18.98 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) % 19.07/18.98 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 19.07/18.98 & ~ hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_inj__uminus,axiom, % 19.07/18.98 ! [V_A_2,T_b] : % 19.07/18.98 ( class_Groups_Oordered__ab__group__add(T_b) % 19.07/18.98 => c_Fun_Oinj__on(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b),V_A_2) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_inj__on__empty,axiom, % 19.07/18.98 ! [V_f_2,T_c,T_b] : c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ). % 19.07/18.98 % 19.07/18.98 fof(fact_inj__Inl,axiom, % 19.07/18.98 ! [V_A_2,T_c,T_b] : c_Fun_Oinj__on(T_b,tc_sum(T_b,T_c),c_Sum__Type_OInl(T_b,T_c),V_A_2) ). % 19.07/18.98 % 19.07/18.98 fof(fact_inj__Some,axiom, % 19.07/18.98 ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,tc_Option_Ooption(T_b),c_Option_Ooption_OSome(T_b),V_A_2) ). % 19.07/18.98 % 19.07/18.98 fof(fact_inj__Suc,axiom, % 19.07/18.98 ! [V_N_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,V_N_2) ). % 19.07/18.98 % 19.07/18.98 fof(fact_inj__Inr,axiom, % 19.07/18.98 ! [V_A_2,T_c,T_b] : c_Fun_Oinj__on(T_b,tc_sum(T_c,T_b),c_Sum__Type_OInr(T_b,T_c),V_A_2) ). % 19.07/18.98 % 19.07/18.98 fof(fact_inj__on__add__nat,axiom, % 19.07/18.98 ! [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) ). % 19.07/18.98 % 19.07/18.98 fof(fact_swap__inj__on,axiom, % 19.07/18.98 ! [V_A_2,T_c,T_b] : c_Fun_Oinj__on(tc_prod(T_b,T_c),tc_prod(T_c,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_prod(T_c,T_b)),hAPP(c_COMBC(T_c,T_b,tc_prod(T_c,T_b)),c_Product__Type_OPair(T_c,T_b))),V_A_2) ). % 19.07/18.98 % 19.07/18.98 fof(fact_inj__on__def,axiom, % 19.07/18.98 ! [V_A_2,V_f_2,T_c,T_b] : % 19.07/18.98 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 19.07/18.98 <=> ! [B_x] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 19.07/18.98 => ! [B_xa] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2)) % 19.07/18.98 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_xa) % 19.07/18.98 => B_x = B_xa ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_image__ident,axiom, % 19.07/18.98 ! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2 ). % 19.07/18.98 % 19.07/18.98 fof(fact_inj__on__id2,axiom, % 19.07/18.98 ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_COMBI(T_b),V_A_2) ). % 19.07/18.98 % 19.07/18.98 fof(fact_inj__on__contraD,axiom, % 19.07/18.98 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 19.07/18.98 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 19.07/18.98 => ( V_x_2 != V_y_2 % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 19.07/18.98 => hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_inj__on__iff,axiom, % 19.07/18.98 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 19.07/18.98 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 19.07/18.98 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 19.07/18.98 <=> V_x_2 = V_y_2 ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_inj__onD,axiom, % 19.07/18.98 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 19.07/18.98 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 19.07/18.98 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 19.07/18.98 => V_x_2 = V_y_2 ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_subset__inj__on,axiom, % 19.07/18.98 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] : % 19.07/18.98 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 19.07/18.98 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_inj__on__Int,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 19.07/18.98 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 19.07/18.98 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) % 19.07/18.98 => c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_inj__on__diff,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 19.07/18.98 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 19.07/18.98 => c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_Cantors__paradox,axiom, % 19.07/18.98 ! [V_A_2,T_b] : % 19.07/18.98 ~ ? [B_f] : hAPP(c_Set_Oimage(T_b,tc_fun(T_b,tc_HOL_Obool),B_f),V_A_2) = hAPP(c_Set_OPow(T_b),V_A_2) ). % 19.07/18.98 % 19.07/18.98 fof(fact_inj__on__Un__image__eq__iff,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 19.07/18.98 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 19.07/18.98 => ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2) % 19.07/18.98 <=> V_A_2 = V_B_2 ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_inj__on__strict__subset,axiom, % 19.07/18.98 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] : % 19.07/18.98 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 19.07/18.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2))) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_inj__on__image__Int,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] : % 19.07/18.98 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 19.07/18.98 => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_inj__on__image__set__diff,axiom, % 19.07/18.98 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] : % 19.07/18.98 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 19.07/18.98 => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_inj__on__iff__surj,axiom, % 19.07/18.98 ! [V_A_H_2,T_c,T_b,V_A_2] : % 19.07/18.98 ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.98 => ( ? [B_f] : % 19.07/18.98 ( c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2) % 19.07/18.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,B_f),V_A_2)),V_A_H_2)) ) % 19.07/18.98 <=> ? [B_g] : hAPP(c_Set_Oimage(T_c,T_b,B_g),V_A_H_2) = V_A_2 ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_ex__nat__less,axiom, % 19.07/18.98 ! [V_Pa_2,V_n_2] : % 19.07/18.98 ( ? [B_m] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2)) % 19.07/18.98 & hBOOL(hAPP(V_Pa_2,B_m)) ) % 19.07/18.98 <=> ? [B_x] : % 19.07/18.98 ( 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))) % 19.07/18.98 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_all__nat__less,axiom, % 19.07/18.98 ! [V_Pa_2,V_n_2] : % 19.07/18.98 ( ! [B_m] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2)) % 19.07/18.98 => hBOOL(hAPP(V_Pa_2,B_m)) ) % 19.07/18.98 <=> ! [B_x] : % 19.07/18.98 ( 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))) % 19.07/18.98 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_aset_I6_J,axiom, % 19.07/18.98 ! [V_A_2,V_t_2,V_D_2] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 19.07/18.98 => ( 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)) % 19.07/18.98 => ! [B_x] : % 19.07/18.98 ( ! [B_xa] : % 19.07/18.98 ( 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))) % 19.07/18.98 => ! [B_xb] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 19.07/18.98 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2)) % 19.07/18.98 => 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)) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_bset_I8_J,axiom, % 19.07/18.98 ! [V_B_2,V_t_2,V_D_2] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 19.07/18.98 => ( 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)) % 19.07/18.98 => ! [B_x] : % 19.07/18.98 ( ! [B_xa] : % 19.07/18.98 ( 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))) % 19.07/18.98 => ! [B_xb] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 19.07/18.98 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x)) % 19.07/18.98 => 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))) ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_bset_I3_J,axiom, % 19.07/18.98 ! [V_B_2,V_t_2,V_D_2] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 19.07/18.98 => ( 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)) % 19.07/18.98 => ( ! [B_x] : % 19.07/18.98 ( 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))) % 19.07/18.98 => ! [B_xa] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_B_2)) % 19.07/18.98 => V_t_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xa),B_x) ) ) % 19.07/18.98 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_aset_I4_J,axiom, % 19.07/18.98 ! [V_A_2,V_t_2,V_D_2] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2)) % 19.07/18.98 => ! [B_x] : % 19.07/18.98 ( ! [B_xa] : % 19.07/18.98 ( 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))) % 19.07/18.98 => ! [B_xb] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 19.07/18.98 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 19.07/18.98 => ( B_x != V_t_2 % 19.07/18.98 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_bset_I4_J,axiom, % 19.07/18.98 ! [V_B_2,V_t_2,V_D_2] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2)) % 19.07/18.98 => ! [B_x] : % 19.07/18.98 ( ! [B_xa] : % 19.07/18.98 ( 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))) % 19.07/18.98 => ! [B_xb] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 19.07/18.98 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 19.07/18.98 => ( B_x != V_t_2 % 19.07/18.98 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ). % 19.07/18.98 % 19.07/18.98 fof(fact_bset_I7_J,axiom, % 19.07/18.98 ! [V_B_2,V_t_2,V_D_2] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 19.07/18.98 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2)) % 19.07/18.98 => ! [B_x] : % 19.07/18.98 ( ! [B_xa] : % 19.07/18.98 ( 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))) % 19.07/18.98 => ! [B_xb] : % 19.07/18.98 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 19.07/18.99 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x)) % 19.07/18.99 => 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))) ) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_aset_I3_J,axiom, % 19.07/18.99 ! [V_A_2,V_t_2,V_D_2] : % 19.07/18.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 19.07/18.99 => ( 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)) % 19.07/18.99 => ( ! [B_x] : % 19.07/18.99 ( 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))) % 19.07/18.99 => ! [B_xa] : % 19.07/18.99 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_A_2)) % 19.07/18.99 => V_t_2 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xa),B_x) ) ) % 19.07/18.99 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_aset_I5_J,axiom, % 19.07/18.99 ! [V_A_2,V_t_2,V_D_2] : % 19.07/18.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2)) % 19.07/18.99 => ! [B_x] : % 19.07/18.99 ( ! [B_xa] : % 19.07/18.99 ( 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))) % 19.07/18.99 => ! [B_xb] : % 19.07/18.99 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 19.07/18.99 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2)) % 19.07/18.99 => 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)) ) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_bset_I6_J,axiom, % 19.07/18.99 ! [V_t_2,V_B_2,V_D_2] : % 19.07/18.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 19.07/18.99 => ! [B_x] : % 19.07/18.99 ( ! [B_xa] : % 19.07/18.99 ( 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))) % 19.07/18.99 => ! [B_xb] : % 19.07/18.99 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 19.07/18.99 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2)) % 19.07/18.99 => 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)) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_aset_I8_J,axiom, % 19.07/18.99 ! [V_t_2,V_A_2,V_D_2] : % 19.07/18.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 19.07/18.99 => ! [B_x] : % 19.07/18.99 ( ! [B_xa] : % 19.07/18.99 ( 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))) % 19.07/18.99 => ! [B_xb] : % 19.07/18.99 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 19.07/18.99 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x)) % 19.07/18.99 => 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))) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_periodic__finite__ex,axiom, % 19.07/18.99 ! [V_Pa_2,V_d_2] : % 19.07/18.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) % 19.07/18.99 => ( ! [B_x,B_k] : % 19.07/18.99 ( hBOOL(hAPP(V_Pa_2,B_x)) % 19.07/18.99 <=> hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B_k),V_d_2)))) ) % 19.07/18.99 => ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 19.07/18.99 <=> ? [B_x] : % 19.07/18.99 ( 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))) % 19.07/18.99 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_bset_I5_J,axiom, % 19.07/18.99 ! [V_t_2,V_B_2,V_D_2] : % 19.07/18.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 19.07/18.99 => ! [B_x] : % 19.07/18.99 ( ! [B_xa] : % 19.07/18.99 ( 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))) % 19.07/18.99 => ! [B_xb] : % 19.07/18.99 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 19.07/18.99 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2)) % 19.07/18.99 => 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)) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_aset_I7_J,axiom, % 19.07/18.99 ! [V_t_2,V_A_2,V_D_2] : % 19.07/18.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 19.07/18.99 => ! [B_x] : % 19.07/18.99 ( ! [B_xa] : % 19.07/18.99 ( 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))) % 19.07/18.99 => ! [B_xb] : % 19.07/18.99 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 19.07/18.99 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x)) % 19.07/18.99 => 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))) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_image__minus__const__atLeastLessThan__nat,axiom, % 19.07/18.99 ! [V_x_2,V_y_2,V_c_2] : % 19.07/18.99 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_c_2),V_y_2)) % 19.07/18.99 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_c_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_c_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_y_2),V_c_2)) ) % 19.07/18.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_c_2),V_y_2)) % 19.07/18.99 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) % 19.07/18.99 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_c_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ) % 19.07/18.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) % 19.07/18.99 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_c_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_aset_I10_J,axiom, % 19.07/18.99 ! [V_t_2,V_A_2,V_D_2,V_d_2] : % 19.07/18.99 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_D_2)) % 19.07/18.99 => ! [B_x] : % 19.07/18.99 ( ! [B_xa] : % 19.07/18.99 ( 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))) % 19.07/18.99 => ! [B_xb] : % 19.07/18.99 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 19.07/18.99 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 19.07/18.99 => ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_t_2))) % 19.07/18.99 => ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2)),V_t_2))) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_finite__atLeastLessThan,axiom, % 19.07/18.99 ! [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))) ). % 19.07/18.99 % 19.07/18.99 fof(fact_atLeastLessThan__eq__iff,axiom, % 19.07/18.99 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] : % 19.07/18.99 ( class_Orderings_Olinorder(T_b) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2)) % 19.07/18.99 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2) % 19.07/18.99 <=> ( V_a_2 = V_c_2 % 19.07/18.99 & V_b_2 = V_d_2 ) ) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_atLeastLessThan__inj_I1_J,axiom, % 19.07/18.99 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] : % 19.07/18.99 ( class_Orderings_Olinorder(T_b) % 19.07/18.99 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2)) % 19.07/18.99 => V_a_2 = V_c_2 ) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_atLeastLessThan__inj_I2_J,axiom, % 19.07/18.99 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] : % 19.07/18.99 ( class_Orderings_Olinorder(T_b) % 19.07/18.99 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2)) % 19.07/18.99 => V_b_2 = V_d_2 ) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_all__nat__less__eq,axiom, % 19.07/18.99 ! [V_Pa_2,V_n_2] : % 19.07/18.99 ( ! [B_m] : % 19.07/18.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) % 19.07/18.99 => hBOOL(hAPP(V_Pa_2,B_m)) ) % 19.07/18.99 <=> ! [B_x] : % 19.07/18.99 ( 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))) % 19.07/18.99 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_ex__nat__less__eq,axiom, % 19.07/18.99 ! [V_Pa_2,V_n_2] : % 19.07/18.99 ( ? [B_m] : % 19.07/18.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) % 19.07/18.99 & hBOOL(hAPP(V_Pa_2,B_m)) ) % 19.07/18.99 <=> ? [B_x] : % 19.07/18.99 ( 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))) % 19.07/18.99 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_atLeastLessThanSuc__atLeastAtMost,axiom, % 19.07/18.99 ! [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) ). % 19.07/18.99 % 19.07/18.99 fof(fact_atLeastLessThan0,axiom, % 19.07/18.99 ! [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)) ). % 19.07/18.99 % 19.07/18.99 fof(fact_card__atLeastLessThan,axiom, % 19.07/18.99 ! [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) ). % 19.07/18.99 % 19.07/18.99 fof(fact_image__Suc__atLeastLessThan,axiom, % 19.07/18.99 ! [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)) ). % 19.07/18.99 % 19.07/18.99 fof(fact_atLeastLessThan__empty,axiom, % 19.07/18.99 ! [V_a_2,V_b_2,T_b] : % 19.07/18.99 ( class_Orderings_Oorder(T_b) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2)) % 19.07/18.99 => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_atLeastLessThan__empty__iff,axiom, % 19.07/18.99 ! [V_b_2,V_a_2,T_b] : % 19.07/18.99 ( class_Orderings_Oorder(T_b) % 19.07/18.99 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.99 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_atLeastLessThan__empty__iff2,axiom, % 19.07/18.99 ! [V_b_2,V_a_2,T_b] : % 19.07/18.99 ( class_Orderings_Oorder(T_b) % 19.07/18.99 => ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) % 19.07/18.99 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_atLeastLessThan__subset__iff,axiom, % 19.07/18.99 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] : % 19.07/18.99 ( class_Orderings_Olinorder(T_b) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2))) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2)) % 19.07/18.99 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2)) % 19.07/18.99 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2)) ) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_ivl__disj__un_I17_J,axiom, % 19.07/18.99 ! [V_u_2,V_m_2,V_l_2,T_b] : % 19.07/18.99 ( class_Orderings_Olinorder(T_b) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2)) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2)) % 19.07/18.99 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_ivl__diff,axiom, % 19.07/18.99 ! [V_m_2,V_n_2,V_i_2,T_b] : % 19.07/18.99 ( class_Orderings_Olinorder(T_b) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_n_2)) % 19.07/18.99 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_i_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_i_2),V_n_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_n_2),V_m_2) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_ivl__disj__int_I11_J,axiom, % 19.07/18.99 ! [V_u_2,V_m_2,V_l_2,T_b] : % 19.07/18.99 ( class_Orderings_Oorder(T_b) % 19.07/18.99 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_atLeastSucLessThan__greaterThanLessThan,axiom, % 19.07/18.99 ! [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) ). % 19.07/18.99 % 19.07/18.99 fof(fact_image__add__atLeastLessThan,axiom, % 19.07/18.99 ! [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)) ). % 19.07/18.99 % 19.07/18.99 fof(fact_atLeastLessThan__singleton,axiom, % 19.07/18.99 ! [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))) ). % 19.07/18.99 % 19.07/18.99 fof(fact_ivl__disj__un_I21_J,axiom, % 19.07/18.99 ! [V_u_2,V_m_2,V_l_2,T_b] : % 19.07/18.99 ( class_Orderings_Olinorder(T_b) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2)) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2)) % 19.07/18.99 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_atLeastLessThan__add__Un,axiom, % 19.07/18.99 ! [V_k_2,V_j_2,V_i_2] : % 19.07/18.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 19.07/18.99 => 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))) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_ivl__disj__int_I15_J,axiom, % 19.07/18.99 ! [V_u_2,V_m_2,V_l_2,T_b] : % 19.07/18.99 ( class_Orderings_Oorder(T_b) % 19.07/18.99 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_Int__atLeastLessThan,axiom, % 19.07/18.99 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] : % 19.07/18.99 ( class_Orderings_Olinorder(T_b) % 19.07/18.99 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_subset__card__intvl__is__intvl,axiom, % 19.07/18.99 ! [V_k_2,V_A_2] : % 19.07/18.99 ( 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))))) % 19.07/18.99 => 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))) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_ivl__disj__int_I9_J,axiom, % 19.07/18.99 ! [V_u_2,V_m_2,V_l_2,T_b] : % 19.07/18.99 ( class_Orderings_Oorder(T_b) % 19.07/18.99 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_image__uminus__greaterThanAtMost,axiom, % 19.07/18.99 ! [V_y_2,V_x_2,T_b] : % 19.07/18.99 ( class_Groups_Oordered__ab__group__add(T_b) % 19.07/18.99 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_x_2,V_y_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_image__uminus__atLeastLessThan,axiom, % 19.07/18.99 ! [V_y_2,V_x_2,T_b] : % 19.07/18.99 ( class_Groups_Oordered__ab__group__add(T_b) % 19.07/18.99 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_x_2),V_y_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_atLeastLessThanSuc,axiom, % 19.07/18.99 ! [V_n_2,V_m_2] : % 19.07/18.99 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 19.07/18.99 => 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)) ) % 19.07/18.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 19.07/18.99 => 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)) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_ivl__disj__un_I15_J,axiom, % 19.07/18.99 ! [V_u_2,V_m_2,V_l_2,T_b] : % 19.07/18.99 ( class_Orderings_Olinorder(T_b) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2)) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2)) % 19.07/18.99 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_ivl__disj__un_I6_J,axiom, % 19.07/18.99 ! [V_u_2,V_l_2,T_b] : % 19.07/18.99 ( class_Orderings_Olinorder(T_b) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) % 19.07/18.99 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_ivl__disj__un_I3_J,axiom, % 19.07/18.99 ! [V_u_2,V_l_2,T_b] : % 19.07/18.99 ( class_Orderings_Olinorder(T_b) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2)) % 19.07/18.99 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_ivl__disj__un_I18_J,axiom, % 19.07/18.99 ! [V_u_2,V_m_2,V_l_2,T_b] : % 19.07/18.99 ( class_Orderings_Olinorder(T_b) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2)) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2)) % 19.07/18.99 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_bset_I9_J,axiom, % 19.07/18.99 ! [V_t_2,V_B_2,V_D_2,V_d_2] : % 19.07/18.99 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_D_2)) % 19.07/18.99 => ! [B_x] : % 19.07/18.99 ( ! [B_xa] : % 19.07/18.99 ( 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))) % 19.07/18.99 => ! [B_xb] : % 19.07/18.99 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 19.07/18.99 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_t_2))) % 19.07/18.99 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2)),V_t_2))) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_aset_I9_J,axiom, % 19.07/18.99 ! [V_t_2,V_A_2,V_D_2,V_d_2] : % 19.07/18.99 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_D_2)) % 19.07/18.99 => ! [B_x] : % 19.07/18.99 ( ! [B_xa] : % 19.07/18.99 ( 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))) % 19.07/18.99 => ! [B_xb] : % 19.07/18.99 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 19.07/18.99 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_t_2))) % 19.07/18.99 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2)),V_t_2))) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_bset_I10_J,axiom, % 19.07/18.99 ! [V_t_2,V_B_2,V_D_2,V_d_2] : % 19.07/18.99 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_D_2)) % 19.07/18.99 => ! [B_x] : % 19.07/18.99 ( ! [B_xa] : % 19.07/18.99 ( 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))) % 19.07/18.99 => ! [B_xb] : % 19.07/18.99 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 19.07/18.99 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 19.07/18.99 => ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_t_2))) % 19.07/18.99 => ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2)),V_t_2))) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_finite__atLeastLessThan__int,axiom, % 19.07/18.99 ! [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))) ). % 19.07/18.99 % 19.07/18.99 fof(fact_finite__atLeastZeroLessThan__int,axiom, % 19.07/18.99 ! [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))) ). % 19.07/18.99 % 19.07/18.99 fof(fact_atLeastLessThanPlusOne__atLeastAtMost__int,axiom, % 19.07/18.99 ! [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) ). % 19.07/18.99 % 19.07/18.99 fof(fact_image__add__int__atLeastLessThan,axiom, % 19.07/18.99 ! [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) ). % 19.07/18.99 % 19.07/18.99 fof(fact_card__atLeastZeroLessThan__int,axiom, % 19.07/18.99 ! [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) ). % 19.07/18.99 % 19.07/18.99 fof(fact_card__atLeastLessThan__int,axiom, % 19.07/18.99 ! [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)) ). % 19.07/18.99 % 19.07/18.99 fof(fact_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom, % 19.07/18.99 ! [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) ). % 19.07/18.99 % 19.07/18.99 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I1_J,axiom, % 19.07/18.99 ! [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))) ). % 19.07/18.99 % 19.07/18.99 fof(fact_fun__upd__image,axiom, % 19.07/18.99 ! [V_y_2,V_f_2,T_c,V_A_2,V_x_2,T_b] : % 19.07/18.99 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.99 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) % 19.07/18.99 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.99 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2)),V_A_2) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_the__inv__into__into,axiom, % 19.07/18.99 ! [V_B_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 19.07/18.99 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 19.07/18.99 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_x_2)),V_B_2)) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_fun__upd__triv,axiom, % 19.07/18.99 ! [V_x_2,V_f_2,T_c,T_b] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),hAPP(V_f_2,V_x_2)) = V_f_2 ). % 19.07/18.99 % 19.07/18.99 fof(fact_finite__atMost,axiom, % 19.07/18.99 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2))) ). % 19.07/18.99 % 19.07/18.99 fof(fact_atMost__eq__iff,axiom, % 19.07/18.99 ! [V_y_2,V_x_2,T_b] : % 19.07/18.99 ( class_Orderings_Olinorder(T_b) % 19.07/18.99 => ( hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_y_2) % 19.07/18.99 <=> V_x_2 = V_y_2 ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_fun__upd__def,axiom, % 19.07/18.99 ! [V_b_2,V_f_2,T_c,T_b,V_a_2,V_x_2] : % 19.07/18.99 ( ( V_x_2 = V_a_2 % 19.07/18.99 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_a_2),V_b_2),V_x_2) = V_b_2 ) % 19.07/18.99 & ( V_x_2 != V_a_2 % 19.07/18.99 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_a_2),V_b_2),V_x_2) = hAPP(V_f_2,V_x_2) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_fun__upd__idem,axiom, % 19.07/18.99 ! [T_b,T_c,V_y_2,V_x_2,V_f_2] : % 19.07/18.99 ( hAPP(V_f_2,V_x_2) = V_y_2 % 19.07/18.99 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,T_b),V_f_2),V_x_2),V_y_2) = V_f_2 ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_fun__upd__other,axiom, % 19.07/18.99 ! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] : % 19.07/18.99 ( V_z_2 != V_x_2 % 19.07/18.99 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2),V_z_2) = hAPP(V_f_2,V_z_2) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_fun__upd__twist,axiom, % 19.07/18.99 ! [V_d_2,V_b_2,V_m_2,T_c,T_b,V_c_2,V_a_2] : % 19.07/18.99 ( V_a_2 != V_c_2 % 19.07/18.99 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_m_2),V_a_2),V_b_2)),V_c_2),V_d_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_m_2),V_c_2),V_d_2)),V_a_2),V_b_2) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_fun__upd__apply,axiom, % 19.07/18.99 ! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] : % 19.07/18.99 ( ( V_z_2 = V_x_2 % 19.07/18.99 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2),V_z_2) = V_y_2 ) % 19.07/18.99 & ( V_z_2 != V_x_2 % 19.07/18.99 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2),V_z_2) = hAPP(V_f_2,V_z_2) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_fun__upd__same,axiom, % 19.07/18.99 ! [V_y_2,V_x_2,V_f_2,T_b,T_c] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,T_b),V_f_2),V_x_2),V_y_2),V_x_2) = V_y_2 ). % 19.07/18.99 % 19.07/18.99 fof(fact_fun__upd__upd,axiom, % 19.07/18.99 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_c,T_b] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2)),V_x_2),V_z_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_z_2) ). % 19.07/18.99 % 19.07/18.99 fof(fact_fun__upd__idem__iff,axiom, % 19.07/18.99 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] : % 19.07/18.99 ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2) = V_f_2 % 19.07/18.99 <=> hAPP(V_f_2,V_x_2) = V_y_2 ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_atLeast0AtMost,axiom, % 19.07/18.99 ! [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) ). % 19.07/18.99 % 19.07/18.99 fof(fact_card__atMost,axiom, % 19.07/18.99 ! [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) ). % 19.07/18.99 % 19.07/18.99 fof(fact_atMost__Suc,axiom, % 19.07/18.99 ! [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)) ). % 19.07/18.99 % 19.07/18.99 fof(fact_atMost__iff,axiom, % 19.07/18.99 ! [V_k_2,V_i_2,T_b] : % 19.07/18.99 ( class_Orderings_Oord(T_b) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2))) % 19.07/18.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_k_2)) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_atMost__subset__iff,axiom, % 19.07/18.99 ! [V_y_2,V_x_2,T_b] : % 19.07/18.99 ( class_Orderings_Oorder(T_b) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_y_2))) % 19.07/18.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_UN__le__add__shift,axiom, % 19.07/18.99 ! [V_k_2,V_M_2,V_n_2,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool),tc_Nat_Onat),V_M_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_k_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2))),V_M_2) ). % 19.07/18.99 % 19.07/18.99 fof(fact_the__inv__into__f__f,axiom, % 19.07/18.99 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] : % 19.07/18.99 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.99 => hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_the__inv__into__f__eq,axiom, % 19.07/18.99 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 19.07/18.99 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 19.07/18.99 => ( hAPP(V_f_2,V_x_2) = V_y_2 % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.99 => hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_inj__on__the__inv__into,axiom, % 19.07/18.99 ! [V_A_2,V_f_2,T_c,T_b] : % 19.07/18.99 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 19.07/18.99 => c_Fun_Oinj__on(T_c,T_b,c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_the__inv__into__onto,axiom, % 19.07/18.99 ! [V_A_2,V_f_2,T_c,T_b] : % 19.07/18.99 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 19.07/18.99 => hAPP(c_Set_Oimage(T_c,T_b,c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = V_A_2 ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_inj__on__fun__updI,axiom, % 19.07/18.99 ! [V_x_2,V_y_2,V_A_2,V_f_2,T_c,T_b] : % 19.07/18.99 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 19.07/18.99 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) % 19.07/18.99 => c_Fun_Oinj__on(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2),V_A_2) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_the__inv__into__def,axiom, % 19.07/18.99 ! [V_x_2,V_f_2,V_A_2,T_c,T_b] : hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_x_2) = c_HOL_OThe(T_b,hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),V_x_2))) ). % 19.07/18.99 % 19.07/18.99 fof(fact_atMost__0,axiom, % 19.07/18.99 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))) ). % 19.07/18.99 % 19.07/18.99 fof(fact_Int__atLeastAtMostL1,axiom, % 19.07/18.99 ! [V_d_2,V_b_2,V_a_2,T_b] : % 19.07/18.99 ( class_Orderings_Olinorder(T_b) % 19.07/18.99 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_Int__atLeastAtMostR1,axiom, % 19.07/18.99 ! [V_d_2,V_c_2,V_b_2,T_b] : % 19.07/18.99 ( class_Orderings_Olinorder(T_b) % 19.07/18.99 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_ivl__disj__un_I9_J,axiom, % 19.07/18.99 ! [V_u_2,V_l_2,T_b] : % 19.07/18.99 ( class_Orderings_Olinorder(T_b) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) % 19.07/18.99 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_u_2) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_ivl__disj__int_I3_J,axiom, % 19.07/18.99 ! [V_u_2,V_l_2,T_b] : % 19.07/18.99 ( class_Orderings_Oorder(T_b) % 19.07/18.99 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_ivl__disj__int_I1_J,axiom, % 19.07/18.99 ! [V_u_2,V_l_2,T_b] : % 19.07/18.99 ( class_Orderings_Oorder(T_b) % 19.07/18.99 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_f__the__inv__into__f,axiom, % 19.07/18.99 ! [V_y_2,V_A_2,V_f_2,T_c,T_b] : % 19.07/18.99 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) % 19.07/18.99 => hAPP(V_f_2,hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_y_2)) = V_y_2 ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_UN__le__eq__Un0,axiom, % 19.07/18.99 ! [V_M_2,V_n_2,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2)),V_M_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n_2)),V_M_2)),hAPP(V_M_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 19.07/18.99 % 19.07/18.99 fof(fact_map__upd__nonempty,axiom, % 19.07/18.99 ! [V_x_2,V_k_2,V_t_2,T_c,T_b] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_t_2),V_k_2),hAPP(c_Option_Ooption_OSome(T_c),V_x_2)) != hAPP(c_COMBK(tc_Option_Ooption(T_c),T_b),c_Option_Ooption_ONone(T_c)) ). % 19.07/18.99 % 19.07/18.99 fof(fact_image__atLeastZeroLessThan__int,axiom, % 19.07/18.99 ! [V_u_2] : % 19.07/18.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2)) % 19.07/18.99 => 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))) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_image__map__upd,axiom, % 19.07/18.99 ! [V_y_2,V_m_2,T_c,V_A_2,V_x_2,T_b] : % 19.07/18.99 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.99 => hAPP(c_Set_Oimage(T_b,tc_Option_Ooption(T_c),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_m_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2))),V_A_2) = hAPP(c_Set_Oimage(T_b,tc_Option_Ooption(T_c),V_m_2),V_A_2) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_finite__lessThan,axiom, % 19.07/18.99 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2))) ). % 19.07/18.99 % 19.07/18.99 fof(fact_card__lessThan,axiom, % 19.07/18.99 ! [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 ). % 19.07/18.99 % 19.07/18.99 fof(fact_lessThan__eq__iff,axiom, % 19.07/18.99 ! [V_y_2,V_x_2,T_b] : % 19.07/18.99 ( class_Orderings_Olinorder(T_b) % 19.07/18.99 => ( hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_y_2) % 19.07/18.99 <=> V_x_2 = V_y_2 ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_atLeast0LessThan,axiom, % 19.07/18.99 ! [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) ). % 19.07/18.99 % 19.07/18.99 fof(fact_lessThan__0,axiom, % 19.07/18.99 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)) ). % 19.07/18.99 % 19.07/18.99 fof(fact_lessThan__Suc,axiom, % 19.07/18.99 ! [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)) ). % 19.07/18.99 % 19.07/18.99 fof(fact_lessThan__Suc__atMost,axiom, % 19.07/18.99 ! [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) ). % 19.07/18.99 % 19.07/18.99 fof(fact_lessThan__iff,axiom, % 19.07/18.99 ! [V_k_2,V_i_2,T_b] : % 19.07/18.99 ( class_Orderings_Oord(T_b) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2))) % 19.07/18.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_i_2),V_k_2)) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_lessThan__subset__iff,axiom, % 19.07/18.99 ! [V_y_2,V_x_2,T_b] : % 19.07/18.99 ( class_Orderings_Olinorder(T_b) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_y_2))) % 19.07/18.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_lessThan__strict__subset__iff,axiom, % 19.07/18.99 ! [V_n_2,V_m_2,T_b] : % 19.07/18.99 ( class_Orderings_Olinorder(T_b) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_m_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_n_2))) % 19.07/18.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_n_2)) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_map__upd__Some__unfold,axiom, % 19.07/18.99 ! [V_y_2,V_x_2,V_b_2,V_a_2,V_m_2,T_b,T_c] : % 19.07/18.99 ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_b_2)),V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2) % 19.07/18.99 <=> ( ( V_x_2 = V_a_2 % 19.07/18.99 & V_b_2 = V_y_2 ) % 19.07/18.99 | ( V_x_2 != V_a_2 % 19.07/18.99 & hAPP(V_m_2,V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_map__upd__triv,axiom, % 19.07/18.99 ! [T_c,V_x_2,T_b,V_k_2,V_t_2] : % 19.07/18.99 ( hAPP(V_t_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2) % 19.07/18.99 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),V_t_2),V_k_2),hAPP(c_Option_Ooption_OSome(T_b),V_x_2)) = V_t_2 ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_map__upd__eqD1,axiom, % 19.07/18.99 ! [V_y_2,V_n_2,V_x_2,V_a_2,V_m_2,T_c,T_b] : % 19.07/18.99 ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_c),V_x_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_n_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2)) % 19.07/18.99 => V_x_2 = V_y_2 ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_single__Diff__lessThan,axiom, % 19.07/18.99 ! [V_k_2,T_b] : % 19.07/18.99 ( class_Orderings_Oorder(T_b) % 19.07/18.99 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_ivl__disj__un_I8_J,axiom, % 19.07/18.99 ! [V_u_2,V_l_2,T_b] : % 19.07/18.99 ( class_Orderings_Olinorder(T_b) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) % 19.07/18.99 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_u_2) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_ivl__disj__int_I4_J,axiom, % 19.07/18.99 ! [V_u_2,V_l_2,T_b] : % 19.07/18.99 ( class_Orderings_Oorder(T_b) % 19.07/18.99 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_ivl__disj__int_I2_J,axiom, % 19.07/18.99 ! [V_u_2,V_l_2,T_b] : % 19.07/18.99 ( class_Orderings_Oorder(T_b) % 19.07/18.99 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_empty__upd__none,axiom, % 19.07/18.99 ! [V_xa_2,V_x_2,T_b,T_c] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),hAPP(c_COMBK(tc_Option_Ooption(T_b),T_c),c_Option_Ooption_ONone(T_b))),V_x_2),c_Option_Ooption_ONone(T_b)),V_xa_2) = c_Option_Ooption_ONone(T_b) ). % 19.07/18.99 % 19.07/18.99 fof(fact_lessThan__Suc__eq__insert__0,axiom, % 19.07/18.99 ! [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))) ). % 19.07/18.99 % 19.07/18.99 fof(fact_ivl__disj__un_I2_J,axiom, % 19.07/18.99 ! [V_u_2,T_b] : % 19.07/18.99 ( class_Orderings_Olinorder(T_b) % 19.07/18.99 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_u_2) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_ivl__disj__un_I10_J,axiom, % 19.07/18.99 ! [V_u_2,V_l_2,T_b] : % 19.07/18.99 ( class_Orderings_Olinorder(T_b) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) % 19.07/18.99 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_u_2) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_ivl__disj__un_I7_J,axiom, % 19.07/18.99 ! [V_u_2,V_l_2,T_b] : % 19.07/18.99 ( class_Orderings_Olinorder(T_b) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2)) % 19.07/18.99 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_u_2) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_arith__series__int,axiom, % 19.07/18.99 ! [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)))) ). % 19.07/18.99 % 19.07/18.99 fof(fact_ran__map__upd,axiom, % 19.07/18.99 ! [V_b_2,T_c,T_b,V_a_2,V_m_2] : % 19.07/18.99 ( hAPP(V_m_2,V_a_2) = c_Option_Ooption_ONone(T_b) % 19.07/18.99 => c_Map_Oran(T_c,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_b_2))) = hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Map_Oran(T_c,T_b,V_m_2)) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_fun__upd__None__restrict,axiom, % 19.07/18.99 ! [V_m_2,T_c,V_D_2,V_x_2,T_b] : % 19.07/18.99 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2)) % 19.07/18.99 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Orestrict__map(T_b,T_c,V_m_2,V_D_2)),V_x_2),c_Option_Ooption_ONone(T_c)) = c_Map_Orestrict__map(T_b,T_c,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) ) % 19.07/18.99 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2)) % 19.07/18.99 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Orestrict__map(T_b,T_c,V_m_2,V_D_2)),V_x_2),c_Option_Ooption_ONone(T_c)) = c_Map_Orestrict__map(T_b,T_c,V_m_2,V_D_2) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum__abs,axiom, % 19.07/18.99 ! [V_A_2,V_f_2,T_c,T_b] : % 19.07/18.99 ( class_Groups_Oordered__ab__group__add__abs(T_b) % 19.07/18.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2))) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum__abs__ge__zero,axiom, % 19.07/18.99 ! [V_A_2,V_f_2,T_c,T_b] : % 19.07/18.99 ( class_Groups_Oordered__ab__group__add__abs(T_b) % 19.07/18.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2))) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_restrict__in,axiom, % 19.07/18.99 ! [V_m_2,T_c,V_A_2,V_x_2,T_b] : % 19.07/18.99 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.99 => hAPP(c_Map_Orestrict__map(T_b,T_c,V_m_2,V_A_2),V_x_2) = hAPP(V_m_2,V_x_2) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_restrict__restrict,axiom, % 19.07/18.99 ! [V_B_2,V_A_2,V_m_2,T_c,T_b] : c_Map_Orestrict__map(T_b,T_c,c_Map_Orestrict__map(T_b,T_c,V_m_2,V_A_2),V_B_2) = c_Map_Orestrict__map(T_b,T_c,V_m_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum_Oempty,axiom, % 19.07/18.99 ! [V_g_2,T_c,T_b] : % 19.07/18.99 ( class_Groups_Ocomm__monoid__add(T_b) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_g_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(T_b) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum__empty,axiom, % 19.07/18.99 ! [V_f_2,T_c,T_b] : % 19.07/18.99 ( class_Groups_Ocomm__monoid__add(T_b) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(T_b) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum_Oinfinite,axiom, % 19.07/18.99 ! [V_g_2,V_A_2,T_b,T_c] : % 19.07/18.99 ( class_Groups_Ocomm__monoid__add(T_c) % 19.07/18.99 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum__infinite,axiom, % 19.07/18.99 ! [V_f_2,V_A_2,T_b,T_c] : % 19.07/18.99 ( class_Groups_Ocomm__monoid__add(T_c) % 19.07/18.99 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum__divide__distrib,axiom, % 19.07/18.99 ! [V_r_2,V_A_2,V_f_2,T_c,T_b] : % 19.07/18.99 ( class_Fields_Ofield(T_b) % 19.07/18.99 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),V_r_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Rings_Oinverse__class_Odivide(T_b)),V_f_2)),V_r_2)),V_A_2) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_abs__setsum__abs,axiom, % 19.07/18.99 ! [V_A_2,V_f_2,T_c,T_b] : % 19.07/18.99 ( class_Groups_Oordered__ab__group__add__abs(T_b) % 19.07/18.99 => hAPP(c_Groups_Oabs__class_Oabs(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum__negf,axiom, % 19.07/18.99 ! [V_A_2,V_f_2,T_c,T_b] : % 19.07/18.99 ( class_Groups_Oab__group__add(T_b) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Ouminus__class_Ouminus(T_b)),V_f_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum__0,axiom, % 19.07/18.99 ! [V_A_2,T_c,T_b] : % 19.07/18.99 ( class_Groups_Ocomm__monoid__add(T_b) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(c_COMBK(T_b,T_c),c_Groups_Ozero__class_Ozero(T_b))),V_A_2) = c_Groups_Ozero__class_Ozero(T_b) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_of__nat__setsum,axiom, % 19.07/18.99 ! [V_A_2,V_f_2,T_c,T_b] : % 19.07/18.99 ( class_Rings_Osemiring__1(T_b) % 19.07/18.99 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,T_c),c_Nat_Osemiring__1__class_Oof__nat(T_b)),V_f_2)),V_A_2) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_of__int__setsum,axiom, % 19.07/18.99 ! [V_A_2,V_f_2,T_c,T_b] : % 19.07/18.99 ( class_Rings_Oring__1(T_b) % 19.07/18.99 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Int_Oint),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_b,T_c),c_Int_Oring__1__class_Oof__int(T_b)),V_f_2)),V_A_2) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum__commute,axiom, % 19.07/18.99 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] : % 19.07/18.99 ( class_Groups_Ocomm__monoid__add(T_b) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_b),T_d),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b)),hAPP(c_COMBC(T_c,T_d,T_b),V_f_2))),V_A_2)),V_B_2) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum__right__distrib,axiom, % 19.07/18.99 ! [V_A_2,V_f_2,T_c,V_r_2,T_b] : % 19.07/18.99 ( class_Rings_Osemiring__0(T_b) % 19.07/18.99 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_r_2),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),hAPP(c_Groups_Otimes__class_Otimes(T_b),V_r_2)),V_f_2)),V_A_2) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum__left__distrib,axiom, % 19.07/18.99 ! [V_r_2,V_A_2,V_f_2,T_c,T_b] : % 19.07/18.99 ( class_Rings_Osemiring__0(T_b) % 19.07/18.99 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),V_r_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2)),V_r_2)),V_A_2) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum__product,axiom, % 19.07/18.99 ! [V_B_2,V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] : % 19.07/18.99 ( class_Rings_Osemiring__0(T_b) % 19.07/18.99 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b),V_g_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,T_b),tc_fun(T_d,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_b),tc_fun(tc_fun(T_d,T_b),tc_fun(T_d,T_b)),T_c),c_COMBB(T_b,T_b,T_d)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2))),V_g_2))),V_B_2)),V_A_2) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum__addf,axiom, % 19.07/18.99 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] : % 19.07/18.99 ( class_Groups_Ocomm__monoid__add(T_b) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Oplus__class_Oplus(T_b)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_g_2),V_A_2)) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum__subtractf,axiom, % 19.07/18.99 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] : % 19.07/18.99 ( class_Groups_Oab__group__add(T_b) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_g_2),V_A_2)) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_restrict__map__empty,axiom, % 19.07/18.99 ! [V_x_2,V_D_2,T_b,T_c] : hAPP(c_Map_Orestrict__map(T_c,T_b,hAPP(c_COMBK(tc_Option_Ooption(T_b),T_c),c_Option_Ooption_ONone(T_b)),V_D_2),V_x_2) = c_Option_Ooption_ONone(T_b) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum_Odistrib,axiom, % 19.07/18.99 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] : % 19.07/18.99 ( class_Groups_Ocomm__monoid__add(T_c) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Groups_Oplus__class_Oplus(T_c)),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_h_2),V_A_2)) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum__shift__bounds__Suc__ivl,axiom, % 19.07/18.99 ! [V_n_2,V_m_2,V_f_2,T_b] : % 19.07/18.99 ( class_Groups_Ocomm__monoid__add(T_b) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum__shift__bounds__nat__ivl,axiom, % 19.07/18.99 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_b] : % 19.07/18.99 ( class_Groups_Ocomm__monoid__add(T_b) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum__shift__bounds__cl__Suc__ivl,axiom, % 19.07/18.99 ! [V_n_2,V_m_2,V_f_2,T_b] : % 19.07/18.99 ( class_Groups_Ocomm__monoid__add(T_b) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum__shift__bounds__cl__nat__ivl,axiom, % 19.07/18.99 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_b] : % 19.07/18.99 ( class_Groups_Ocomm__monoid__add(T_b) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_restrict__out,axiom, % 19.07/18.99 ! [V_m_2,T_c,V_A_2,V_x_2,T_b] : % 19.07/18.99 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.99 => hAPP(c_Map_Orestrict__map(T_b,T_c,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_c) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_restrict__map__insert,axiom, % 19.07/18.99 ! [V_A_2,V_a_2,V_f_2,T_c,T_b] : c_Map_Orestrict__map(T_b,T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Orestrict__map(T_b,T_c,V_f_2,V_A_2)),V_a_2),hAPP(V_f_2,V_a_2)) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum__add__nat__ivl,axiom, % 19.07/18.99 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_b] : % 19.07/18.99 ( class_Groups_Ocomm__monoid__add(T_b) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2)) % 19.07/18.99 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_n_2),V_p_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_p_2)) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum__diff__nat__ivl,axiom, % 19.07/18.99 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_b] : % 19.07/18.99 ( class_Groups_Oab__group__add(T_b) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2)) % 19.07/18.99 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_p_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_n_2),V_p_2)) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum__delta_H,axiom, % 19.07/18.99 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] : % 19.07/18.99 ( class_Groups_Ocomm__monoid__add(T_c) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 19.07/18.99 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = hAPP(V_b_2,V_a_2) ) % 19.07/18.99 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum__delta,axiom, % 19.07/18.99 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] : % 19.07/18.99 ( class_Groups_Ocomm__monoid__add(T_c) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 19.07/18.99 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = hAPP(V_b_2,V_a_2) ) % 19.07/18.99 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_restrict__map__def,axiom, % 19.07/18.99 ! [V_m_2,T_c,V_A_2,V_x_2,T_b] : % 19.07/18.99 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.99 => hAPP(c_Map_Orestrict__map(T_b,T_c,V_m_2,V_A_2),V_x_2) = hAPP(V_m_2,V_x_2) ) % 19.07/18.99 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.99 => hAPP(c_Map_Orestrict__map(T_b,T_c,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_c) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_restrict__map__to__empty,axiom, % 19.07/18.99 ! [V_x_2,V_m_2,T_b,T_c] : hAPP(c_Map_Orestrict__map(T_c,T_b,V_m_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),V_x_2) = c_Option_Ooption_ONone(T_b) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum__constant,axiom, % 19.07/18.99 ! [V_A_2,V_y_2,T_c,T_b] : % 19.07/18.99 ( class_Rings_Osemiring__1(T_b) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(c_COMBK(T_b,T_c),V_y_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(c_Finite__Set_Ocard(T_c),V_A_2))),V_y_2) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum__lessThan__Suc,axiom, % 19.07/18.99 ! [V_n_2,V_f_2,T_b] : % 19.07/18.99 ( class_Groups_Ocomm__monoid__add(T_b) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))),hAPP(V_f_2,V_n_2)) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum__atMost__Suc,axiom, % 19.07/18.99 ! [V_n_2,V_f_2,T_b] : % 19.07/18.99 ( class_Groups_Ocomm__monoid__add(T_b) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2))),hAPP(V_f_2,hAPP(c_Nat_OSuc,V_n_2))) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum_Oinsert,axiom, % 19.07/18.99 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] : % 19.07/18.99 ( class_Groups_Ocomm__monoid__add(T_c) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.99 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum__insert,axiom, % 19.07/18.99 ! [V_f_2,V_a_2,V_F_2,T_b,T_c] : % 19.07/18.99 ( class_Groups_Ocomm__monoid__add(T_c) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 19.07/18.99 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_F_2)) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_F_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_F_2)) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum__Un__Int,axiom, % 19.07/18.99 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 19.07/18.99 ( class_Groups_Ocomm__monoid__add(T_c) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 19.07/18.99 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_B_2)) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum__diff,axiom, % 19.07/18.99 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] : % 19.07/18.99 ( class_Groups_Oab__group__add(T_c) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2)) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum_Oeq__fold,axiom, % 19.07/18.99 ! [V_g_2,V_A_2,T_b,T_c] : % 19.07/18.99 ( class_Groups_Ocomm__monoid__add(T_c) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Oplus__class_Oplus(T_c)),V_g_2),c_Groups_Ozero__class_Ozero(T_c)),V_A_2) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum_OF__eq,axiom, % 19.07/18.99 ! [V_g_2,V_A_2,T_b,T_c] : % 19.07/18.99 ( class_Groups_Ocomm__monoid__add(T_c) % 19.07/18.99 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Oplus__class_Oplus(T_c)),V_g_2),c_Groups_Ozero__class_Ozero(T_c)),V_A_2) ) % 19.07/18.99 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum__shift__lb__Suc0__0__upt,axiom, % 19.07/18.99 ! [V_k_2,V_f_2,T_b] : % 19.07/18.99 ( class_Groups_Ocomm__monoid__add(T_b) % 19.07/18.99 => ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_b) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum__head__upt__Suc,axiom, % 19.07/18.99 ! [V_f_2,V_n_2,V_m_2,T_b] : % 19.07/18.99 ( class_Groups_Ocomm__monoid__add(T_b) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_f_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),V_n_2))) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum__head__Suc,axiom, % 19.07/18.99 ! [V_f_2,V_n_2,V_m_2,T_b] : % 19.07/18.99 ( class_Groups_Ocomm__monoid__add(T_b) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_f_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2),V_n_2))) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum__restrict__set,axiom, % 19.07/18.99 ! [V_B_2,V_f_2,V_A_2,T_b,T_c] : % 19.07/18.99 ( class_Groups_Ocomm__monoid__add(T_c) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_f_2)),c_Groups_Ozero__class_Ozero(T_c))),V_A_2) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_ranI,axiom, % 19.07/18.99 ! [T_c,V_b_2,T_b,V_a_2,V_m_2] : % 19.07/18.99 ( hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_b),V_b_2) % 19.07/18.99 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Map_Oran(T_c,T_b,V_m_2))) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum_Oinsert__remove,axiom, % 19.07/18.99 ! [V_x_2,V_g_2,V_A_2,T_b,T_c] : % 19.07/18.99 ( class_Groups_Ocomm__monoid__add(T_c) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum__Un__disjoint,axiom, % 19.07/18.99 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 19.07/18.99 ( class_Groups_Ocomm__monoid__add(T_c) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 19.07/18.99 => ( 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)) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_B_2)) ) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum__Un,axiom, % 19.07/18.99 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] : % 19.07/18.99 ( class_Groups_Oab__group__add(T_c) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum__op__ivl__Suc,axiom, % 19.07/18.99 ! [V_f_2,V_m_2,V_n_2,T_b] : % 19.07/18.99 ( class_Groups_Ocomm__monoid__add(T_b) % 19.07/18.99 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2))) = c_Groups_Ozero__class_Ozero(T_b) ) % 19.07/18.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2))),hAPP(V_f_2,V_n_2)) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum__cl__ivl__Suc,axiom, % 19.07/18.99 ! [V_f_2,V_m_2,V_n_2,T_b] : % 19.07/18.99 ( class_Groups_Ocomm__monoid__add(T_b) % 19.07/18.99 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))) = c_Groups_Ozero__class_Ozero(T_b) ) % 19.07/18.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2))),hAPP(V_f_2,hAPP(c_Nat_OSuc,V_n_2))) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum__head,axiom, % 19.07/18.99 ! [V_Pa_2,V_n_2,V_m_2,T_b] : % 19.07/18.99 ( class_Groups_Ocomm__monoid__add(T_b) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_Pa_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_Pa_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_Pa_2),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_m_2,V_n_2))) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum__ub__add__nat,axiom, % 19.07/18.99 ! [V_p_2,V_f_2,V_n_2,V_m_2,T_b] : % 19.07/18.99 ( class_Groups_Ocomm__monoid__add(T_b) % 19.07/18.99 => ( 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)))) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_p_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_p_2)))) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_fun__upd__restrict,axiom, % 19.07/18.99 ! [V_y_2,V_x_2,V_D_2,V_m_2,T_c,T_b] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Orestrict__map(T_b,T_c,V_m_2,V_D_2)),V_x_2),V_y_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Orestrict__map(T_b,T_c,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),V_x_2),V_y_2) ). % 19.07/18.99 % 19.07/18.99 fof(fact_ran__empty,axiom, % 19.07/18.99 ! [T_b,T_c] : c_Map_Oran(T_c,T_b,hAPP(c_COMBK(tc_Option_Ooption(T_b),T_c),c_Option_Ooption_ONone(T_b))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum__diff1_H,axiom, % 19.07/18.99 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] : % 19.07/18.99 ( class_Groups_Ocomm__monoid__add(T_c) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum_Oremove,axiom, % 19.07/18.99 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] : % 19.07/18.99 ( class_Groups_Ocomm__monoid__add(T_c) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum__diff1__ring,axiom, % 19.07/18.99 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] : % 19.07/18.99 ( class_Rings_Oring(T_c) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum__diff1,axiom, % 19.07/18.99 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] : % 19.07/18.99 ( class_Groups_Oab__group__add(T_c) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.99 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) ) % 19.07/18.99 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2) ) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_geometric__sum,axiom, % 19.07/18.99 ! [V_n_2,V_x_2,T_b] : % 19.07/18.99 ( class_Fields_Ofield(T_b) % 19.07/18.99 => ( V_x_2 != c_Groups_Oone__class_Oone(T_b) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(c_Power_Opower__class_Opower(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),V_n_2)),c_Groups_Oone__class_Oone(T_b))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_x_2),c_Groups_Oone__class_Oone(T_b))) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_gauss__sum,axiom, % 19.07/18.99 ! [V_n_2,T_b] : % 19.07/18.99 ( class_Rings_Ocomm__semiring__1(T_b) % 19.07/18.99 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Oone__class_Oone(T_b)),c_Groups_Oone__class_Oone(T_b))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),c_Nat_Osemiring__1__class_Oof__nat(T_b)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),c_Groups_Oone__class_Oone(T_b))) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum__natinterval__difff,axiom, % 19.07/18.99 ! [V_f_2,V_n_2,V_m_2,T_b] : % 19.07/18.99 ( class_Groups_Oab__group__add(T_b) % 19.07/18.99 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(V_f_2,V_m_2)),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) % 19.07/18.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_fun__upd__restrict__conv,axiom, % 19.07/18.99 ! [V_y_2,V_m_2,T_c,V_D_2,V_x_2,T_b] : % 19.07/18.99 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2)) % 19.07/18.99 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Orestrict__map(T_b,T_c,V_m_2,V_D_2)),V_x_2),V_y_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Orestrict__map(T_b,T_c,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),V_x_2),V_y_2) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_restrict__fun__upd,axiom, % 19.07/18.99 ! [V_y_2,V_m_2,T_c,V_D_2,V_x_2,T_b] : % 19.07/18.99 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2)) % 19.07/18.99 => c_Map_Orestrict__map(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_m_2),V_x_2),V_y_2),V_D_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Orestrict__map(T_b,T_c,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),V_x_2),V_y_2) ) % 19.07/18.99 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2)) % 19.07/18.99 => c_Map_Orestrict__map(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_m_2),V_x_2),V_y_2),V_D_2) = c_Map_Orestrict__map(T_b,T_c,V_m_2,V_D_2) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_restrict__complement__singleton__eq,axiom, % 19.07/18.99 ! [V_x_2,V_f_2,T_c,T_b] : c_Map_Orestrict__map(T_b,T_c,V_f_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_f_2),V_x_2),c_Option_Ooption_ONone(T_c)) ). % 19.07/18.99 % 19.07/18.99 fof(fact_restrict__upd__same,axiom, % 19.07/18.99 ! [V_y_2,V_x_2,V_m_2,T_c,T_b] : c_Map_Orestrict__map(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_m_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = c_Map_Orestrict__map(T_b,T_c,V_m_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) ). % 19.07/18.99 % 19.07/18.99 fof(fact_arith__series__general,axiom, % 19.07/18.99 ! [V_n_2,V_d_2,V_a_2,T_b] : % 19.07/18.99 ( class_Rings_Ocomm__semiring__1(T_b) % 19.07/18.99 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Oone__class_Oone(T_b)),c_Groups_Oone__class_Oone(T_b))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(T_b)),c_Nat_Osemiring__1__class_Oof__nat(T_b))),V_d_2))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_d_2)))) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum__mono2,axiom, % 19.07/18.99 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] : % 19.07/18.99 ( class_Groups_Oordered__comm__monoid__add(T_c) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 19.07/18.99 => ( ! [B_b] : % 19.07/18.99 ( hBOOL(hAPP(hAPP(c_member(T_b),B_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))) % 19.07/18.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_b))) ) % 19.07/18.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2))) ) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum__bounded,axiom, % 19.07/18.99 ! [V_K_2,V_f_2,V_A_2,T_b,T_c] : % 19.07/18.99 ( ( class_Groups_Oordered__ab__semigroup__add(T_c) % 19.07/18.99 & class_Rings_Osemiring__1(T_c) ) % 19.07/18.99 => ( ! [B_i] : % 19.07/18.99 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_A_2)) % 19.07/18.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_i)),V_K_2)) ) % 19.07/18.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))),V_K_2))) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum_Ounion__inter__neutral,axiom, % 19.07/18.99 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 19.07/18.99 ( class_Groups_Ocomm__monoid__add(T_c) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 19.07/18.99 => ( ! [B_x] : % 19.07/18.99 ( 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))) % 19.07/18.99 => hAPP(V_g_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_B_2)) ) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum__eq__0__iff,axiom, % 19.07/18.99 ! [V_f_2,V_F_2,T_b] : % 19.07/18.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 19.07/18.99 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_F_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 19.07/18.99 <=> ! [B_x] : % 19.07/18.99 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2)) % 19.07/18.99 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_card__eq__setsum,axiom, % 19.07/18.99 ! [V_A_2,T_b] : hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,T_b),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_A_2) ). % 19.07/18.99 % 19.07/18.99 fof(fact_int__setsum,axiom, % 19.07/18.99 ! [V_A_2,V_f_2,T_b] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum__eq__Suc0__iff,axiom, % 19.07/18.99 ! [V_f_2,V_A_2,T_b] : % 19.07/18.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.99 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 19.07/18.99 <=> ? [B_x] : % 19.07/18.99 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 19.07/18.99 & hAPP(V_f_2,B_x) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 19.07/18.99 & ! [B_xa] : % 19.07/18.99 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2)) % 19.07/18.99 => ( B_x != B_xa % 19.07/18.99 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum__eq__1__iff,axiom, % 19.07/18.99 ! [V_f_2,V_A_2,T_b] : % 19.07/18.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.99 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 19.07/18.99 <=> ? [B_x] : % 19.07/18.99 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 19.07/18.99 & hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 19.07/18.99 & ! [B_xa] : % 19.07/18.99 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2)) % 19.07/18.99 => ( B_x != B_xa % 19.07/18.99 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum__shift__lb__Suc0__0,axiom, % 19.07/18.99 ! [V_k_2,V_f_2] : % 19.07/18.99 ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 19.07/18.99 => 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)) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_transfer__nat__int__sum__prod2_I1_J,axiom, % 19.07/18.99 ! [V_A_2,V_f_2,T_b] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2)) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum__diff__nat,axiom, % 19.07/18.99 ! [V_f_2,V_A_2,V_B_2,T_b] : % 19.07/18.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_B_2)) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_transfer__nat__int__sum__prod_I1_J,axiom, % 19.07/18.99 ! [V_A_2,V_f_2,T_b] : % 19.07/18.99 ( ( class_Groups_Ocomm__monoid__add(T_b) % 19.07/18.99 & class_Groups_Ocomm__monoid__mult(T_b) ) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),V_f_2),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum__diff1__nat,axiom, % 19.07/18.99 ! [V_f_2,V_A_2,V_a_2,T_b] : % 19.07/18.99 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) ) % 19.07/18.99 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum__Un__nat,axiom, % 19.07/18.99 ! [V_f_2,V_B_2,V_A_2,T_b] : % 19.07/18.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_transfer__int__nat__sum__prod_I1_J,axiom, % 19.07/18.99 ! [V_f_2,V_A_2,T_b] : % 19.07/18.99 ( ( class_Groups_Ocomm__monoid__add(T_b) % 19.07/18.99 & class_Groups_Ocomm__monoid__mult(T_b) ) % 19.07/18.99 => ( c_Nat__Transfer_Onat__set(V_A_2) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_b,tc_Nat_Onat),V_f_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_arith__series__nat,axiom, % 19.07/18.99 ! [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)))) ). % 19.07/18.99 % 19.07/18.99 fof(fact_transfer__int__nat__sum__prod2_I1_J,axiom, % 19.07/18.99 ! [V_f_2,V_A_2,T_b] : % 19.07/18.99 ( ! [B_x] : % 19.07/18.99 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 19.07/18.99 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) ) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Int_Oint),V_f_2),V_A_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,T_b),c_Int_Onat),V_f_2)),V_A_2)) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum__Un__zero,axiom, % 19.07/18.99 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] : % 19.07/18.99 ( class_Groups_Ocomm__monoid__add(T_c) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 19.07/18.99 => ( ! [B_x] : % 19.07/18.99 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))) % 19.07/18.99 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_S_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_T_2)) ) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum__mono3,axiom, % 19.07/18.99 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] : % 19.07/18.99 ( ( class_Groups_Ocomm__monoid__add(T_c) % 19.07/18.99 & class_Groups_Oordered__ab__semigroup__add(T_c) ) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 19.07/18.99 => ( ! [B_x] : % 19.07/18.99 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))) % 19.07/18.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) ) % 19.07/18.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2))) ) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum__nonneg__leq__bound,axiom, % 19.07/18.99 ! [V_i_2,V_B_2,V_f_2,V_s_2,T_b,T_c] : % 19.07/18.99 ( class_Groups_Oordered__ab__group__add(T_c) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2)) % 19.07/18.99 => ( ! [B_i] : % 19.07/18.99 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2)) % 19.07/18.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))) ) % 19.07/18.99 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_s_2) = V_B_2 % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2)) % 19.07/18.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_i_2)),V_B_2)) ) ) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum__nonneg__0,axiom, % 19.07/18.99 ! [V_i_2,V_f_2,V_s_2,T_b,T_c] : % 19.07/18.99 ( class_Groups_Oordered__ab__group__add(T_c) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2)) % 19.07/18.99 => ( ! [B_i] : % 19.07/18.99 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2)) % 19.07/18.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))) ) % 19.07/18.99 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_s_2) = c_Groups_Ozero__class_Ozero(T_c) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2)) % 19.07/18.99 => hAPP(V_f_2,V_i_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_sum__diff__distrib,axiom, % 19.07/18.99 ! [V_n_2,V_Pa_2,V_Qa_2] : % 19.07/18.99 ( ! [B_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_Qa_2,B_x)),hAPP(V_Pa_2,B_x))) % 19.07/18.99 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_Pa_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_Qa_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_Pa_2)),V_Qa_2)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2)) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum__mono__zero__right,axiom, % 19.07/18.99 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] : % 19.07/18.99 ( class_Groups_Ocomm__monoid__add(T_c) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) % 19.07/18.99 => ( ! [B_x] : % 19.07/18.99 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2))) % 19.07/18.99 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_T_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_S_2) ) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum__mono__zero__left,axiom, % 19.07/18.99 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] : % 19.07/18.99 ( class_Groups_Ocomm__monoid__add(T_c) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) % 19.07/18.99 => ( ! [B_x] : % 19.07/18.99 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2))) % 19.07/18.99 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_T_2) ) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_folding__one__idem_Ounion__idem,axiom, % 19.07/18.99 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] : % 19.07/18.99 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 19.07/18.99 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.99 => 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)) ) ) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_folding__one__idem_Oidem,axiom, % 19.07/18.99 ! [V_x_2,V_F_2,V_f_2,T_b] : % 19.07/18.99 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) % 19.07/18.99 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_folding__one__idem_Oin__idem,axiom, % 19.07/18.99 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] : % 19.07/18.99 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.99 => hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_folding__one__idem_Oinsert__idem,axiom, % 19.07/18.99 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] : % 19.07/18.99 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.99 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_folding__one__idem_Osubset__idem,axiom, % 19.07/18.99 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] : % 19.07/18.99 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.99 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 19.07/18.99 => 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) ) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_finite__subset__induct,axiom, % 19.07/18.99 ! [V_Pa_2,V_A_2,V_F_2,T_b] : % 19.07/18.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_A_2)) % 19.07/18.99 => ( hBOOL(hAPP(V_Pa_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) % 19.07/18.99 => ( ! [B_a,B_F] : % 19.07/18.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_F)) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2)) % 19.07/18.99 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_F)) % 19.07/18.99 => ( hBOOL(hAPP(V_Pa_2,B_F)) % 19.07/18.99 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_F))) ) ) ) ) % 19.07/18.99 => hBOOL(hAPP(V_Pa_2,V_F_2)) ) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum__strict__mono,axiom, % 19.07/18.99 ! [V_g_2,V_f_2,V_A_2,T_b,T_c] : % 19.07/18.99 ( ( class_Groups_Ocomm__monoid__add(T_c) % 19.07/18.99 & class_Groups_Oordered__cancel__ab__semigroup__add(T_c) ) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.99 => ( ! [B_x] : % 19.07/18.99 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 19.07/18.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 19.07/18.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2))) ) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_atMost__Int__atLeast,axiom, % 19.07/18.99 ! [V_n_2,T_b] : % 19.07/18.99 ( class_Orderings_Oorder(T_b) % 19.07/18.99 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_n_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_n_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_n_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_atLeast__eq__iff,axiom, % 19.07/18.99 ! [V_y_2,V_x_2,T_b] : % 19.07/18.99 ( class_Orderings_Olinorder(T_b) % 19.07/18.99 => ( hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_y_2) % 19.07/18.99 <=> V_x_2 = V_y_2 ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_atLeast__iff,axiom, % 19.07/18.99 ! [V_k_2,V_i_2,T_b] : % 19.07/18.99 ( class_Orderings_Oord(T_b) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2))) % 19.07/18.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_k_2),V_i_2)) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_atLeast__subset__iff,axiom, % 19.07/18.99 ! [V_y_2,V_x_2,T_b] : % 19.07/18.99 ( class_Orderings_Oorder(T_b) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_y_2))) % 19.07/18.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_Compl__atLeast,axiom, % 19.07/18.99 ! [V_k_2,T_b] : % 19.07/18.99 ( class_Orderings_Olinorder(T_b) % 19.07/18.99 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_Compl__lessThan,axiom, % 19.07/18.99 ! [V_k_2,T_b] : % 19.07/18.99 ( class_Orderings_Olinorder(T_b) % 19.07/18.99 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_ivl__disj__un_I14_J,axiom, % 19.07/18.99 ! [V_u_2,V_l_2,T_b] : % 19.07/18.99 ( class_Orderings_Olinorder(T_b) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) % 19.07/18.99 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_l_2) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_ivl__disj__int_I8_J,axiom, % 19.07/18.99 ! [V_u_2,V_l_2,T_b] : % 19.07/18.99 ( class_Orderings_Oorder(T_b) % 19.07/18.99 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_Int__atLeastAtMostR2,axiom, % 19.07/18.99 ! [V_d_2,V_c_2,V_a_2,T_b] : % 19.07/18.99 ( class_Orderings_Olinorder(T_b) % 19.07/18.99 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_a_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),V_d_2) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_Int__atLeastAtMostL2,axiom, % 19.07/18.99 ! [V_c_2,V_b_2,V_a_2,T_b] : % 19.07/18.99 ( class_Orderings_Olinorder(T_b) % 19.07/18.99 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_c_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),V_b_2) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_ivl__disj__int_I6_J,axiom, % 19.07/18.99 ! [V_u_2,V_l_2,T_b] : % 19.07/18.99 ( class_Orderings_Oorder(T_b) % 19.07/18.99 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_image__uminus__atLeast,axiom, % 19.07/18.99 ! [V_x_2,T_b] : % 19.07/18.99 ( class_Groups_Oordered__ab__group__add(T_b) % 19.07/18.99 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_image__uminus__atMost,axiom, % 19.07/18.99 ! [V_x_2,T_b] : % 19.07/18.99 ( class_Groups_Oordered__ab__group__add(T_b) % 19.07/18.99 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_atLeast__Suc,axiom, % 19.07/18.99 ! [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)))) ). % 19.07/18.99 % 19.07/18.99 fof(fact_ivl__disj__un_I12_J,axiom, % 19.07/18.99 ! [V_u_2,V_l_2,T_b] : % 19.07/18.99 ( class_Orderings_Olinorder(T_b) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2)) % 19.07/18.99 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_l_2) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_ivl__disj__un_I13_J,axiom, % 19.07/18.99 ! [V_u_2,V_l_2,T_b] : % 19.07/18.99 ( class_Orderings_Olinorder(T_b) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) % 19.07/18.99 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_l_2) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_ivl__disj__un_I1_J,axiom, % 19.07/18.99 ! [V_l_2,T_b] : % 19.07/18.99 ( class_Orderings_Olinorder(T_b) % 19.07/18.99 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_l_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_l_2) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_atLeast__Suc__greaterThan,axiom, % 19.07/18.99 ! [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) ). % 19.07/18.99 % 19.07/18.99 fof(fact_greaterThan__eq__iff,axiom, % 19.07/18.99 ! [V_y_2,V_x_2,T_b] : % 19.07/18.99 ( class_Orderings_Olinorder(T_b) % 19.07/18.99 => ( hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_y_2) % 19.07/18.99 <=> V_x_2 = V_y_2 ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_greaterThan__iff,axiom, % 19.07/18.99 ! [V_k_2,V_i_2,T_b] : % 19.07/18.99 ( class_Orderings_Oord(T_b) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2))) % 19.07/18.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_i_2)) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_greaterThan__subset__iff,axiom, % 19.07/18.99 ! [V_y_2,V_x_2,T_b] : % 19.07/18.99 ( class_Orderings_Olinorder(T_b) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_y_2))) % 19.07/18.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_Compl__greaterThan,axiom, % 19.07/18.99 ! [V_k_2,T_b] : % 19.07/18.99 ( class_Orderings_Olinorder(T_b) % 19.07/18.99 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_Compl__atMost,axiom, % 19.07/18.99 ! [V_k_2,T_b] : % 19.07/18.99 ( class_Orderings_Olinorder(T_b) % 19.07/18.99 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_ivl__disj__int_I7_J,axiom, % 19.07/18.99 ! [V_u_2,V_l_2,T_b] : % 19.07/18.99 ( class_Orderings_Oorder(T_b) % 19.07/18.99 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_ivl__disj__un_I11_J,axiom, % 19.07/18.99 ! [V_u_2,V_l_2,T_b] : % 19.07/18.99 ( class_Orderings_Olinorder(T_b) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) % 19.07/18.99 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_l_2) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_image__uminus__greaterThan,axiom, % 19.07/18.99 ! [V_x_2,T_b] : % 19.07/18.99 ( class_Groups_Oordered__ab__group__add(T_b) % 19.07/18.99 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_image__uminus__lessThan,axiom, % 19.07/18.99 ! [V_x_2,T_b] : % 19.07/18.99 ( class_Groups_Oordered__ab__group__add(T_b) % 19.07/18.99 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_ivl__disj__int_I5_J,axiom, % 19.07/18.99 ! [V_u_2,V_l_2,T_b] : % 19.07/18.99 ( class_Orderings_Oorder(T_b) % 19.07/18.99 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_greaterThan__Suc,axiom, % 19.07/18.99 ! [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)))) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum__Plus,axiom, % 19.07/18.99 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] : % 19.07/18.99 ( class_Groups_Ocomm__monoid__add(T_d) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_sum(T_b,T_c),T_d),V_f_2),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(c_Fun_Ocomp(tc_sum(T_b,T_c),T_d,T_b,V_f_2),c_Sum__Type_OInl(T_b,T_c))),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),hAPP(c_Fun_Ocomp(tc_sum(T_b,T_c),T_d,T_c,V_f_2),c_Sum__Type_OInr(T_c,T_b))),V_B_2)) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_transfer__nat__int__sum__prod__cong_I2_J,axiom, % 19.07/18.99 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] : % 19.07/18.99 ( ( class_Groups_Ocomm__monoid__add(T_b) % 19.07/18.99 & class_Groups_Ocomm__monoid__mult(T_b) ) % 19.07/18.99 => ( V_A_2 = V_B_2 % 19.07/18.99 => ( c_Nat__Transfer_Onat__set(V_B_2) % 19.07/18.99 => ( ! [B_x] : % 19.07/18.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 19.07/18.99 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_b),V_g_2),V_B_2) ) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_dom__eq__singleton__conv,axiom, % 19.07/18.99 ! [V_x_2,V_f_2,T_c,T_b] : % 19.07/18.99 ( c_Map_Odom(T_b,T_c,V_f_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) % 19.07/18.99 <=> ? [B_v] : V_f_2 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),hAPP(c_COMBK(tc_Option_Ooption(T_c),T_b),c_Option_Ooption_ONone(T_c))),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),B_v)) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_o__assoc,axiom, % 19.07/18.99 ! [V_h_2,V_g_2,T_e,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),hAPP(c_Fun_Ocomp(T_e,T_d,T_b,V_g_2),V_h_2)) = hAPP(c_Fun_Ocomp(T_e,T_c,T_b,hAPP(c_Fun_Ocomp(T_d,T_c,T_e,V_f_2),V_g_2)),V_h_2) ). % 19.07/18.99 % 19.07/18.99 fof(fact_o__apply,axiom, % 19.07/18.99 ! [V_x_2,V_g_2,V_f_2,T_d,T_b,T_c] : hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2),V_x_2) = hAPP(V_f_2,hAPP(V_g_2,V_x_2)) ). % 19.07/18.99 % 19.07/18.99 fof(fact_o__eq__dest,axiom, % 19.07/18.99 ! [V_v_2,V_d_2,V_c_2,T_e,V_b_2,V_a_2,T_b,T_c,T_d] : % 19.07/18.99 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_e,T_c,T_b,V_c_2),V_d_2) % 19.07/18.99 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,hAPP(V_d_2,V_v_2)) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_o__eq__elim,axiom, % 19.07/18.99 ! [V_d_2,V_c_2,T_e,V_b_2,V_a_2,T_b,T_c,T_d] : % 19.07/18.99 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_e,T_c,T_b,V_c_2),V_d_2) % 19.07/18.99 => ! [B_v] : hAPP(V_a_2,hAPP(V_b_2,B_v)) = hAPP(V_c_2,hAPP(V_d_2,B_v)) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_o__def,axiom, % 19.07/18.99 ! [V_x_2,V_g_2,V_f_2,T_d,T_b,T_c] : hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2),V_x_2) = hAPP(V_f_2,hAPP(V_g_2,V_x_2)) ). % 19.07/18.99 % 19.07/18.99 fof(fact_comp__cong,axiom, % 19.07/18.99 ! [T_f,T_e,T_d,T_b,T_c,V_x_H_2,V_g_H_2,V_f_H_2,V_x_2,V_g_2,V_f_2] : % 19.07/18.99 ( 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)) % 19.07/18.99 => hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Fun_Ocomp(T_e,T_b,T_f,V_f_H_2),V_g_H_2),V_x_H_2) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_apfst__compose,axiom, % 19.07/18.99 ! [V_x_2,V_g_2,T_e,V_f_2,T_c,T_b,T_d] : hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),hAPP(c_Product__Type_Oapfst(T_e,T_d,T_c,V_g_2),V_x_2)) = hAPP(c_Product__Type_Oapfst(T_e,T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_b,T_e,V_f_2),V_g_2)),V_x_2) ). % 19.07/18.99 % 19.07/18.99 fof(fact_apsnd__compose,axiom, % 19.07/18.99 ! [V_x_2,V_g_2,T_e,V_f_2,T_b,T_c,T_d] : hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(c_Product__Type_Oapsnd(T_e,T_d,T_b,V_g_2),V_x_2)) = hAPP(c_Product__Type_Oapsnd(T_e,T_c,T_b,hAPP(c_Fun_Ocomp(T_d,T_c,T_e,V_f_2),V_g_2)),V_x_2) ). % 19.07/18.99 % 19.07/18.99 fof(fact_finite__dom__body,axiom, % 19.07/18.99 hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))) ). % 19.07/18.99 % 19.07/18.99 fof(fact_inj__on__imageI2,axiom, % 19.07/18.99 ! [V_A_2,V_f_2,V_f_H_2,T_d,T_c,T_b] : % 19.07/18.99 ( c_Fun_Oinj__on(T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_H_2),V_f_2),V_A_2) % 19.07/18.99 => c_Fun_Oinj__on(T_b,T_d,V_f_2,V_A_2) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_fun__upd__comp,axiom, % 19.07/18.99 ! [V_y_2,V_x_2,V_g_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_d),V_g_2),V_x_2),V_y_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),V_g_2)),V_x_2),hAPP(V_f_2,V_y_2)) ). % 19.07/18.99 % 19.07/18.99 fof(fact_image__compose,axiom, % 19.07/18.99 ! [V_r_2,V_g_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,hAPP(c_Fun_Ocomp(T_d,T_b,T_c,V_f_2),V_g_2)),V_r_2) = hAPP(c_Set_Oimage(T_d,T_b,V_f_2),hAPP(c_Set_Oimage(T_c,T_d,V_g_2),V_r_2)) ). % 19.07/18.99 % 19.07/18.99 fof(fact_inj__on__imageI,axiom, % 19.07/18.99 ! [V_A_2,V_f_2,V_g_2,T_d,T_c,T_b] : % 19.07/18.99 ( c_Fun_Oinj__on(T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_g_2),V_f_2),V_A_2) % 19.07/18.99 => c_Fun_Oinj__on(T_d,T_c,V_g_2,hAPP(c_Set_Oimage(T_b,T_d,V_f_2),V_A_2)) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_comp__inj__on,axiom, % 19.07/18.99 ! [V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] : % 19.07/18.99 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 19.07/18.99 => ( c_Fun_Oinj__on(T_c,T_d,V_g_2,hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) % 19.07/18.99 => c_Fun_Oinj__on(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_g_2),V_f_2),V_A_2) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_comp__inj__on__iff,axiom, % 19.07/18.99 ! [V_f_H_2,T_d,V_A_2,V_f_2,T_c,T_b] : % 19.07/18.99 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 19.07/18.99 => ( c_Fun_Oinj__on(T_c,T_d,V_f_H_2,hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) % 19.07/18.99 <=> c_Fun_Oinj__on(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_f_H_2),V_f_2),V_A_2) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_domIff,axiom, % 19.07/18.99 ! [V_m_2,T_c,V_a_2,T_b] : % 19.07/18.99 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Map_Odom(T_b,T_c,V_m_2))) % 19.07/18.99 <=> hAPP(V_m_2,V_a_2) != c_Option_Ooption_ONone(T_c) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_domI,axiom, % 19.07/18.99 ! [T_c,V_b_2,T_b,V_a_2,V_m_2] : % 19.07/18.99 ( hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_b),V_b_2) % 19.07/18.99 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),c_Map_Odom(T_c,T_b,V_m_2))) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_insert__dom,axiom, % 19.07/18.99 ! [T_c,V_y_2,T_b,V_x_2,V_f_2] : % 19.07/18.99 ( hAPP(V_f_2,V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2) % 19.07/18.99 => hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Map_Odom(T_c,T_b,V_f_2)) = c_Map_Odom(T_c,T_b,V_f_2) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_dom__restrict,axiom, % 19.07/18.99 ! [V_A_2,V_m_2,T_c,T_b] : c_Map_Odom(T_b,T_c,c_Map_Orestrict__map(T_b,T_c,V_m_2,V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_c,V_m_2)),V_A_2) ). % 19.07/18.99 % 19.07/18.99 fof(fact_dom__empty,axiom, % 19.07/18.99 ! [T_c,T_b] : c_Map_Odom(T_b,T_c,hAPP(c_COMBK(tc_Option_Ooption(T_c),T_b),c_Option_Ooption_ONone(T_c))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 19.07/18.99 % 19.07/18.99 fof(fact_dom__eq__empty__conv,axiom, % 19.07/18.99 ! [V_f_2,T_c,T_b] : % 19.07/18.99 ( c_Map_Odom(T_b,T_c,V_f_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.99 <=> V_f_2 = hAPP(c_COMBK(tc_Option_Ooption(T_c),T_b),c_Option_Ooption_ONone(T_c)) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum__reindex,axiom, % 19.07/18.99 ! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] : % 19.07/18.99 ( class_Groups_Ocomm__monoid__add(T_d) % 19.07/18.99 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_h_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)),V_B_2) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setprod__reindex__cong,axiom, % 19.07/18.99 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] : % 19.07/18.99 ( class_Groups_Ocomm__monoid__mult(T_d) % 19.07/18.99 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 19.07/18.99 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) % 19.07/18.99 => ( V_g_2 = hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_d),V_g_2),V_A_2) ) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setprod__reindex,axiom, % 19.07/18.99 ! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] : % 19.07/18.99 ( class_Groups_Ocomm__monoid__mult(T_d) % 19.07/18.99 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_h_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_d),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)),V_B_2) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_dom__minus,axiom, % 19.07/18.99 ! [V_A_2,T_c,T_b,V_x_2,V_f_2] : % 19.07/18.99 ( hAPP(V_f_2,V_x_2) = c_Option_Ooption_ONone(T_b) % 19.07/18.99 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),c_Map_Odom(T_c,T_b,V_f_2)),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),c_Map_Odom(T_c,T_b,V_f_2)),V_A_2) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum_Oreindex,axiom, % 19.07/18.99 ! [V_g_2,V_h_2,V_A_2,T_b,T_c] : % 19.07/18.99 ( class_Groups_Ocomm__monoid__add(T_c) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.99 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(c_Fun_Ocomp(T_b,T_c,T_b,V_g_2),V_h_2)),V_A_2) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setprod_Oreindex,axiom, % 19.07/18.99 ! [V_g_2,V_h_2,V_A_2,T_b,T_c] : % 19.07/18.99 ( class_Groups_Ocomm__monoid__mult(T_c) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.99 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(c_Fun_Ocomp(T_b,T_c,T_b,V_g_2),V_h_2)),V_A_2) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_the__inv__into__comp,axiom, % 19.07/18.99 ! [V_x_2,V_A_2,V_g_2,T_d,V_f_2,T_c,T_b] : % 19.07/18.99 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2)) % 19.07/18.99 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,V_A_2) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2)))) % 19.07/18.99 => hAPP(c_Fun_Othe__inv__into(T_d,T_c,V_A_2,hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_2),V_g_2)),V_x_2) = hAPP(hAPP(c_Fun_Ocomp(T_b,T_d,T_c,c_Fun_Othe__inv__into(T_d,T_b,V_A_2,V_g_2)),c_Fun_Othe__inv__into(T_b,T_c,hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2),V_f_2)),V_x_2) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_fold__image__reindex,axiom, % 19.07/18.99 ! [V_z_2,V_g_2,V_h_2,T_c,V_A_2,T_b,T_d] : % 19.07/18.99 ( class_Groups_Oab__semigroup__mult(T_d) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.99 => ( c_Fun_Oinj__on(T_b,T_c,V_h_2,V_A_2) % 19.07/18.99 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d)),V_g_2),V_z_2),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_A_2)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_b,c_Groups_Otimes__class_Otimes(T_d)),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_g_2),V_h_2)),V_z_2),V_A_2) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_dom__fun__upd,axiom, % 19.07/18.99 ! [V_x_2,V_f_2,T_c,T_b,V_y_2] : % 19.07/18.99 ( ( V_y_2 = c_Option_Ooption_ONone(T_b) % 19.07/18.99 => c_Map_Odom(T_c,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),V_f_2),V_x_2),V_y_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),c_Map_Odom(T_c,T_b,V_f_2)),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) ) % 19.07/18.99 & ( V_y_2 != c_Option_Ooption_ONone(T_b) % 19.07/18.99 => c_Map_Odom(T_c,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),V_f_2),V_x_2),V_y_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Map_Odom(T_c,T_b,V_f_2)) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_folding_Oremove,axiom, % 19.07/18.99 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 19.07/18.99 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.99 => hAPP(V_F_2,V_A_2) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(V_f_2,V_x_2)) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_folding__image_Oreindex,axiom, % 19.07/18.99 ! [V_g_2,V_h_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] : % 19.07/18.99 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 19.07/18.99 => ( c_Fun_Oinj__on(T_c,T_c,V_h_2,V_A_2) % 19.07/18.99 => hAPP(hAPP(V_F_2,V_g_2),hAPP(c_Set_Oimage(T_c,T_c,V_h_2),V_A_2)) = hAPP(hAPP(V_F_2,hAPP(c_Fun_Ocomp(T_c,T_b,T_c,V_g_2),V_h_2)),V_A_2) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_folding_Ounion,axiom, % 19.07/18.99 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 19.07/18.99 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 19.07/18.99 => ( 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)) % 19.07/18.99 => 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(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_folding_Ocommute__comps_I1_J,axiom, % 19.07/18.99 ! [V_h_2,V_g_2,T_g,V_f_2,T_d,T_e,T_f,V_F_2,V_fa_2,T_c,T_b] : % 19.07/18.99 ( c_Finite__Set_Ofolding(T_b,T_c,V_fa_2,V_F_2) % 19.07/18.99 => hAPP(c_Fun_Ocomp(T_f,T_e,T_d,V_f_2),hAPP(c_Fun_Ocomp(T_g,T_f,T_d,V_g_2),V_h_2)) = hAPP(c_Fun_Ocomp(T_g,T_e,T_d,hAPP(c_Fun_Ocomp(T_f,T_e,T_g,V_f_2),V_g_2)),V_h_2) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_folding_Ocommute__comp,axiom, % 19.07/18.99 ! [V_x_2,V_y_2,V_F_2,V_f_2,T_c,T_b] : % 19.07/18.99 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 19.07/18.99 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_y_2)),hAPP(V_f_2,V_x_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_folding_Ocommute__left__comp,axiom, % 19.07/18.99 ! [V_g_2,V_x_2,V_y_2,T_d,V_F_2,V_f_2,T_c,T_b] : % 19.07/18.99 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 19.07/18.99 => hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_y_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_y_2)),V_g_2)) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_UN__o,axiom, % 19.07/18.99 ! [V_f_2,V_g_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Fun_Ocomp(T_d,tc_fun(T_b,tc_HOL_Obool),T_c,V_g_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),V_g_2) ). % 19.07/18.99 % 19.07/18.99 fof(fact_folding__image_Odistrib,axiom, % 19.07/18.99 ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] : % 19.07/18.99 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 19.07/18.99 => hAPP(hAPP(V_F_2,hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),V_f_2),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(V_f_2,hAPP(hAPP(V_F_2,V_g_2),V_A_2)),hAPP(hAPP(V_F_2,V_h_2),V_A_2)) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_split__comp,axiom, % 19.07/18.99 ! [V_x_2,V_g_2,V_f_2,T_e,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),hAPP(c_Fun_Ocomp(T_e,tc_fun(T_d,T_b),T_c,V_f_2),V_g_2)),V_x_2) = hAPP(hAPP(V_f_2,hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_x_2))),hAPP(c_Product__Type_Osnd(T_c,T_d),V_x_2)) ). % 19.07/18.99 % 19.07/18.99 fof(fact_folding_Ocommute__left__comp_H_H,axiom, % 19.07/18.99 ! [V_g_2,T_d,V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 19.07/18.99 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 19.07/18.99 => hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_B_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_A_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_A_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_B_2)),V_g_2)) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_folding_Ocommute__comp_H_H,axiom, % 19.07/18.99 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 19.07/18.99 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 19.07/18.99 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_B_2)),hAPP(V_F_2,V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_folding_Ocommute__left__comp_H,axiom, % 19.07/18.99 ! [V_g_2,V_x_2,T_d,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 19.07/18.99 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.99 => hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_A_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_A_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),V_g_2)) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_folding_Ocommute__comp_H,axiom, % 19.07/18.99 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 19.07/18.99 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.99 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_F_2,V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_number__of__code__numeral__def,axiom, % 19.07/18.99 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) ). % 19.07/18.99 % 19.07/18.99 fof(fact_int__of__def,axiom, % 19.07/18.99 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) ). % 19.07/18.99 % 19.07/18.99 fof(fact_folding__image_Oeq__fold,axiom, % 19.07/18.99 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] : % 19.07/18.99 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 19.07/18.99 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),V_A_2) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_folding_Oinsert,axiom, % 19.07/18.99 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 19.07/18.99 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.99 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.99 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_folding_Ounion__inter,axiom, % 19.07/18.99 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 19.07/18.99 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 19.07/18.99 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_folding_Oinsert__remove,axiom, % 19.07/18.99 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 19.07/18.99 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.99 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(V_f_2,V_x_2)) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_hoare__derivs_OIf,axiom, % 19.07/18.99 ! [V_d_2,V_Qa_2,V_c_2,V_b_2,V_Pa_2,V_G_2,T_b] : % 19.07/18.99 ( 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),c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,V_b_2)),V_c_2),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) % 19.07/18.99 => ( 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),c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2))),V_d_2),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) % 19.07/18.99 => 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),V_Pa_2),c_Com_Ocom_OCond(V_b_2,V_c_2,V_d_2)),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_Loop,axiom, % 19.07/18.99 ! [V_c_2,V_b_2,V_Pa_2,V_G_2,T_b] : % 19.07/18.99 ( 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),c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,V_b_2)),V_c_2),V_Pa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) % 19.07/18.99 => 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),V_Pa_2),c_Com_Ocom_OWhile(V_b_2,V_c_2)),c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_Nitpick_Onum__def,axiom, % 19.07/18.99 ! [T_b] : c_Nitpick_Onum(T_b) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,T_b,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(T_b)) ). % 19.07/18.99 % 19.07/18.99 fof(fact_peek__and__def,axiom, % 19.07/18.99 ! [V_s_2,V_Z_2,V_p_2,V_Pa_2,T_b] : % 19.07/18.99 ( hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,V_p_2),V_Z_2),V_s_2)) % 19.07/18.99 <=> ( hBOOL(hAPP(hAPP(V_Pa_2,V_Z_2),V_s_2)) % 19.07/18.99 & hBOOL(hAPP(V_p_2,V_s_2)) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_Nitpick_Odenom__def,axiom, % 19.07/18.99 ! [T_b] : c_Nitpick_Odenom(T_b) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,T_b,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(T_b)) ). % 19.07/18.99 % 19.07/18.99 fof(fact_setsum__reindex__nonzero,axiom, % 19.07/18.99 ! [T_c,V_h_2,V_f_2,V_S_2,T_b,T_d] : % 19.07/18.99 ( class_Groups_Ocomm__monoid__add(T_d) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 19.07/18.99 => ( ! [B_x] : % 19.07/18.99 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) % 19.07/18.99 => ! [B_y] : % 19.07/18.99 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_S_2)) % 19.07/18.99 => ( B_x != B_y % 19.07/18.99 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) % 19.07/18.99 => hAPP(V_h_2,hAPP(V_f_2,B_x)) = c_Groups_Ozero__class_Ozero(T_d) ) ) ) ) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_h_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_S_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)),V_S_2) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_Random__Sequence_Omap__def,axiom, % 19.07/18.99 ! [V_Pa_2,V_f_2,T_b,T_c] : c_Random__Sequence_Omap(T_c,T_b,V_f_2,V_Pa_2) = c_Random__Sequence_Obind(T_c,T_b,V_Pa_2,hAPP(c_Fun_Ocomp(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))))),T_c,c_Random__Sequence_Osingle(T_b)),V_f_2)) ). % 19.07/18.99 % 19.07/18.99 fof(fact_folding__idem_Ounion__idem,axiom, % 19.07/18.99 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 19.07/18.99 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 19.07/18.99 => 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(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_folding__idem_Oidem__left__comp,axiom, % 19.07/18.99 ! [V_g_2,V_x_2,T_d,V_F_2,V_f_2,T_c,T_b] : % 19.07/18.99 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) % 19.07/18.99 => hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),V_g_2) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_folding__idem_Oidem__comp,axiom, % 19.07/18.99 ! [V_x_2,V_F_2,V_f_2,T_c,T_b] : % 19.07/18.99 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) % 19.07/18.99 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_f_2,V_x_2) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_folding__idem_Oin__comp__idem,axiom, % 19.07/18.99 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 19.07/18.99 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.99 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_F_2,V_A_2) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_folding__idem_Oinsert__idem,axiom, % 19.07/18.99 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 19.07/18.99 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.99 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_folding__idem_Osubset__comp__idem,axiom, % 19.07/18.99 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 19.07/18.99 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 19.07/18.99 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) = hAPP(V_F_2,V_A_2) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_strong__setprod__reindex__cong,axiom, % 19.07/18.99 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] : % 19.07/18.99 ( class_Groups_Ocomm__monoid__mult(T_d) % 19.07/18.99 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 19.07/18.99 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) % 19.07/18.99 => ( ! [B_x] : % 19.07/18.99 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 19.07/18.99 => hAPP(V_g_2,B_x) = hAPP(hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2),B_x) ) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_d),V_g_2),V_A_2) ) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_fold__graph__permute__diff,axiom, % 19.07/18.99 ! [V_a_2,V_x_2,V_A_2,V_b_2,T_b] : % 19.07/18.99 ( class_Groups_Oab__semigroup__mult(T_b) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_b_2,V_A_2),V_x_2)) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 19.07/18.99 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2)) % 19.07/18.99 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_a_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),V_x_2)) ) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_ran__restrictD,axiom, % 19.07/18.99 ! [V_A_2,V_m_2,T_c,V_y_2,T_b] : % 19.07/18.99 ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),c_Map_Oran(T_c,T_b,c_Map_Orestrict__map(T_c,T_b,V_m_2,V_A_2)))) % 19.07/18.99 => ? [B_x] : % 19.07/18.99 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 19.07/18.99 & hAPP(V_m_2,B_x) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_fold__graph__imp__finite,axiom, % 19.07/18.99 ! [V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] : % 19.07/18.99 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2)) % 19.07/18.99 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_empty__fold__graphE,axiom, % 19.07/18.99 ! [V_x_2,V_z_2,V_f_2,T_c,T_b] : % 19.07/18.99 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_x_2)) % 19.07/18.99 => V_x_2 = V_z_2 ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_fold__graph_OemptyI,axiom, % 19.07/18.99 ! [V_z_2,V_f_2,T_c,T_b] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_z_2)) ). % 19.07/18.99 % 19.07/18.99 fof(fact_fold__graph_Oequations_I1_J,axiom, % 19.07/18.99 ! [V_z_2,V_f_2,T_c,T_b] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_z_2)) ). % 19.07/18.99 % 19.07/18.99 fof(fact_fold__graph_OinsertI,axiom, % 19.07/18.99 ! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] : % 19.07/18.99 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2)) % 19.07/18.99 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),hAPP(hAPP(V_f_2,V_x_2),V_y_2))) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_fold__graph__insert__swap,axiom, % 19.07/18.99 ! [V_z_2,V_y_2,V_A_2,V_b_2,T_b] : % 19.07/18.99 ( class_Groups_Oab__semigroup__mult(T_b) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_b_2,V_A_2),V_y_2)) % 19.07/18.99 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2)) % 19.07/18.99 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_z_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_z_2),V_y_2))) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_Diff1__fold__graph,axiom, % 19.07/18.99 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] : % 19.07/18.99 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_y_2)) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/18.99 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),hAPP(hAPP(V_f_2,V_x_2),V_y_2))) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_fold1Set_Ointros,axiom, % 19.07/18.99 ! [V_x_2,V_A_2,V_a_2,V_f_2,T_b] : % 19.07/18.99 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,V_a_2,V_A_2),V_x_2)) % 19.07/18.99 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 19.07/18.99 => hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),V_x_2)) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_compl__unique,axiom, % 19.07/18.99 ! [V_y,V_x,T_a] : % 19.07/18.99 ( class_Lattices_Oboolean__algebra(T_a) % 19.07/18.99 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = c_Orderings_Obot__class_Obot(T_a) % 19.07/18.99 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = c_Orderings_Otop__class_Otop(T_a) % 19.07/18.99 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = V_y ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_transfer__nat__int__sum__prod__cong_I1_J,axiom, % 19.07/18.99 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] : % 19.07/18.99 ( ( class_Groups_Ocomm__monoid__add(T_b) % 19.07/18.99 & class_Groups_Ocomm__monoid__mult(T_b) ) % 19.07/18.99 => ( V_A_2 = V_B_2 % 19.07/18.99 => ( c_Nat__Transfer_Onat__set(V_B_2) % 19.07/18.99 => ( ! [B_x] : % 19.07/18.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 19.07/18.99 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) % 19.07/18.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_g_2),V_B_2) ) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_UNIV__I,axiom, % 19.07/18.99 ! [V_x_2,T_b] : hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ). % 19.07/18.99 % 19.07/18.99 fof(fact_UNIV__option__conv,axiom, % 19.07/18.99 ! [T_b] : c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(tc_Option_Ooption(T_b)),c_Option_Ooption_ONone(T_b)),hAPP(c_Set_Oimage(T_b,tc_Option_Ooption(T_b),c_Option_Ooption_OSome(T_b)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ). % 19.07/18.99 % 19.07/18.99 fof(fact_range__composition,axiom, % 19.07/18.99 ! [V_g_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,hAPP(hAPP(c_COMBB(T_d,T_b,T_c),V_f_2),V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = hAPP(c_Set_Oimage(T_d,T_b,V_f_2),hAPP(c_Set_Oimage(T_c,T_d,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ). % 19.07/18.99 % 19.07/18.99 fof(fact_UN__atMost__UNIV,axiom, % 19.07/18.99 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)) ). % 19.07/18.99 % 19.07/18.99 fof(fact_inj__int,axiom, % 19.07/18.99 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))) ). % 19.07/18.99 % 19.07/18.99 fof(fact_injD,axiom, % 19.07/18.99 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] : % 19.07/18.99 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 19.07/18.99 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 19.07/18.99 => V_x_2 = V_y_2 ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_inj__eq,axiom, % 19.07/18.99 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] : % 19.07/18.99 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 19.07/18.99 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 19.07/18.99 <=> V_x_2 = V_y_2 ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_top__greatest,axiom, % 19.07/18.99 ! [V_x,T_a] : % 19.07/18.99 ( class_Orderings_Otop(T_a) % 19.07/18.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Orderings_Otop__class_Otop(T_a))) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_subset__UNIV,axiom, % 19.07/18.99 ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ). % 19.07/18.99 % 19.07/18.99 fof(fact_Int__UNIV__right,axiom, % 19.07/18.99 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = V_A_2 ). % 19.07/18.99 % 19.07/18.99 fof(fact_Int__UNIV__left,axiom, % 19.07/18.99 ! [V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = V_B_2 ). % 19.07/18.99 % 19.07/18.99 fof(fact_inf__eq__top__iff,axiom, % 19.07/18.99 ! [V_y_2,V_x_2,T_b] : % 19.07/18.99 ( class_Lattices_Obounded__lattice__top(T_b) % 19.07/18.99 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = c_Orderings_Otop__class_Otop(T_b) % 19.07/18.99 <=> ( V_x_2 = c_Orderings_Otop__class_Otop(T_b) % 19.07/18.99 & V_y_2 = c_Orderings_Otop__class_Otop(T_b) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_inf__top__right,axiom, % 19.07/18.99 ! [V_x,T_a] : % 19.07/18.99 ( class_Lattices_Obounded__lattice__top(T_a) % 19.07/18.99 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = V_x ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_inf__top__left,axiom, % 19.07/18.99 ! [V_x,T_a] : % 19.07/18.99 ( class_Lattices_Obounded__lattice__top(T_a) % 19.07/18.99 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = V_x ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_sup__top__right,axiom, % 19.07/18.99 ! [V_x,T_a] : % 19.07/18.99 ( class_Lattices_Obounded__lattice__top(T_a) % 19.07/18.99 => 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) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_sup__top__left,axiom, % 19.07/18.99 ! [V_x,T_a] : % 19.07/18.99 ( class_Lattices_Obounded__lattice__top(T_a) % 19.07/18.99 => 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) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_Un__UNIV__right,axiom, % 19.07/18.99 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ). % 19.07/18.99 % 19.07/18.99 fof(fact_Un__UNIV__left,axiom, % 19.07/18.99 ! [V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ). % 19.07/18.99 % 19.07/18.99 fof(fact_UNIV__not__empty,axiom, % 19.07/18.99 ! [T_b] : c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 19.07/18.99 % 19.07/18.99 fof(fact_top__apply,axiom, % 19.07/18.99 ! [V_x_2,T_c,T_b] : % 19.07/18.99 ( class_Orderings_Otop(T_b) % 19.07/18.99 => hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Otop__class_Otop(T_b) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_equiv__intrel,axiom, % 19.07/18.99 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) ). % 19.07/18.99 % 19.07/18.99 fof(fact_UNIV__Plus__UNIV,axiom, % 19.07/18.99 ! [T_c,T_b] : c_Sum__Type_OPlus(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_b,T_c),tc_HOL_Obool)) ). % 19.07/18.99 % 19.07/18.99 fof(fact_card__UNIV__unit,axiom, % 19.07/18.99 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) ). % 19.07/18.99 % 19.07/18.99 fof(fact_Pow__UNIV,axiom, % 19.07/18.99 ! [T_b] : hAPP(c_Set_OPow(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) ). % 19.07/18.99 % 19.07/18.99 fof(fact_UN__lessThan__UNIV,axiom, % 19.07/18.99 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)) ). % 19.07/18.99 % 19.07/18.99 fof(fact_infinite__UNIV__int,axiom, % 19.07/18.99 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) ). % 19.07/18.99 % 19.07/18.99 fof(fact_finite__UNIV,axiom, % 19.07/18.99 ! [T_b] : % 19.07/18.99 ( class_Finite__Set_Ofinite(T_b) % 19.07/18.99 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_infinite__UNIV__nat,axiom, % 19.07/18.99 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ). % 19.07/18.99 % 19.07/18.99 fof(fact_finite__option__UNIV,axiom, % 19.07/18.99 ! [T_b] : % 19.07/18.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool)))) % 19.07/18.99 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_finite__Plus__UNIV__iff,axiom, % 19.07/18.99 ! [T_c,T_b] : % 19.07/18.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_b,T_c),tc_HOL_Obool)))) % 19.07/18.99 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 19.07/18.99 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_finite__fun__UNIVD2,axiom, % 19.07/18.99 ! [T_c,T_b] : % 19.07/18.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,T_c),tc_HOL_Obool)))) % 19.07/18.99 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_finite__Prod__UNIV,axiom, % 19.07/18.99 ! [T_c,T_b] : % 19.07/18.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) % 19.07/18.99 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)))) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_fold1Set__nonempty,axiom, % 19.07/18.99 ! [V_x_2,V_A_2,V_f_2,T_b] : % 19.07/18.99 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,V_A_2),V_x_2)) % 19.07/18.99 => V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_empty__fold1SetE,axiom, % 19.07/18.99 ! [V_x_2,V_f_2,T_b] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_x_2)) ). % 19.07/18.99 % 19.07/18.99 fof(fact_range__eqI,axiom, % 19.07/18.99 ! [T_c,T_b,V_x_2,V_f_2,V_b_2] : % 19.07/18.99 ( V_b_2 = hAPP(V_f_2,V_x_2) % 19.07/18.99 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_rangeI,axiom, % 19.07/18.99 ! [T_c,V_x_2,V_f_2,T_b] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ). % 19.07/18.99 % 19.07/18.99 fof(fact_UN__atLeast__UNIV,axiom, % 19.07/18.99 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)) ). % 19.07/18.99 % 19.07/18.99 fof(fact_Diff__UNIV,axiom, % 19.07/18.99 ! [V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 19.07/18.99 % 19.07/18.99 fof(fact_comp__surj,axiom, % 19.07/18.99 ! [V_g_2,T_d,V_f_2,T_b,T_c] : % 19.07/18.99 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.99 => ( hAPP(c_Set_Oimage(T_b,T_d,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)) % 19.07/18.99 => hAPP(c_Set_Oimage(T_c,T_d,hAPP(c_Fun_Ocomp(T_b,T_d,T_c,V_g_2),V_f_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom, % 19.07/18.99 ! [V_A_2,T_b] : % 19.07/18.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 19.07/18.99 => ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 19.07/18.99 => V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_inj__image__eq__iff,axiom, % 19.07/18.99 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 19.07/18.99 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 19.07/18.99 => ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2) % 19.07/18.99 <=> V_A_2 = V_B_2 ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_inj__comp,axiom, % 19.07/18.99 ! [V_g_2,T_d,V_f_2,T_c,T_b] : % 19.07/18.99 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 19.07/18.99 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) % 19.07/18.99 => c_Fun_Oinj__on(T_d,T_c,hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_2),V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_Compl__UNIV__eq,axiom, % 19.07/18.99 ! [T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 19.07/18.99 % 19.07/18.99 fof(fact_Compl__empty__eq,axiom, % 19.07/18.99 ! [T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ). % 19.07/18.99 % 19.07/18.99 fof(fact_finite__compl,axiom, % 19.07/18.99 ! [V_A_2,T_b] : % 19.07/18.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/18.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) % 19.07/18.99 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_Compl__partition2,axiom, % 19.07/18.99 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ). % 19.07/18.99 % 19.07/18.99 fof(fact_Compl__partition,axiom, % 19.07/18.99 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ). % 19.07/18.99 % 19.07/18.99 fof(fact_Compl__eq__Diff__UNIV,axiom, % 19.07/18.99 ! [V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_A_2) ). % 19.07/18.99 % 19.07/18.99 fof(fact_code__numeral_Oof__nat__inject,axiom, % 19.07/18.99 ! [V_y_2,V_x_2] : % 19.07/18.99 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 19.07/18.99 => ( hAPP(c_Code__Numeral_Oof__nat,V_x_2) = hAPP(c_Code__Numeral_Oof__nat,V_y_2) % 19.07/18.99 <=> V_x_2 = V_y_2 ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_SUP__UN__eq,axiom, % 19.07/18.99 ! [V_x_2,V_r_2,T_c,T_b] : % 19.07/18.99 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c))),V_r_2)),V_x_2)) % 19.07/18.99 <=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_finite__range__imageI,axiom, % 19.07/18.99 ! [V_f_2,T_d,V_g_2,T_c,T_b] : % 19.07/18.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) % 19.07/18.99 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(c_Set_Oimage(T_c,T_d,hAPP(hAPP(c_COMBB(T_b,T_d,T_c),V_f_2),V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_nat__of,axiom, % 19.07/18.99 ! [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)))) ). % 19.07/18.99 % 19.07/18.99 fof(fact_the__inv__f__f,axiom, % 19.07/18.99 ! [V_x_2,V_f_2,T_c,T_b] : % 19.07/18.99 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 19.07/18.99 => hAPP(c_Fun_Othe__inv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_finite__fun__UNIVD1,axiom, % 19.07/18.99 ! [T_c,T_b] : % 19.07/18.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,T_c),tc_HOL_Obool)))) % 19.07/18.99 => ( hAPP(c_Finite__Set_Ocard(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 19.07/18.99 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_inj__of__nat,axiom, % 19.07/18.99 ! [T_b] : % 19.07/18.99 ( class_Nat_Osemiring__char__0(T_b) % 19.07/18.99 => c_Fun_Oinj__on(tc_Nat_Onat,T_b,c_Nat_Osemiring__1__class_Oof__nat(T_b),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_dom__const,axiom, % 19.07/18.99 ! [V_f_2,T_c,T_b] : c_Map_Odom(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_Option_Ooption(T_c),T_b),c_Option_Ooption_OSome(T_c)),V_f_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ). % 19.07/18.99 % 19.07/18.99 fof(fact_atLeast__0,axiom, % 19.07/18.99 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)) ). % 19.07/18.99 % 19.07/18.99 fof(fact_inj__fun,axiom, % 19.07/18.99 ! [T_d,V_f_2,T_c,T_b] : % 19.07/18.99 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 19.07/18.99 => c_Fun_Oinj__on(T_b,tc_fun(T_d,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_d,T_c),T_b),c_COMBK(T_c,T_d)),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_compl__bot__eq,axiom, % 19.07/18.99 ! [T_a] : % 19.07/18.99 ( class_Lattices_Oboolean__algebra(T_a) % 19.07/18.99 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Otop__class_Otop(T_a) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_compl__top__eq,axiom, % 19.07/18.99 ! [T_a] : % 19.07/18.99 ( class_Lattices_Oboolean__algebra(T_a) % 19.07/18.99 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Obot__class_Obot(T_a) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_compl__sup__top,axiom, % 19.07/18.99 ! [V_x,T_a] : % 19.07/18.99 ( class_Lattices_Oboolean__algebra(T_a) % 19.07/18.99 => 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) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_sup__compl__top,axiom, % 19.07/18.99 ! [V_x,T_a] : % 19.07/18.99 ( class_Lattices_Oboolean__algebra(T_a) % 19.07/18.99 => 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) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_inj__image__mem__iff,axiom, % 19.07/18.99 ! [V_A_2,V_a_2,V_f_2,T_c,T_b] : % 19.07/18.99 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) % 19.07/18.99 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_range__ex1__eq,axiom, % 19.07/18.99 ! [V_b_2,V_f_2,T_c,T_b] : % 19.07/18.99 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) % 19.07/18.99 <=> ? [B_x] : % 19.07/18.99 ( V_b_2 = hAPP(V_f_2,B_x) % 19.07/18.99 & ! [B_y] : % 19.07/18.99 ( V_b_2 = hAPP(V_f_2,B_y) % 19.07/18.99 => B_y = B_x ) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_finite__UNIV__surj__inj,axiom, % 19.07/18.99 ! [V_f_2,T_b] : % 19.07/18.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 19.07/18.99 => ( hAPP(c_Set_Oimage(T_b,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.99 => c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_finite__UNIV__inj__surj,axiom, % 19.07/18.99 ! [V_f_2,T_b] : % 19.07/18.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 19.07/18.99 => ( c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 19.07/18.99 => hAPP(c_Set_Oimage(T_b,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_inj__image__subset__iff,axiom, % 19.07/18.99 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 19.07/18.99 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2))) % 19.07/18.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_image__Int,axiom, % 19.07/18.99 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 19.07/18.99 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 19.07/18.99 => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_image__set__diff,axiom, % 19.07/18.99 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 19.07/18.99 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 19.07/18.99 => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_surj__Compl__image__subset,axiom, % 19.07/18.99 ! [V_A_2,V_f_2,T_b,T_c] : % 19.07/18.99 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)))) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_of__nat__inverse,axiom, % 19.07/18.99 ! [V_y_2] : % 19.07/18.99 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 19.07/18.99 => hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_y_2)) = V_y_2 ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_fold1Set__sing,axiom, % 19.07/18.99 ! [V_b_2,V_a_2,V_f_2,T_b] : % 19.07/18.99 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_b_2)) % 19.07/18.99 <=> V_a_2 = V_b_2 ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_finite__range__updI,axiom, % 19.07/18.99 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] : % 19.07/18.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_b)),hAPP(c_Set_Oimage(T_c,tc_Option_Ooption(T_b),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) % 19.07/18.99 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_b)),hAPP(c_Set_Oimage(T_c,tc_Option_Ooption(T_b),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),V_f_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_b_2))),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_UN__UN__finite__eq,axiom, % 19.07/18.99 ! [V_A_2,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2) ). % 19.07/18.99 % 19.07/18.99 fof(fact_inj__singleton,axiom, % 19.07/18.99 ! [T_b] : c_Fun_Oinj__on(T_b,tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ). % 19.07/18.99 % 19.07/18.99 fof(fact_finite__UNIV__card__ge__0,axiom, % 19.07/18.99 ! [T_b] : % 19.07/18.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 19.07/18.99 => 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_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_card__UNIV__bool,axiom, % 19.07/18.99 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))) ). % 19.07/18.99 % 19.07/18.99 fof(fact_inj__image__Compl__subset,axiom, % 19.07/18.99 ! [V_A_2,V_f_2,T_c,T_b] : % 19.07/18.99 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 19.07/18.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_greaterThan__0,axiom, % 19.07/18.99 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))) ). % 19.07/18.99 % 19.07/18.99 fof(fact_SUP__UN__eq2,axiom, % 19.07/18.99 ! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] : % 19.07/18.99 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),T_b),hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_c,T_d)))),c_Product__Type_OPair(T_c,T_d))))),V_r_2)),V_x_2),V_y_2)) % 19.07/18.99 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_UN__finite2__subset,axiom, % 19.07/18.99 ! [V_B_2,V_k_2,V_A_2,T_b] : % 19.07/18.99 ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_n),V_k_2))),V_B_2))) % 19.07/18.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_B_2))) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_UN__finite2__eq,axiom, % 19.07/18.99 ! [V_B_2,V_k_2,V_A_2,T_b] : % 19.07/18.99 ( ! [B_n] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_n),V_k_2))),V_B_2) % 19.07/18.99 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_B_2) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_UN__finite__subset,axiom, % 19.07/18.99 ! [V_C_2,V_A_2,T_b] : % 19.07/18.99 ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)),V_A_2)),V_C_2)) % 19.07/18.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2)),V_C_2)) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_top1I,axiom, % 19.07/18.99 ! [V_x_2,T_b] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_x_2)) ). % 19.07/18.99 % 19.07/18.99 fof(fact_Integ__def,axiom, % 19.07/18.99 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) ). % 19.07/18.99 % 19.07/18.99 fof(fact_iso__tuple__UNIV__I,axiom, % 19.07/18.99 ! [V_x_2,T_b] : hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ). % 19.07/18.99 % 19.07/18.99 fof(fact_equivp__equiv,axiom, % 19.07/18.99 ! [V_A_2,T_b] : % 19.07/18.99 ( c_Equiv__Relations_Oequiv(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_A_2) % 19.07/18.99 <=> c_Equiv__Relations_Oequivp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_A_2)) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_equivp__transp,axiom, % 19.07/18.99 ! [V_z_2,V_y_2,V_x_2,V_R_2,T_b] : % 19.07/18.99 ( c_Equiv__Relations_Oequivp(T_b,V_R_2) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2)) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2)) % 19.07/18.99 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_equivp__symp,axiom, % 19.07/18.99 ! [V_y_2,V_x_2,V_R_2,T_b] : % 19.07/18.99 ( c_Equiv__Relations_Oequivp(T_b,V_R_2) % 19.07/18.99 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2)) % 19.07/18.99 => hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_equivp__reflp,axiom, % 19.07/18.99 ! [V_x_2,V_R_2,T_b] : % 19.07/18.99 ( c_Equiv__Relations_Oequivp(T_b,V_R_2) % 19.07/18.99 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_equivp__def,axiom, % 19.07/18.99 ! [V_R_2,T_b] : % 19.07/18.99 ( c_Equiv__Relations_Oequivp(T_b,V_R_2) % 19.07/18.99 <=> ! [B_x,B_y] : % 19.07/18.99 ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y)) % 19.07/18.99 <=> hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_identity__equivp,axiom, % 19.07/18.99 ! [T_b] : c_Equiv__Relations_Oequivp(T_b,c_fequal) ). % 19.07/18.99 % 19.07/18.99 fof(fact_Rep__Integ,axiom, % 19.07/18.99 ! [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)) ). % 19.07/18.99 % 19.07/18.99 fof(fact_o__eq__dest__lhs,axiom, % 19.07/18.99 ! [V_v_2,V_c_2,V_b_2,V_a_2,T_b,T_c,T_d] : % 19.07/18.99 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = V_c_2 % 19.07/18.99 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,V_v_2) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_K__record__comp,axiom, % 19.07/18.99 ! [V_x_2,V_f_2,V_c_2,T_d,T_b,T_c] : hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,hAPP(c_COMBK(T_b,T_c),V_c_2)),V_f_2),V_x_2) = V_c_2 ). % 19.07/18.99 % 19.07/18.99 fof(fact_type__definition__Integ,axiom, % 19.07/18.99 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) ). % 19.07/18.99 % 19.07/18.99 fof(fact_inj__vimage__singleton,axiom, % 19.07/18.99 ! [V_a_2,V_f_2,T_c,T_b] : % 19.07/18.99 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 19.07/18.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(T_b),c_HOL_OThe(T_b,hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),V_a_2))),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_type__definition__code__numeral,axiom, % 19.07/18.99 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))) ). % 19.07/18.99 % 19.07/18.99 fof(fact_vimageI,axiom, % 19.07/18.99 ! [T_c,V_B_2,T_b,V_b_2,V_a_2,V_f_2] : % 19.07/18.99 ( hAPP(V_f_2,V_a_2) = V_b_2 % 19.07/18.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_B_2)) % 19.07/18.99 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2))) ) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_image__vimage__subset,axiom, % 19.07/18.99 ! [V_A_2,V_f_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2))),V_A_2)) ). % 19.07/18.99 % 19.07/18.99 fof(fact_vimage__compose,axiom, % 19.07/18.99 ! [V_x_2,V_f_2,V_g_2,T_d,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_g_2),V_f_2)),V_x_2) = hAPP(c_Set_Ovimage(T_b,T_d,V_f_2),hAPP(c_Set_Ovimage(T_d,T_c,V_g_2),V_x_2)) ). % 19.07/18.99 % 19.07/18.99 fof(fact_vimage__Diff,axiom, % 19.07/18.99 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)) ). % 19.07/18.99 % 19.07/18.99 fof(fact_vimage__ident,axiom, % 19.07/18.99 ! [V_Y_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2 ). % 19.07/18.99 % 19.07/18.99 fof(fact_vimage__code,axiom, % 19.07/18.99 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] : % 19.07/18.99 ( hBOOL(hAPP(hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2),V_x_2)) % 19.07/18.99 <=> hBOOL(hAPP(V_A_2,hAPP(V_f_2,V_x_2))) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_vimage__Compl,axiom, % 19.07/18.99 ! [V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)) ). % 19.07/18.99 % 19.07/18.99 fof(fact_vimage__empty,axiom, % 19.07/18.99 ! [V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 19.07/18.99 % 19.07/18.99 fof(fact_vimage__eq,axiom, % 19.07/18.99 ! [V_B_2,V_f_2,T_c,V_a_2,T_b] : % 19.07/18.99 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2))) % 19.07/18.99 <=> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_B_2)) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_vimageD,axiom, % 19.07/18.99 ! [V_A_2,V_f_2,T_c,V_a_2,T_b] : % 19.07/18.99 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2))) % 19.07/18.99 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_A_2)) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_vimageI2,axiom, % 19.07/18.99 ! [T_c,V_A_2,V_a_2,V_f_2,T_b] : % 19.07/18.99 ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_A_2)) % 19.07/18.99 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2))) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_vimage__Un,axiom, % 19.07/18.99 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)) ). % 19.07/18.99 % 19.07/18.99 fof(fact_vimage__Int,axiom, % 19.07/18.99 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)) ). % 19.07/18.99 % 19.07/18.99 fof(fact_vimage__mono,axiom, % 19.07/18.99 ! [V_f_2,T_c,V_B_2,V_A_2,T_b] : % 19.07/18.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 19.07/18.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2))) ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_vimage__UN,axiom, % 19.07/18.99 ! [V_B_2,V_A_2,T_d,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Set_Ovimage(T_b,T_c,V_f_2)),V_B_2)) ). % 19.07/18.99 % 19.07/18.99 fof(fact_vimage__UNIV,axiom, % 19.07/18.99 ! [V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ). % 19.07/18.99 % 19.07/18.99 fof(fact_surj__image__vimage__eq,axiom, % 19.07/18.99 ! [V_A_2,V_f_2,T_b,T_c] : % 19.07/18.99 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) % 19.07/18.99 => hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2)) = V_A_2 ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_vimage__singleton__eq,axiom, % 19.07/18.99 ! [V_b_2,V_f_2,T_c,V_a_2,T_b] : % 19.07/18.99 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))) % 19.07/18.99 <=> hAPP(V_f_2,V_a_2) = V_b_2 ) ). % 19.07/18.99 % 19.07/18.99 fof(fact_vimage__insert,axiom, % 19.07/18.99 ! [V_B_2,V_a_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)) ). % 19.07/18.99 % 19.07/18.99 fof(fact_finite__vimageD,axiom, % 19.07/18.99 ! [V_F_2,V_h_2,T_c,T_b] : % 19.07/18.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_c,V_h_2),V_F_2))) % 19.07/18.99 => ( hAPP(c_Set_Oimage(T_b,T_c,V_h_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) % 19.07/18.99 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_vimage__subsetD,axiom, % 19.07/19.00 ! [V_A_2,V_B_2,V_f_2,T_b,T_c] : % 19.07/19.00 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2)),V_A_2)) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_image__vimage__eq,axiom, % 19.07/19.00 ! [V_A_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ). % 19.07/19.00 % 19.07/19.00 fof(fact_finite__vimageI,axiom, % 19.07/19.00 ! [V_h_2,T_c,V_F_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 19.07/19.00 => ( c_Fun_Oinj__on(T_c,T_b,V_h_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 19.07/19.00 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Ovimage(T_c,T_b,V_h_2),V_F_2))) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_inj__vimage__image__eq,axiom, % 19.07/19.00 ! [V_A_2,V_f_2,T_c,T_b] : % 19.07/19.00 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 19.07/19.00 => hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = V_A_2 ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_vimage__const,axiom, % 19.07/19.00 ! [T_c,V_A_2,V_c_2,T_b] : % 19.07/19.00 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) % 19.07/19.00 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(c_COMBK(T_b,T_c),V_c_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) % 19.07/19.00 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) % 19.07/19.00 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(c_COMBK(T_b,T_c),V_c_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_vimage__eq__UN,axiom, % 19.07/19.00 ! [V_B_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Set_Ovimage(T_b,T_c,V_f_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),c_Set_Oinsert(T_c)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))) ). % 19.07/19.00 % 19.07/19.00 fof(fact_vimage__subsetI,axiom, % 19.07/19.00 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] : % 19.07/19.00 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 19.07/19.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)),V_A_2)) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_vimage__if,axiom, % 19.07/19.00 ! [V_B_2,T_c,V_d_2,V_A_2,V_c_2,T_b] : % 19.07/19.00 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) % 19.07/19.00 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2)) % 19.07/19.00 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) % 19.07/19.00 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2)) % 19.07/19.00 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = V_B_2 ) ) ) % 19.07/19.00 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) % 19.07/19.00 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2)) % 19.07/19.00 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_B_2) ) % 19.07/19.00 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2)) % 19.07/19.00 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_type__definition_ORep__range,axiom, % 19.07/19.00 ! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] : % 19.07/19.00 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) % 19.07/19.00 => hAPP(c_Set_Oimage(T_b,T_c,V_Rep_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = V_A_2 ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_type__definition_OAbs__image,axiom, % 19.07/19.00 ! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] : % 19.07/19.00 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) % 19.07/19.00 => hAPP(c_Set_Oimage(T_c,T_b,V_Abs_2),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_type__definition_OAbs__inject,axiom, % 19.07/19.00 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] : % 19.07/19.00 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) % 19.07/19.00 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 19.07/19.00 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2)) % 19.07/19.00 => ( hAPP(V_Abs_2,V_x_2) = hAPP(V_Abs_2,V_y_2) % 19.07/19.00 <=> V_x_2 = V_y_2 ) ) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_type__definition_ORep__inverse,axiom, % 19.07/19.00 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] : % 19.07/19.00 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) % 19.07/19.00 => hAPP(V_Abs_2,hAPP(V_Rep_2,V_x_2)) = V_x_2 ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_type__definition_ORep__inject,axiom, % 19.07/19.00 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] : % 19.07/19.00 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) % 19.07/19.00 => ( hAPP(V_Rep_2,V_x_2) = hAPP(V_Rep_2,V_y_2) % 19.07/19.00 <=> V_x_2 = V_y_2 ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_type__definition_ORep,axiom, % 19.07/19.00 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] : % 19.07/19.00 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_Rep_2,V_x_2)),V_A_2)) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_type__definition_OAbs__inverse,axiom, % 19.07/19.00 ! [V_y_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] : % 19.07/19.00 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) % 19.07/19.00 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2)) % 19.07/19.00 => hAPP(V_Rep_2,hAPP(V_Abs_2,V_y_2)) = V_y_2 ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_max__extp_Oequations,axiom, % 19.07/19.00 ! [V_a2_2,V_a1_2,V_R_2,T_b] : % 19.07/19.00 ( c_Wellfounded_Omax__extp(T_b,V_R_2,V_a1_2,V_a2_2) % 19.07/19.00 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2)) % 19.07/19.00 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2)) % 19.07/19.00 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.00 & ! [B_x] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2)) % 19.07/19.00 => ? [B_xa] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2)) % 19.07/19.00 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_max__ext_Ointros,axiom, % 19.07/19.00 ! [V_R_2,V_Y_2,V_X_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2)) % 19.07/19.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Y_2)) % 19.07/19.00 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.00 => ( ! [B_x] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_X_2)) % 19.07/19.00 => ? [B_xa] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_Y_2)) % 19.07/19.00 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_xa)),V_R_2)) ) ) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_Y_2)),c_Wellfounded_Omax__ext(T_b,V_R_2))) ) ) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_fold1Set_Oequations,axiom, % 19.07/19.00 ! [V_a3_2,V_a2_2,V_a1_2,V_f_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),V_a2_2)),V_a3_2)) % 19.07/19.00 <=> ? [B_a,B_A] : % 19.07/19.00 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),V_a2_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A) % 19.07/19.00 & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_a3_2)) % 19.07/19.00 & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_insert__fold1SetE,axiom, % 19.07/19.00 ! [V_x_2,V_X_2,V_a_2,V_f_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_X_2)),V_x_2)) % 19.07/19.00 => ~ ! [B_a,B_A] : % 19.07/19.00 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_X_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A) % 19.07/19.00 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_x_2)) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) ) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_image__split__eq__Sigma,axiom, % 19.07/19.00 ! [V_A_2,V_g_2,V_f_2,T_c,T_b,T_d] : hAPP(c_Set_Oimage(T_d,tc_prod(T_b,T_c),hAPP(hAPP(c_COMBS(T_d,T_c,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),T_d),c_Product__Type_OPair(T_b,T_c)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_Oimage(T_d,T_b,V_f_2),V_A_2)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_Oimage(T_d,T_c,V_g_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_b),c_Set_Ovimage(T_d,T_b,V_f_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),V_A_2))) ). % 19.07/19.00 % 19.07/19.00 fof(fact_fold1__Un,axiom, % 19.07/19.00 ! [V_B_2,V_A_2,T_b] : % 19.07/19.00 ( class_Groups_Oab__semigroup__mult(T_b) % 19.07/19.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.00 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 19.07/19.00 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.00 => ( 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)) % 19.07/19.00 => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_B_2)) ) ) ) ) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_SigmaI,axiom, % 19.07/19.00 ! [V_B_2,V_b_2,T_c,V_A_2,V_a_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 19.07/19.00 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Times__eq__cancel2,axiom, % 19.07/19.00 ! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2)) % 19.07/19.00 => ( hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2)) = hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2)) % 19.07/19.00 <=> V_A_2 = V_B_2 ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Sigma__empty1,axiom, % 19.07/19.00 ! [V_B_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Sigma__Diff__distrib2,axiom, % 19.07/19.00 ! [V_B_2,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_B_2)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Times__Diff__distrib1,axiom, % 19.07/19.00 ! [V_C_2,V_B_2,V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_B_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Sigma__Diff__distrib1,axiom, % 19.07/19.00 ! [V_C_2,V_J_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_J_2)),V_C_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_J_2),V_C_2)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_card__cartesian__product,axiom, % 19.07/19.00 ! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Finite__Set_Ocard(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_setsum__cartesian__product,axiom, % 19.07/19.00 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] : % 19.07/19.00 ( class_Groups_Ocomm__monoid__add(T_b) % 19.07/19.00 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(T_c,T_d),T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_B_2))) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Times__empty,axiom, % 19.07/19.00 ! [V_B_2,V_A_2,T_c,T_b] : % 19.07/19.00 ( hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) % 19.07/19.00 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.00 | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Sigma__empty2,axiom, % 19.07/19.00 ! [V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Compl__Times__UNIV2,axiom, % 19.07/19.00 ! [V_A_2,T_c,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Compl__Times__UNIV1,axiom, % 19.07/19.00 ! [V_A_2,T_c,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_A_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2))) ). % 19.07/19.00 % 19.07/19.00 fof(fact_setprod__cartesian__product,axiom, % 19.07/19.00 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] : % 19.07/19.00 ( class_Groups_Ocomm__monoid__mult(T_b) % 19.07/19.00 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_d,T_b)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(T_c,T_d),T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_B_2))) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Sigma__Un__distrib1,axiom, % 19.07/19.00 ! [V_C_2,V_J_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_J_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_J_2),V_C_2)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Times__Un__distrib1,axiom, % 19.07/19.00 ! [V_C_2,V_B_2,V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_B_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Sigma__Un__distrib2,axiom, % 19.07/19.00 ! [V_B_2,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_B_2)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_swap__product,axiom, % 19.07/19.00 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(c_Set_Oimage(tc_prod(T_c,T_b),tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_prod(T_b,T_c)),hAPP(c_COMBC(T_b,T_c,tc_prod(T_b,T_c)),c_Product__Type_OPair(T_b,T_c)))),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_B_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_A_2)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_finite__cartesian__product,axiom, % 19.07/19.00 ! [V_B_2,T_c,V_A_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 19.07/19.00 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)))) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_fold1__singleton,axiom, % 19.07/19.00 ! [V_a_2,V_f_2,T_b] : hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_a_2 ). % 19.07/19.00 % 19.07/19.00 fof(fact_fold1__singleton__def,axiom, % 19.07/19.00 ! [V_a_2,V_f_2,T_b,V_g_2] : % 19.07/19.00 ( V_g_2 = c_Finite__Set_Ofold1(T_b,V_f_2) % 19.07/19.00 => hAPP(V_g_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_a_2 ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_equiv__type,axiom, % 19.07/19.00 ! [V_r_2,V_A_2,T_b] : % 19.07/19.00 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Sigma__Int__distrib1,axiom, % 19.07/19.00 ! [V_C_2,V_J_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_J_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_J_2),V_C_2)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Times__Int__distrib1,axiom, % 19.07/19.00 ! [V_C_2,V_B_2,V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_B_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Sigma__Int__distrib2,axiom, % 19.07/19.00 ! [V_B_2,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_B_2)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Id__on__subset__Times,axiom, % 19.07/19.00 ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Relation_OId__on(T_b,V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) ). % 19.07/19.00 % 19.07/19.00 fof(fact_UNIV__Times__UNIV,axiom, % 19.07/19.00 ! [T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_mem__Sigma__iff,axiom, % 19.07/19.00 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) % 19.07/19.00 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 19.07/19.00 & hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_SigmaD1,axiom, % 19.07/19.00 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_SigmaD2,axiom, % 19.07/19.00 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_SigmaE2,axiom, % 19.07/19.00 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) % 19.07/19.00 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 19.07/19.00 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_folding__one_Oeq__fold,axiom, % 19.07/19.00 ! [V_A_2,V_F_2,V_f_2,T_b] : % 19.07/19.00 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 19.07/19.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.00 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_card__cartesian__product__singleton,axiom, % 19.07/19.00 ! [V_A_2,V_x_2,T_c,T_b] : hAPP(c_Finite__Set_Ocard(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_A_2))) = hAPP(c_Finite__Set_Ocard(T_c),V_A_2) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Times__subset__cancel2,axiom, % 19.07/19.00 ! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2)) % 19.07/19.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2)))) % 19.07/19.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Image__subset,axiom, % 19.07/19.00 ! [V_C_2,V_B_2,V_A_2,V_r_2,T_c,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)))) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_C_2)),V_B_2)) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_finite__cartesian__productD1,axiom, % 19.07/19.00 ! [V_B_2,V_A_2,T_c,T_b] : % 19.07/19.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)))) % 19.07/19.00 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 19.07/19.00 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_finite__cartesian__productD2,axiom, % 19.07/19.00 ! [V_B_2,V_A_2,T_c,T_b] : % 19.07/19.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)))) % 19.07/19.00 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.00 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_fst__image__times,axiom, % 19.07/19.00 ! [V_A_2,T_c,T_b,V_B_2] : % 19.07/19.00 ( ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.00 => hAPP(c_Set_Oimage(tc_prod(T_c,T_b),T_c,c_Product__Type_Ofst(T_c,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) % 19.07/19.00 & ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.00 => hAPP(c_Set_Oimage(tc_prod(T_c,T_b),T_c,c_Product__Type_Ofst(T_c,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2))) = V_A_2 ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_snd__image__times,axiom, % 19.07/19.00 ! [V_B_2,T_c,T_b,V_A_2] : % 19.07/19.00 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.00 => hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_c,c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) % 19.07/19.00 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.00 => hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_c,c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))) = V_B_2 ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_fold1__def,axiom, % 19.07/19.00 ! [V_A_2,V_f_2,T_b] : hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) = c_HOL_OThe(T_b,c_Finite__Set_Ofold1Set(T_b,V_f_2,V_A_2)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Sup__fin_OF__eq,axiom, % 19.07/19.00 ! [V_A_2,T_b] : % 19.07/19.00 ( class_Lattices_Olattice(T_b) % 19.07/19.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.00 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_A_2) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Inf__fin_OF__eq,axiom, % 19.07/19.00 ! [V_A_2,T_b] : % 19.07/19.00 ( class_Lattices_Olattice(T_b) % 19.07/19.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.00 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_A_2) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Min_OF__eq,axiom, % 19.07/19.00 ! [V_A_2,T_b] : % 19.07/19.00 ( class_Orderings_Olinorder(T_b) % 19.07/19.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.00 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Max_OF__eq,axiom, % 19.07/19.00 ! [V_A_2,T_b] : % 19.07/19.00 ( class_Orderings_Olinorder(T_b) % 19.07/19.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.00 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omax(T_b)),V_A_2) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_min__max_OInf__fin_OF__eq,axiom, % 19.07/19.00 ! [V_A_2,T_b] : % 19.07/19.00 ( class_Orderings_Olinorder(T_b) % 19.07/19.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.00 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_min__max_OSup__fin_OF__eq,axiom, % 19.07/19.00 ! [V_A_2,T_b] : % 19.07/19.00 ( class_Orderings_Olinorder(T_b) % 19.07/19.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.00 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omax(T_b)),V_A_2) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_insert__times__insert,axiom, % 19.07/19.00 ! [V_B_2,V_b_2,V_A_2,V_a_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),V_B_2))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),V_B_2)))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)))) ). % 19.07/19.00 % 19.07/19.00 fof(fact_finite__equiv__class,axiom, % 19.07/19.00 ! [V_X_2,V_r_2,V_A_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) % 19.07/19.00 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) % 19.07/19.00 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2)) ) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_UN__Times__distrib,axiom, % 19.07/19.00 ! [V_F_2,V_E_2,V_B_2,V_A_2,T_c,T_b,T_e,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(T_d,T_e),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_d,T_e),V_A_2),hAPP(c_COMBK(tc_fun(T_e,tc_HOL_Obool),T_d),V_B_2))),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_e,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),tc_fun(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_e,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),tc_fun(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),T_d),c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_e)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_d),c_Product__Type_OSigma(T_b,T_c)),V_E_2))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),T_e),c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b)),V_F_2)))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_E_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_F_2))) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Sigma__def,axiom, % 19.07/19.00 ! [V_B_2,V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_b),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),V_B_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_c),c_Set_Oinsert(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))))) ). % 19.07/19.00 % 19.07/19.00 fof(fact_fold1__belowI,axiom, % 19.07/19.00 ! [V_a_2,V_A_2,T_b] : % 19.07/19.00 ( class_Lattices_Osemilattice__inf(T_b) % 19.07/19.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.00 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_A_2)),V_a_2)) ) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_finite__quotient,axiom, % 19.07/19.00 ! [V_r_2,V_A_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) % 19.07/19.00 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_below__fold1__iff,axiom, % 19.07/19.00 ! [V_x_2,V_A_2,T_b] : % 19.07/19.00 ( class_Lattices_Osemilattice__inf(T_b) % 19.07/19.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.00 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_A_2))) % 19.07/19.00 <=> ! [B_x] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_min__max_Ofold1__belowI,axiom, % 19.07/19.00 ! [V_a_2,V_A_2,T_b] : % 19.07/19.00 ( class_Orderings_Olinorder(T_b) % 19.07/19.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.00 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)),V_a_2)) ) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_fold1__insert__idem,axiom, % 19.07/19.00 ! [V_x_2,V_A_2,T_b] : % 19.07/19.00 ( class_Lattices_Oab__semigroup__idem__mult(T_b) % 19.07/19.00 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.00 => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)) ) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_fold1__below__iff,axiom, % 19.07/19.00 ! [V_x_2,V_A_2,T_b] : % 19.07/19.00 ( class_Orderings_Olinorder(T_b) % 19.07/19.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.00 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)),V_x_2)) % 19.07/19.00 <=> ? [B_x] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 19.07/19.00 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_x_2)) ) ) ) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_min__max_Obelow__fold1__iff,axiom, % 19.07/19.00 ! [V_x_2,V_A_2,T_b] : % 19.07/19.00 ( class_Orderings_Olinorder(T_b) % 19.07/19.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.00 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2))) % 19.07/19.00 <=> ! [B_x] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_fold1__Un2,axiom, % 19.07/19.00 ! [V_B_2,V_A_2,T_b] : % 19.07/19.00 ( class_Lattices_Oab__semigroup__idem__mult(T_b) % 19.07/19.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.00 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 19.07/19.00 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.00 => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_B_2)) ) ) ) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_strict__below__fold1__iff,axiom, % 19.07/19.00 ! [V_x_2,V_A_2,T_b] : % 19.07/19.00 ( class_Orderings_Olinorder(T_b) % 19.07/19.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.00 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2))) % 19.07/19.00 <=> ! [B_x] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),B_x)) ) ) ) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_fold1__strict__below__iff,axiom, % 19.07/19.00 ! [V_x_2,V_A_2,T_b] : % 19.07/19.00 ( class_Orderings_Olinorder(T_b) % 19.07/19.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.00 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)),V_x_2)) % 19.07/19.00 <=> ? [B_x] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 19.07/19.00 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_x_2)) ) ) ) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_vimage__Times,axiom, % 19.07/19.00 ! [V_B_2,V_A_2,V_f_2,T_d,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,tc_prod(T_c,T_d),V_f_2),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,hAPP(c_Fun_Ocomp(tc_prod(T_c,T_d),T_c,T_b,c_Product__Type_Ofst(T_c,T_d)),V_f_2)),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_d,hAPP(c_Fun_Ocomp(tc_prod(T_c,T_d),T_d,T_b,c_Product__Type_Osnd(T_c,T_d)),V_f_2)),V_B_2)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_fold1__insert,axiom, % 19.07/19.00 ! [V_x_2,V_A_2,T_b] : % 19.07/19.00 ( class_Groups_Oab__semigroup__mult(T_b) % 19.07/19.00 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.00 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/19.00 => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)) ) ) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_fold1__antimono,axiom, % 19.07/19.00 ! [V_B_2,V_A_2,T_b] : % 19.07/19.00 ( class_Orderings_Olinorder(T_b) % 19.07/19.00 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 19.07/19.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_B_2)),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2))) ) ) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_semilattice__big_OF__eq,axiom, % 19.07/19.00 ! [V_A_2,V_F_2,V_f_2,T_b] : % 19.07/19.00 ( c_Big__Operators_Osemilattice__big(T_b,V_f_2,V_F_2) % 19.07/19.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.00 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Ex__inj__on__UNION__Sigma,axiom, % 19.07/19.00 ! [V_A_2,V_I_2,T_c,T_b] : % 19.07/19.00 ? [B_f] : % 19.07/19.00 ( c_Fun_Oinj__on(T_b,tc_prod(T_c,T_b),B_f,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) % 19.07/19.00 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,tc_prod(T_c,T_b),B_f),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2))),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_I_2),V_A_2))) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_fold__image__Sigma,axiom, % 19.07/19.00 ! [V_g_2,V_B_2,T_c,V_A_2,T_b,T_d] : % 19.07/19.00 ( class_Groups_Ocomm__monoid__mult(T_d) % 19.07/19.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.00 => ( ! [B_x] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 19.07/19.00 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) ) % 19.07/19.00 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_b,c_Groups_Otimes__class_Otimes(T_d)),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBC(T_b,T_d,tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_d),tc_fun(T_d,tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d)),T_b),c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d))),V_g_2)),c_Groups_Oone__class_Oone(T_d))),V_B_2)),c_Groups_Oone__class_Oone(T_d)),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,tc_prod(T_b,T_c),c_Groups_Otimes__class_Otimes(T_d)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_g_2)),c_Groups_Oone__class_Oone(T_d)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)) ) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_setprod__Sigma,axiom, % 19.07/19.00 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] : % 19.07/19.00 ( class_Groups_Ocomm__monoid__mult(T_d) % 19.07/19.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.00 => ( ! [B_x] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 19.07/19.00 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) ) % 19.07/19.00 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_d),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_d),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d),T_b),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(T_b,T_c),T_d),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)) ) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_setsum__Sigma,axiom, % 19.07/19.00 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] : % 19.07/19.00 ( class_Groups_Ocomm__monoid__add(T_d) % 19.07/19.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.00 => ( ! [B_x] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 19.07/19.00 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) ) % 19.07/19.00 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_d),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d),T_b),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(T_b,T_c),T_d),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)) ) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_card__SigmaI,axiom, % 19.07/19.00 ! [V_B_2,T_c,V_A_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.00 => ( ! [B_x] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 19.07/19.00 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) ) % 19.07/19.00 => hAPP(c_Finite__Set_Ocard(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_Nat_Onat,T_b),c_Finite__Set_Ocard(T_c)),V_B_2)),V_A_2) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_fold1__in,axiom, % 19.07/19.00 ! [V_A_2,T_b] : % 19.07/19.00 ( class_Groups_Oab__semigroup__mult(T_b) % 19.07/19.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.00 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.00 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)),V_A_2)) ) ) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_finite__SigmaI,axiom, % 19.07/19.00 ! [V_B_2,T_c,V_A_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.00 => ( ! [B_a] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2)) % 19.07/19.00 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a))) ) % 19.07/19.00 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_hom__fold1__commute,axiom, % 19.07/19.00 ! [V_N_2,V_h_2,T_b] : % 19.07/19.00 ( class_Lattices_Oab__semigroup__idem__mult(T_b) % 19.07/19.00 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_x),B_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y)) % 19.07/19.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 19.07/19.00 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.00 => hAPP(V_h_2,hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_N_2)) = hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_SigmaE,axiom, % 19.07/19.00 ! [V_B_2,V_A_2,V_c_2,T_c,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_c_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) % 19.07/19.00 => ~ ! [B_x] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 19.07/19.00 => ! [B_y] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(T_c),B_y),hAPP(V_B_2,B_x))) % 19.07/19.00 => V_c_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y) ) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_map__pair__surj,axiom, % 19.07/19.00 ! [V_g_2,T_d,T_e,V_f_2,T_b,T_c] : % 19.07/19.00 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.00 => ( hAPP(c_Set_Oimage(T_e,T_d,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_e,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)) % 19.07/19.00 => hAPP(c_Set_Oimage(tc_prod(T_c,T_e),tc_prod(T_b,T_d),c_Product__Type_Omap__pair(T_c,T_b,T_e,T_d,V_f_2,V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_c,T_e),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_map__pair__imageI,axiom, % 19.07/19.00 ! [V_g_2,V_f_2,T_e,T_d,V_R_2,V_b_2,V_a_2,T_c,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_R_2)) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_e)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),hAPP(V_f_2,V_a_2)),hAPP(V_g_2,V_b_2))),hAPP(c_Set_Oimage(tc_prod(T_b,T_c),tc_prod(T_d,T_e),c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,V_f_2,V_g_2)),V_R_2))) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_fst__map__pair,axiom, % 19.07/19.00 ! [V_x_2,V_g_2,V_f_2,T_e,T_d,T_c,T_b] : hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_e),V_x_2)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_snd__prod__fun,axiom, % 19.07/19.00 ! [V_x_2,V_g_2,V_f_2,T_e,T_d,T_b,T_c] : hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(c_Product__Type_Omap__pair(T_d,T_c,T_e,T_b,V_f_2,V_g_2),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_d,T_e),V_x_2)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_map__pair__simp,axiom, % 19.07/19.00 ! [V_b_2,V_a_2,V_g_2,V_f_2,T_c,T_e,T_b,T_d] : hAPP(c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),V_a_2),V_b_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,V_a_2)),hAPP(V_g_2,V_b_2)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_map__pair__ident,axiom, % 19.07/19.00 ! [V_z_2,T_c,T_b] : hAPP(c_Product__Type_Omap__pair(T_b,T_b,T_c,T_c,c_COMBI(T_b),c_COMBI(T_c)),V_z_2) = V_z_2 ). % 19.07/19.00 % 19.07/19.00 fof(fact_map__pair_Ocompositionality,axiom, % 19.07/19.00 ! [V_prod_2,V_i_2,V_h_2,T_g,T_f,V_g_2,V_f_2,T_c,T_e,T_b,T_d] : hAPP(c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2),hAPP(c_Product__Type_Omap__pair(T_f,T_d,T_g,T_e,V_h_2,V_i_2),V_prod_2)) = hAPP(c_Product__Type_Omap__pair(T_f,T_b,T_g,T_c,hAPP(c_Fun_Ocomp(T_d,T_b,T_f,V_f_2),V_h_2),hAPP(c_Fun_Ocomp(T_e,T_c,T_g,V_g_2),V_i_2)),V_prod_2) ). % 19.07/19.00 % 19.07/19.00 fof(fact_map__pair__compose,axiom, % 19.07/19.00 ! [V_g2_2,V_g1_2,T_g,V_f2_2,V_f1_2,T_f,T_e,T_c,T_d,T_b] : c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,hAPP(c_Fun_Ocomp(T_f,T_d,T_b,V_f1_2),V_f2_2),hAPP(c_Fun_Ocomp(T_g,T_e,T_c,V_g1_2),V_g2_2)) = hAPP(c_Fun_Ocomp(tc_prod(T_f,T_g),tc_prod(T_d,T_e),tc_prod(T_b,T_c),c_Product__Type_Omap__pair(T_f,T_d,T_g,T_e,V_f1_2,V_g1_2)),c_Product__Type_Omap__pair(T_b,T_f,T_c,T_g,V_f2_2,V_g2_2)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_map__pair_Ocomp,axiom, % 19.07/19.00 ! [V_i_2,V_h_2,V_g_2,V_f_2,T_c,T_b,T_e,T_d,T_g,T_f] : hAPP(c_Fun_Ocomp(tc_prod(T_f,T_g),tc_prod(T_d,T_e),tc_prod(T_b,T_c),c_Product__Type_Omap__pair(T_f,T_d,T_g,T_e,V_f_2,V_g_2)),c_Product__Type_Omap__pair(T_b,T_f,T_c,T_g,V_h_2,V_i_2)) = c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,hAPP(c_Fun_Ocomp(T_f,T_d,T_b,V_f_2),V_h_2),hAPP(c_Fun_Ocomp(T_g,T_e,T_c,V_g_2),V_i_2)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_snd__comp__map__pair,axiom, % 19.07/19.00 ! [V_g_2,V_f_2,T_c,T_b,T_d,T_e] : hAPP(c_Fun_Ocomp(tc_prod(T_e,T_d),T_d,tc_prod(T_b,T_c),c_Product__Type_Osnd(T_e,T_d)),c_Product__Type_Omap__pair(T_b,T_e,T_c,T_d,V_f_2,V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_d,tc_prod(T_b,T_c),V_g_2),c_Product__Type_Osnd(T_b,T_c)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_fst__comp__map__pair,axiom, % 19.07/19.00 ! [V_g_2,V_f_2,T_c,T_b,T_e,T_d] : hAPP(c_Fun_Ocomp(tc_prod(T_d,T_e),T_d,tc_prod(T_b,T_c),c_Product__Type_Ofst(T_d,T_e)),c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,V_f_2,V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_d,tc_prod(T_b,T_c),V_f_2),c_Product__Type_Ofst(T_b,T_c)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_map__pair__def,axiom, % 19.07/19.00 ! [V_g_2,V_f_2,T_e,T_c,T_d,T_b] : c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,V_f_2,V_g_2) = hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_prod(T_d,T_e)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,T_e),tc_fun(T_c,tc_prod(T_d,T_e))),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_prod(T_d,T_e)),tc_fun(tc_fun(T_c,T_e),tc_fun(T_c,tc_prod(T_d,T_e))),T_b),c_COMBB(T_e,tc_prod(T_d,T_e),T_c)),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_e,tc_prod(T_d,T_e)),T_b),c_Product__Type_OPair(T_d,T_e)),V_f_2))),V_g_2)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_map__pair__surj__on,axiom, % 19.07/19.00 ! [V_B_H_2,V_B_2,V_g_2,T_d,T_e,V_A_H_2,V_A_2,V_f_2,T_b,T_c] : % 19.07/19.00 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_A_H_2 % 19.07/19.00 => ( hAPP(c_Set_Oimage(T_e,T_d,V_g_2),V_B_2) = V_B_H_2 % 19.07/19.00 => hAPP(c_Set_Oimage(tc_prod(T_c,T_e),tc_prod(T_b,T_d),c_Product__Type_Omap__pair(T_c,T_b,T_e,T_d,V_f_2,V_g_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_e),V_A_2),hAPP(c_COMBK(tc_fun(T_e,tc_HOL_Obool),T_c),V_B_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_d),V_A_H_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_b),V_B_H_2)) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_map__pair__inj__on,axiom, % 19.07/19.00 ! [V_B_2,V_g_2,T_e,T_d,V_A_2,V_f_2,T_c,T_b] : % 19.07/19.00 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 19.07/19.00 => ( c_Fun_Oinj__on(T_d,T_e,V_g_2,V_B_2) % 19.07/19.00 => c_Fun_Oinj__on(tc_prod(T_b,T_d),tc_prod(T_c,T_e),c_Product__Type_Omap__pair(T_b,T_c,T_d,T_e,V_f_2,V_g_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_b),V_B_2))) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_prod__fun__imageE,axiom, % 19.07/19.00 ! [V_R_2,V_g_2,V_f_2,T_e,T_d,V_c_2,T_c,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_c_2),hAPP(c_Set_Oimage(tc_prod(T_d,T_e),tc_prod(T_b,T_c),c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2)),V_R_2))) % 19.07/19.00 => ~ ! [B_x,B_y] : % 19.07/19.00 ( V_c_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_y)) % 19.07/19.00 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_e)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),B_x),B_y)),V_R_2)) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_refl__on__def,axiom, % 19.07/19.00 ! [V_r_2,V_A_2,T_b] : % 19.07/19.00 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 19.07/19.00 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) % 19.07/19.00 & ! [B_x] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) ) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_refl__on__Id__on,axiom, % 19.07/19.00 ! [V_A_2,T_b] : c_Relation_Orefl__on(T_b,V_A_2,c_Relation_OId__on(T_b,V_A_2)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_refl__on__empty,axiom, % 19.07/19.00 ! [T_b] : c_Relation_Orefl__on(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) ). % 19.07/19.00 % 19.07/19.00 fof(fact_refl__on__Un,axiom, % 19.07/19.00 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] : % 19.07/19.00 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 19.07/19.00 => ( c_Relation_Orefl__on(T_b,V_B_2,V_s_2) % 19.07/19.00 => c_Relation_Orefl__on(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_refl__on__Int,axiom, % 19.07/19.00 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] : % 19.07/19.00 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 19.07/19.00 => ( c_Relation_Orefl__on(T_b,V_B_2,V_s_2) % 19.07/19.00 => c_Relation_Orefl__on(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_refl__onD,axiom, % 19.07/19.00 ! [V_a_2,V_r_2,V_A_2,T_b] : % 19.07/19.00 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 19.07/19.00 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),V_r_2)) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_refl__onD1,axiom, % 19.07/19.00 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] : % 19.07/19.00 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 19.07/19.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_refl__onD2,axiom, % 19.07/19.00 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] : % 19.07/19.00 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 19.07/19.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_refl__onI,axiom, % 19.07/19.00 ! [V_A_2,V_r_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) % 19.07/19.00 => ( ! [B_x] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) ) % 19.07/19.00 => c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_setprod__pos__nat,axiom, % 19.07/19.00 ! [V_f_2,V_S_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 19.07/19.00 => ( ! [B_x] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) % 19.07/19.00 => 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))) ) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_S_2))) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_folding__one__idem_Ohom__commute,axiom, % 19.07/19.00 ! [V_N_2,V_h_2,V_F_2,V_f_2,T_b] : % 19.07/19.00 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) % 19.07/19.00 => ( ! [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)) % 19.07/19.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 19.07/19.00 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.00 => hAPP(V_h_2,hAPP(V_F_2,V_N_2)) = hAPP(V_F_2,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Rep__Integ__cases,axiom, % 19.07/19.00 ! [V_y_2] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg)) % 19.07/19.00 => ~ ! [B_x] : V_y_2 != hAPP(c_Int_ORep__Integ,B_x) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Rep__Integ__induct,axiom, % 19.07/19.00 ! [V_Pa_2,V_y_2] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg)) % 19.07/19.00 => ( ! [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Int_ORep__Integ,B_x))) % 19.07/19.00 => hBOOL(hAPP(V_Pa_2,V_y_2)) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_fun__left__comm__idem__remove,axiom, % 19.07/19.00 ! [T_b] : c_Finite__Set_Ofun__left__comm__idem(T_b,tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) ). % 19.07/19.00 % 19.07/19.00 fof(fact_fun__left__comm__idem_Ofun__comp__idem,axiom, % 19.07/19.00 ! [V_x_2,V_f_2,T_c,T_b] : % 19.07/19.00 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) % 19.07/19.00 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_f_2,V_x_2) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_min__max_Ofun__left__comm__idem__inf,axiom, % 19.07/19.00 ! [T_b] : % 19.07/19.00 ( class_Orderings_Olinorder(T_b) % 19.07/19.00 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_fun__left__comm__idem__sup,axiom, % 19.07/19.00 ! [T_b] : % 19.07/19.00 ( class_Lattices_Osemilattice__sup(T_b) % 19.07/19.00 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_fun__left__comm__idem__inf,axiom, % 19.07/19.00 ! [T_b] : % 19.07/19.00 ( class_Lattices_Osemilattice__inf(T_b) % 19.07/19.00 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_fun__left__comm__idem_Ofun__left__idem,axiom, % 19.07/19.00 ! [V_z_2,V_x_2,V_f_2,T_c,T_b] : % 19.07/19.00 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) % 19.07/19.00 => 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) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_fun__left__comm__idem_Ofun__left__comm__idem__apply,axiom, % 19.07/19.00 ! [V_g_2,T_d,V_f_2,T_c,T_b] : % 19.07/19.00 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) % 19.07/19.00 => c_Finite__Set_Ofun__left__comm__idem(T_d,T_c,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,T_c),T_d),V_f_2),V_g_2)) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_fun__left__comm__idem,axiom, % 19.07/19.00 ! [T_b] : % 19.07/19.00 ( class_Lattices_Oab__semigroup__idem__mult(T_b) % 19.07/19.00 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_min__max_Ofun__left__comm__idem__sup,axiom, % 19.07/19.00 ! [T_b] : % 19.07/19.00 ( class_Orderings_Olinorder(T_b) % 19.07/19.00 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_fun__left__comm__idem__insert,axiom, % 19.07/19.00 ! [T_b] : c_Finite__Set_Ofun__left__comm__idem(T_b,tc_fun(T_b,tc_HOL_Obool),c_Set_Oinsert(T_b)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_folding__image__simple_Ounion__inter__neutral,axiom, % 19.07/19.00 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 19.07/19.00 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 19.07/19.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 19.07/19.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 19.07/19.00 => ( ! [B_x] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) % 19.07/19.00 => hAPP(V_g_2,B_x) = V_z_2 ) % 19.07/19.00 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_card__less__Suc2,axiom, % 19.07/19.00 ! [V_i_2,V_M_2] : % 19.07/19.00 ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) % 19.07/19.00 => 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))))) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_CollectI,axiom, % 19.07/19.00 ! [T_b,V_a_2,V_Pa_2] : % 19.07/19.00 ( hBOOL(hAPP(V_Pa_2,V_a_2)) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_finite__Collect__conjI,axiom, % 19.07/19.00 ! [V_Qa_2,V_Pa_2,T_b] : % 19.07/19.00 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2))) % 19.07/19.00 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Qa_2))) ) % 19.07/19.00 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Pa_2)),V_Qa_2)))) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_finite__Collect__less__nat,axiom, % 19.07/19.00 ! [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)))) ). % 19.07/19.00 % 19.07/19.00 fof(fact_finite__Collect__le__nat,axiom, % 19.07/19.00 ! [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)))) ). % 19.07/19.00 % 19.07/19.00 fof(fact_SetCompr__Sigma__eq,axiom, % 19.07/19.00 ! [V_Qa_2,V_Pa_2,T_c,T_b] : hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Pa_2))),V_Qa_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_OCollect(T_b),V_Pa_2)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),V_Qa_2)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Collect__split,axiom, % 19.07/19.00 ! [V_Qa_2,V_Pa_2,T_c,T_b] : hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Pa_2))),V_Qa_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_OCollect(T_b),V_Pa_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_OCollect(T_c),V_Qa_2))) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Collect__neg__eq,axiom, % 19.07/19.00 ! [V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_Pa_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_vimage__Collect__eq,axiom, % 19.07/19.00 ! [V_Pa_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(c_Set_OCollect(T_c),V_Pa_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(T_c,tc_HOL_Obool,T_b),V_Pa_2),V_f_2)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_CollectE,axiom, % 19.07/19.00 ! [V_Pa_2,V_a_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))) % 19.07/19.00 => hBOOL(hAPP(V_Pa_2,V_a_2)) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_CollectD,axiom, % 19.07/19.00 ! [V_Pa_2,V_a_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))) % 19.07/19.00 => hBOOL(hAPP(V_Pa_2,V_a_2)) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_mem__Collect__eq,axiom, % 19.07/19.00 ! [V_Pa_2,V_a_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))) % 19.07/19.00 <=> hBOOL(hAPP(V_Pa_2,V_a_2)) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Collect__mem__eq,axiom, % 19.07/19.00 ! [V_A_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)) = V_A_2 ). % 19.07/19.00 % 19.07/19.00 fof(fact_UNIV__def,axiom, % 19.07/19.00 ! [T_b] : c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),hAPP(c_COMBK(tc_HOL_Obool,T_b),c_fTrue)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_finite__Collect__disjI,axiom, % 19.07/19.00 ! [V_Qa_2,V_Pa_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),V_Pa_2)),V_Qa_2)))) % 19.07/19.00 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2))) % 19.07/19.00 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Qa_2))) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_insert__Collect,axiom, % 19.07/19.00 ! [V_Pa_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2)))),V_Pa_2)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Collect__conj__eq,axiom, % 19.07/19.00 ! [V_Qa_2,V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Pa_2)),V_Qa_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2)),hAPP(c_Set_OCollect(T_b),V_Qa_2)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Collect__disj__eq,axiom, % 19.07/19.00 ! [V_Qa_2,V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),V_Pa_2)),V_Qa_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2)),hAPP(c_Set_OCollect(T_b),V_Qa_2)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_empty__Collect__eq,axiom, % 19.07/19.00 ! [V_Pa_2,T_b] : % 19.07/19.00 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),V_Pa_2) % 19.07/19.00 <=> ! [B_x] : ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Collect__empty__eq,axiom, % 19.07/19.00 ! [V_Pa_2,T_b] : % 19.07/19.00 ( hAPP(c_Set_OCollect(T_b),V_Pa_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.00 <=> ! [B_x] : ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_empty__def,axiom, % 19.07/19.00 ! [T_b] : c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),hAPP(c_COMBK(tc_HOL_Obool,T_b),c_fFalse)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Collect__def,axiom, % 19.07/19.00 ! [V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),V_Pa_2) = V_Pa_2 ). % 19.07/19.00 % 19.07/19.00 fof(fact_insert__compr,axiom, % 19.07/19.00 ! [V_B_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))) ). % 19.07/19.00 % 19.07/19.00 fof(fact_insert__compr__raw,axiom, % 19.07/19.00 ! [V_B_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Un__def,axiom, % 19.07/19.00 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Int__Collect,axiom, % 19.07/19.00 ! [V_Pa_2,V_A_2,V_x_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)))) % 19.07/19.00 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/19.00 & hBOOL(hAPP(V_Pa_2,V_x_2)) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Int__def,axiom, % 19.07/19.00 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Collect__conv__if,axiom, % 19.07/19.00 ! [T_b,V_a_2,V_Pa_2] : % 19.07/19.00 ( ( hBOOL(hAPP(V_Pa_2,V_a_2)) % 19.07/19.00 => hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_Pa_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) % 19.07/19.00 & ( ~ hBOOL(hAPP(V_Pa_2,V_a_2)) % 19.07/19.00 => hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_Pa_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Collect__conv__if2,axiom, % 19.07/19.00 ! [T_b,V_a_2,V_Pa_2] : % 19.07/19.00 ( ( hBOOL(hAPP(V_Pa_2,V_a_2)) % 19.07/19.00 => hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_a_2))),V_Pa_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) % 19.07/19.00 & ( ~ hBOOL(hAPP(V_Pa_2,V_a_2)) % 19.07/19.00 => hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_a_2))),V_Pa_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_singleton__conv,axiom, % 19.07/19.00 ! [V_a_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ). % 19.07/19.00 % 19.07/19.00 fof(fact_singleton__conv2,axiom, % 19.07/19.00 ! [V_a_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(c_fequal,V_a_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ). % 19.07/19.00 % 19.07/19.00 fof(fact_set__diff__eq,axiom, % 19.07/19.00 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2)))) ). % 19.07/19.00 % 19.07/19.00 fof(fact_finite__Collect__not,axiom, % 19.07/19.00 ! [V_Pa_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2))) % 19.07/19.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_Pa_2)))) % 19.07/19.00 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_insert__def,axiom, % 19.07/19.00 ! [V_B_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_B_2) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Compl__eq,axiom, % 19.07/19.00 ! [V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))) ). % 19.07/19.00 % 19.07/19.00 fof(fact_vimage__def,axiom, % 19.07/19.00 ! [V_B_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(T_c)),V_f_2)),V_B_2)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Collect__imp__eq,axiom, % 19.07/19.00 ! [V_Qa_2,V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),V_Pa_2)),V_Qa_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2))),hAPP(c_Set_OCollect(T_b),V_Qa_2)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_dom__def,axiom, % 19.07/19.00 ! [V_m_2,T_c,T_b] : c_Map_Odom(T_b,T_c,V_m_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,tc_Option_Ooption(T_c),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_c),tc_fun(tc_Option_Ooption(T_c),tc_HOL_Obool),T_b),c_fequal),V_m_2)),c_Option_Ooption_ONone(T_c)))) ). % 19.07/19.00 % 19.07/19.00 fof(fact_finite__M__bounded__by__nat,axiom, % 19.07/19.00 ! [V_i_2,V_Pa_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),V_Pa_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_i_2))))) ). % 19.07/19.00 % 19.07/19.00 fof(fact_setsum__setsum__restrict,axiom, % 19.07/19.00 ! [V_R_2,V_f_2,V_T_2,T_c,V_S_2,T_b,T_d] : % 19.07/19.00 ( class_Groups_Ocomm__monoid__add(T_d) % 19.07/19.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 19.07/19.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2)) % 19.07/19.00 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_d),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d),T_b),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d)),V_f_2)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_T_2)))),V_R_2)))),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_d),tc_fun(tc_fun(T_b,tc_HOL_Obool),T_d),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d)),hAPP(c_COMBC(T_b,T_c,T_d),V_f_2))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Set_OCollect(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)))),hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_R_2))))),V_T_2) ) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_if__image__distrib,axiom, % 19.07/19.00 ! [V_S_2,V_g_2,V_f_2,V_Pa_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),V_Pa_2)),V_f_2)),V_g_2)),V_S_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_c),V_Pa_2)))),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),V_Pa_2))))) ). % 19.07/19.00 % 19.07/19.00 fof(fact_dom__if,axiom, % 19.07/19.00 ! [V_g_2,V_f_2,V_Pa_2,T_c,T_b] : c_Map_Odom(T_b,T_c,hAPP(hAPP(c_COMBS(T_b,tc_Option_Ooption(T_c),tc_Option_Ooption(T_c)),hAPP(hAPP(c_COMBS(T_b,tc_Option_Ooption(T_c),tc_fun(tc_Option_Ooption(T_c),tc_Option_Ooption(T_c))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(T_c),tc_fun(tc_Option_Ooption(T_c),tc_Option_Ooption(T_c))),T_b),c_If(tc_Option_Ooption(T_c))),V_Pa_2)),V_f_2)),V_g_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_c,V_f_2)),hAPP(c_Set_OCollect(T_b),V_Pa_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_c,V_g_2)),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_Pa_2)))) ). % 19.07/19.00 % 19.07/19.00 fof(fact_nat__seg__image__imp__finite,axiom, % 19.07/19.00 ! [V_n_2,V_f_2,T_b,V_A_2] : % 19.07/19.00 ( V_A_2 = hAPP(c_Set_Oimage(tc_Nat_Onat,T_b,V_f_2),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_n_2))) % 19.07/19.00 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_setsum__restrict__set_H,axiom, % 19.07/19.00 ! [V_B_2,V_f_2,V_A_2,T_b,T_c] : % 19.07/19.00 ( class_Groups_Ocomm__monoid__add(T_c) % 19.07/19.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.00 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_f_2)),c_Groups_Ozero__class_Ozero(T_c))),V_A_2) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_setsum__image__gen,axiom, % 19.07/19.00 ! [V_f_2,T_d,V_g_2,V_S_2,T_b,T_c] : % 19.07/19.00 ( class_Groups_Ocomm__monoid__add(T_c) % 19.07/19.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 19.07/19.00 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),T_c,T_d),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Set_OCollect(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)))),hAPP(c_COMBC(T_b,T_d,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,tc_HOL_Obool),T_b),c_fequal),V_f_2)))))),hAPP(c_Set_Oimage(T_b,T_d,V_f_2),V_S_2)) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Image__singleton,axiom, % 19.07/19.00 ! [V_a_2,V_r_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(T_c,T_b),tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_c,T_b))),hAPP(c_Product__Type_OPair(T_c,T_b),V_a_2))),V_r_2)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_setsum__cases,axiom, % 19.07/19.00 ! [V_g_2,V_f_2,V_Pa_2,V_A_2,T_b,T_c] : % 19.07/19.00 ( class_Groups_Ocomm__monoid__add(T_c) % 19.07/19.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.00 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),V_Pa_2)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2))))) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_card__less__Suc,axiom, % 19.07/19.00 ! [V_i_2,V_M_2] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) % 19.07/19.00 => 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))))) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_card__less,axiom, % 19.07/19.00 ! [V_i_2,V_M_2] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) % 19.07/19.00 => 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) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_dom__override__on,axiom, % 19.07/19.00 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] : c_Map_Odom(T_b,T_c,c_Fun_Ooverride__on(T_b,tc_Option_Ooption(T_c),V_f_2,V_g_2,V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_c,V_f_2)),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Map_Odom(T_b,T_c,V_g_2)))))),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Map_Odom(T_b,T_c,V_g_2))))) ). % 19.07/19.00 % 19.07/19.00 fof(fact_setsum__multicount,axiom, % 19.07/19.00 ! [V_k_2,V_R_2,V_T_2,T_c,V_S_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 19.07/19.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2)) % 19.07/19.00 => ( ! [B_x] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_T_2)) % 19.07/19.00 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_R_2),B_x)))) = V_k_2 ) % 19.07/19.00 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_Nat_Onat,T_b),c_Finite__Set_Ocard(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_T_2)))),V_R_2)))),V_S_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(T_c),V_T_2)) ) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_finite__Collect__subsets,axiom, % 19.07/19.00 ! [V_A_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.00 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),V_A_2)))) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Pow__def,axiom, % 19.07/19.00 ! [V_A_2,T_b] : hAPP(c_Set_OPow(T_b),V_A_2) = hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),V_A_2)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_override__on__apply__in,axiom, % 19.07/19.00 ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 19.07/19.00 => hAPP(c_Fun_Ooverride__on(T_b,T_c,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_g_2,V_a_2) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_override__on__apply__notin,axiom, % 19.07/19.00 ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] : % 19.07/19.00 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 19.07/19.00 => hAPP(c_Fun_Ooverride__on(T_b,T_c,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_f_2,V_a_2) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_override__on__emptyset,axiom, % 19.07/19.00 ! [V_g_2,V_f_2,T_c,T_b] : c_Fun_Ooverride__on(T_b,T_c,V_f_2,V_g_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_f_2 ). % 19.07/19.00 % 19.07/19.00 fof(fact_inj__graph,axiom, % 19.07/19.00 ! [T_c,T_b] : c_Fun_Oinj__on(tc_fun(T_b,T_c),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,T_c)),c_Set_OCollect(tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,T_c)),c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool)),hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,T_c),tc_HOL_Obool))) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J,axiom, % 19.07/19.00 ! [V_Pa_2] : c_Nat__Transfer_Onat__set(hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_Pa_2))) ). % 19.07/19.00 % 19.07/19.00 fof(fact_override__on__def,axiom, % 19.07/19.00 ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] : % 19.07/19.00 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 19.07/19.00 => hAPP(c_Fun_Ooverride__on(T_b,T_c,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_g_2,V_a_2) ) % 19.07/19.00 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 19.07/19.00 => hAPP(c_Fun_Ooverride__on(T_b,T_c,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_f_2,V_a_2) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_finite__psubset__def,axiom, % 19.07/19.00 ! [T_b] : c_Wellfounded_Ofinite__psubset(T_b) = hAPP(c_Set_OCollect(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBS(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool))))),c_Finite__Set_Ofinite(T_b)))) ). % 19.07/19.00 % 19.07/19.00 fof(fact_inv__image__def,axiom, % 19.07/19.00 ! [V_f_2,V_r_2,T_b,T_c] : hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),V_r_2),V_f_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_c,T_c)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_c,T_c),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_c,T_c)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_c),tc_fun(T_b,tc_prod(T_c,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_c,T_c)),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,tc_prod(T_c,T_c))),T_b),c_COMBB(T_c,tc_prod(T_c,T_c),T_b)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_prod(T_c,T_c)),T_b),c_Product__Type_OPair(T_c,T_c)),V_f_2))),V_f_2)))),V_r_2))) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J,axiom, % 19.07/19.00 ! [V_Pa_2] : hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_Pa_2)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Nat_Onat),V_Pa_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J,axiom, % 19.07/19.00 ! [V_Pa_2] : hAPP(c_Set_OCollect(tc_Nat_Onat),V_Pa_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),V_Pa_2),c_Int_Onat)))) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Nitpick_Oprod__def,axiom, % 19.07/19.00 ! [V_B_2,V_A_2,T_c,T_b] : c_Nitpick_Oprod(T_b,T_c,V_A_2,V_B_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2)))) ). % 19.07/19.00 % 19.07/19.00 fof(fact_int__ge__less__than2__def,axiom, % 19.07/19.00 ! [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)))) ). % 19.07/19.00 % 19.07/19.00 fof(fact_int__ge__less__than__def,axiom, % 19.07/19.00 ! [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)))) ). % 19.07/19.00 % 19.07/19.00 fof(fact_reflp__def,axiom, % 19.07/19.00 ! [V_r_2,T_b] : % 19.07/19.00 ( c_Predicate_Oreflp(T_b,V_r_2) % 19.07/19.00 <=> c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_reflpE,axiom, % 19.07/19.00 ! [V_x_2,V_r_2,T_b] : % 19.07/19.00 ( c_Predicate_Oreflp(T_b,V_r_2) % 19.07/19.00 => hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_x_2)) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_min__max_Osup__Inf2__distrib,axiom, % 19.07/19.00 ! [V_B_2,V_A_2,T_b] : % 19.07/19.00 ( class_Orderings_Olinorder(T_b) % 19.07/19.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.00 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 19.07/19.00 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.00 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Orderings_Oord__class_Omax(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))))))) ) ) ) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_min__max_Osup__Inf1__distrib,axiom, % 19.07/19.00 ! [V_x_2,V_A_2,T_b] : % 19.07/19.00 ( class_Orderings_Olinorder(T_b) % 19.07/19.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.00 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.00 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))))) ) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_finite__Collect__bounded__ex,axiom, % 19.07/19.00 ! [V_Qa_2,T_c,V_Pa_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2))) % 19.07/19.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Pa_2))),V_Qa_2))))) % 19.07/19.00 <=> ! [B_y] : % 19.07/19.00 ( hBOOL(hAPP(V_Pa_2,B_y)) % 19.07/19.00 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_Qa_2),B_y)))) ) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_finite__image__set,axiom, % 19.07/19.00 ! [V_f_2,T_c,V_Pa_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2))) % 19.07/19.00 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,T_b)),c_fequal)),V_f_2)))),V_Pa_2))))) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_ran__def,axiom, % 19.07/19.00 ! [V_m_2,T_b,T_c] : c_Map_Oran(T_c,T_b,V_m_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_b),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBC(T_c,tc_Option_Ooption(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_b),tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool),T_c),c_fequal),V_m_2))),c_Option_Ooption_OSome(T_b)))) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Pow__Compl,axiom, % 19.07/19.00 ! [V_A_2,T_b] : hAPP(c_Set_OPow(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),c_HOL_OEx(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBS(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),c_Set_OPow(T_b))))) ). % 19.07/19.00 % 19.07/19.00 fof(fact_add__Min__commute,axiom, % 19.07/19.00 ! [V_k_2,V_N_2,T_b] : % 19.07/19.00 ( class_Groups_Olinordered__ab__semigroup__add(T_b) % 19.07/19.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 19.07/19.00 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.00 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_k_2),c_Big__Operators_Olinorder__class_OMin(T_b,V_N_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(T_b),V_k_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_N_2))))) ) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_add__Max__commute,axiom, % 19.07/19.00 ! [V_k_2,V_N_2,T_b] : % 19.07/19.00 ( class_Groups_Olinordered__ab__semigroup__add(T_b) % 19.07/19.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 19.07/19.00 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.00 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_k_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_N_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(T_b),V_k_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_N_2))))) ) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_sup__Inf1__distrib,axiom, % 19.07/19.00 ! [V_x_2,V_A_2,T_b] : % 19.07/19.00 ( class_Lattices_Odistrib__lattice(T_b) % 19.07/19.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.00 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.00 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))))) ) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_sup__Inf2__distrib,axiom, % 19.07/19.00 ! [V_B_2,V_A_2,T_b] : % 19.07/19.00 ( class_Lattices_Odistrib__lattice(T_b) % 19.07/19.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.00 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 19.07/19.00 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.00 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))))))) ) ) ) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_inf__Sup1__distrib,axiom, % 19.07/19.00 ! [V_x_2,V_A_2,T_b] : % 19.07/19.00 ( class_Lattices_Odistrib__lattice(T_b) % 19.07/19.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.00 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.00 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))))) ) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_inf__Sup2__distrib,axiom, % 19.07/19.00 ! [V_B_2,V_A_2,T_b] : % 19.07/19.00 ( class_Lattices_Odistrib__lattice(T_b) % 19.07/19.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.00 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 19.07/19.00 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.00 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))))))) ) ) ) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_min__max_Oinf__Sup1__distrib,axiom, % 19.07/19.00 ! [V_x_2,V_A_2,T_b] : % 19.07/19.00 ( class_Orderings_Olinorder(T_b) % 19.07/19.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.00 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.00 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))))) ) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_min__max_Oinf__Sup2__distrib,axiom, % 19.07/19.00 ! [V_B_2,V_A_2,T_b] : % 19.07/19.00 ( class_Orderings_Olinorder(T_b) % 19.07/19.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.00 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 19.07/19.00 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.00 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Orderings_Oord__class_Omin(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))))))) ) ) ) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_setsum__mult__setsum__if__inj,axiom, % 19.07/19.00 ! [V_B_2,V_A_2,V_g_2,V_f_2,T_c,T_b,T_d] : % 19.07/19.00 ( class_Rings_Osemiring__0(T_d) % 19.07/19.00 => ( c_Fun_Oinj__on(tc_prod(T_b,T_c),T_d,hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,T_d),tc_fun(T_c,T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_d),tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,T_d)),T_b),c_COMBB(T_d,T_d,T_c)),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,T_d),T_b),c_Groups_Otimes__class_Otimes(T_d)),V_f_2))),V_g_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))) % 19.07/19.00 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_d),c_Fun_Oid(T_d)),hAPP(c_Set_OCollect(T_d),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_d),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_d),hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c))),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),T_d),c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),T_d),hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_d),hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj))),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_b,tc_fun(T_c,T_d)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_c,T_d)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),T_d),c_COMBB(tc_fun(T_c,T_d),tc_fun(T_c,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,tc_HOL_Obool)),T_d),c_COMBB(T_d,tc_HOL_Obool,T_c)),c_fequal))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,T_d),tc_fun(T_c,T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_d),tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,T_d)),T_b),c_COMBB(T_d,T_d,T_c)),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,T_d),T_b),c_Groups_Otimes__class_Otimes(T_d)),V_f_2))),V_g_2)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))))))) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_setsum__multicount__gen,axiom, % 19.07/19.00 ! [V_k_2,V_R_2,V_t_2,T_c,V_s_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2)) % 19.07/19.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_t_2)) % 19.07/19.00 => ( ! [B_x] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_t_2)) % 19.07/19.00 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_s_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_R_2),B_x)))) = hAPP(V_k_2,B_x) ) % 19.07/19.00 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_Nat_Onat,T_b),c_Finite__Set_Ocard(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_t_2)))),V_R_2)))),V_s_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),V_k_2),V_t_2) ) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_inj__on__id,axiom, % 19.07/19.00 ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_Fun_Oid(T_b),V_A_2) ). % 19.07/19.00 % 19.07/19.00 fof(fact_o__eq__id__dest,axiom, % 19.07/19.00 ! [V_v_2,V_c_2,V_b_2,V_a_2,T_b,T_c,T_d] : % 19.07/19.00 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_c,T_c,T_b,c_Fun_Oid(T_c)),V_c_2) % 19.07/19.00 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,V_v_2) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_id__o,axiom, % 19.07/19.00 ! [V_g_2,T_b,T_c] : hAPP(c_Fun_Ocomp(T_c,T_c,T_b,c_Fun_Oid(T_c)),V_g_2) = V_g_2 ). % 19.07/19.00 % 19.07/19.00 fof(fact_o__id,axiom, % 19.07/19.00 ! [V_f_2,T_c,T_b] : hAPP(c_Fun_Ocomp(T_b,T_c,T_b,V_f_2),c_Fun_Oid(T_b)) = V_f_2 ). % 19.07/19.00 % 19.07/19.00 fof(fact_id__apply,axiom, % 19.07/19.00 ! [V_x,T_a] : hAPP(c_Fun_Oid(T_a),V_x) = V_x ). % 19.07/19.00 % 19.07/19.00 fof(fact_id__def,axiom, % 19.07/19.00 ! [V_x_1,T_a] : hAPP(c_Fun_Oid(T_a),V_x_1) = V_x_1 ). % 19.07/19.00 % 19.07/19.00 fof(fact_apfst__id,axiom, % 19.07/19.00 ! [T_c,T_b] : c_Product__Type_Oapfst(T_b,T_b,T_c,c_Fun_Oid(T_b)) = c_Fun_Oid(tc_prod(T_b,T_c)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_apsnd__id,axiom, % 19.07/19.00 ! [T_b,T_c] : c_Product__Type_Oapsnd(T_c,T_c,T_b,c_Fun_Oid(T_c)) = c_Fun_Oid(tc_prod(T_b,T_c)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_of__int__eq__id,axiom, % 19.07/19.00 c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint) ). % 19.07/19.00 % 19.07/19.00 fof(fact_vimage__id,axiom, % 19.07/19.00 ! [V_A_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_Fun_Oid(T_b)),V_A_2) = V_A_2 ). % 19.07/19.00 % 19.07/19.00 fof(fact_map__pair_Oid,axiom, % 19.07/19.00 ! [T_c,T_b] : c_Product__Type_Omap__pair(T_b,T_b,T_c,T_c,c_Fun_Oid(T_b),c_Fun_Oid(T_c)) = c_Fun_Oid(tc_prod(T_b,T_c)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_map__pair_Oidentity,axiom, % 19.07/19.00 ! [T_c,T_b] : c_Product__Type_Omap__pair(T_b,T_b,T_c,T_c,c_COMBI(T_b),c_COMBI(T_c)) = c_Fun_Oid(tc_prod(T_b,T_c)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_image__id,axiom, % 19.07/19.00 ! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_Fun_Oid(T_b)),V_Y_2) = V_Y_2 ). % 19.07/19.00 % 19.07/19.00 fof(fact_surj__id,axiom, % 19.07/19.00 ! [T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_Fun_Oid(T_b)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_folding_Oempty,axiom, % 19.07/19.00 ! [V_F_2,V_f_2,T_c,T_b] : % 19.07/19.00 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 19.07/19.00 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Fun_Oid(T_c) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_apfst__def,axiom, % 19.07/19.00 ! [V_f_2,T_c,T_d,T_b] : c_Product__Type_Oapfst(T_b,T_d,T_c,V_f_2) = c_Product__Type_Omap__pair(T_b,T_d,T_c,T_c,V_f_2,c_Fun_Oid(T_c)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_apsnd__def,axiom, % 19.07/19.00 ! [V_f_2,T_b,T_d,T_c] : c_Product__Type_Oapsnd(T_c,T_d,T_b,V_f_2) = c_Product__Type_Omap__pair(T_b,T_b,T_c,T_d,c_Fun_Oid(T_b),V_f_2) ). % 19.07/19.00 % 19.07/19.00 fof(fact_split__Pair,axiom, % 19.07/19.00 ! [T_c,T_b] : hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_prod(T_b,T_c)),c_Product__Type_OPair(T_b,T_c)) = c_Fun_Oid(tc_prod(T_b,T_c)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_setsum__reindex__id,axiom, % 19.07/19.00 ! [V_B_2,V_f_2,T_b,T_c] : % 19.07/19.00 ( class_Groups_Ocomm__monoid__add(T_c) % 19.07/19.00 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) % 19.07/19.00 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_c),c_Fun_Oid(T_c)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_setprod__reindex__id,axiom, % 19.07/19.00 ! [V_B_2,V_f_2,T_b,T_c] : % 19.07/19.00 ( class_Groups_Ocomm__monoid__mult(T_c) % 19.07/19.00 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) % 19.07/19.00 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_c),c_Fun_Oid(T_c)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_finite__conv__nat__seg__image,axiom, % 19.07/19.00 ! [V_A_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.00 <=> ? [B_n,B_f] : V_A_2 = hAPP(c_Set_Oimage(tc_Nat_Onat,T_b,B_f),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),B_n))) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_rel__comp__def,axiom, % 19.07/19.00 ! [V_s_2,V_r_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_r_2),V_s_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_d))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_b),c_COMBS(T_d,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_d),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_b),c_COMBC(T_d,tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_b,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_d),tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_b,T_d)))),c_Product__Type_OPair(T_b,T_d)))),V_r_2))))),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_d,T_c)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_d,T_c),tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_d,T_c)))),hAPP(c_COMBC(T_d,T_c,tc_prod(T_d,T_c)),c_Product__Type_OPair(T_d,T_c))))),V_s_2))))) ). % 19.07/19.00 % 19.07/19.00 fof(fact_rel__compI,axiom, % 19.07/19.00 ! [V_s_2,V_c_2,T_d,V_r_2,V_b_2,V_a_2,T_c,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2)) % 19.07/19.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_b_2),V_c_2)),V_s_2)) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),V_a_2),V_c_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2))) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_rel__comp__UNION__distrib2,axiom, % 19.07/19.00 ! [V_s_2,V_r_2,V_I_2,T_e,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)),V_I_2),V_r_2)),V_s_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBC(T_e,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_e),c_Relation_Orel__comp(T_b,T_d,T_c)),V_r_2)),V_s_2)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_rel__comp__UNION__distrib,axiom, % 19.07/19.00 ! [V_r_2,V_I_2,T_e,V_s_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_s_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool)),V_I_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_e),hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_s_2)),V_r_2)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_rel__comp__mono,axiom, % 19.07/19.00 ! [V_s_2,V_s_H_2,T_d,V_r_2,V_r_H_2,T_c,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_H_2),V_r_2)) % 19.07/19.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_s_H_2),V_s_2)) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_H_2),V_s_H_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2))) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_rel__comp__distrib,axiom, % 19.07/19.00 ! [V_T_2,V_S_2,V_R_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),V_S_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),V_T_2)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_rel__comp__distrib2,axiom, % 19.07/19.00 ! [V_R_2,V_T_2,V_S_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)),V_S_2),V_T_2)),V_R_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_S_2),V_R_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_T_2),V_R_2)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_rel__comp__empty1,axiom, % 19.07/19.00 ! [V_R_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool))),V_R_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_rel__comp__empty2,axiom, % 19.07/19.00 ! [V_R_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_O__assoc,axiom, % 19.07/19.00 ! [V_T_2,V_S_2,V_R_2,T_e,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_e,T_d),V_R_2),V_S_2)),V_T_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_e,T_c),V_R_2),hAPP(hAPP(c_Relation_Orel__comp(T_e,T_d,T_c),V_S_2),V_T_2)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_union__comp__emptyR,axiom, % 19.07/19.00 ! [V_C_2,V_B_2,V_A_2,T_b] : % 19.07/19.00 ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) % 19.07/19.00 => ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) % 19.07/19.00 => hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_B_2),V_C_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_union__comp__emptyL,axiom, % 19.07/19.00 ! [V_B_2,V_C_2,V_A_2,T_b] : % 19.07/19.00 ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) % 19.07/19.00 => ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_B_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) % 19.07/19.00 => hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_rel__comp__subset__Sigma,axiom, % 19.07/19.00 ! [V_C_2,V_s_2,T_d,V_B_2,V_A_2,V_r_2,T_c,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)))) % 19.07/19.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_s_2),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_B_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_C_2)))) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_b),V_C_2)))) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_max__ext__compat,axiom, % 19.07/19.00 ! [V_S_2,V_R_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2)) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Omax__ext(T_b,V_R_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(T_b,V_S_2)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(T_b,V_R_2))) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_min__ext__compat,axiom, % 19.07/19.00 ! [V_S_2,V_R_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2)) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Omin__ext(T_b,V_R_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(T_b,V_S_2)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(T_b,V_R_2))) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_pred__comp__rel__comp__eq,axiom, % 19.07/19.00 ! [V_y_2,V_x_2,V_s_2,V_r_2,T_d,T_c,T_b] : % 19.07/19.00 ( c_Predicate_Opred__comp(T_b,T_c,T_d,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_r_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_c,T_d)))),c_Product__Type_OPair(T_c,T_d)))),V_s_2),V_x_2,V_y_2) % 19.07/19.00 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2))) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_reduction__pairI,axiom, % 19.07/19.00 ! [V_S_2,V_R_2,T_b] : % 19.07/19.00 ( c_Wellfounded_Owf(T_b,V_R_2) % 19.07/19.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2)) % 19.07/19.00 => c_FunDef_Oreduction__pair(T_b,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_wf__less__than,axiom, % 19.07/19.00 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than) ). % 19.07/19.00 % 19.07/19.00 fof(fact_pred__comp_Ointros,axiom, % 19.07/19.00 ! [T_d,T_c,T_b,V_c_2,V_s_2,V_b_2,V_a_2,V_r_2] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 19.07/19.00 => ( hBOOL(hAPP(hAPP(V_s_2,V_b_2),V_c_2)) % 19.07/19.00 => c_Predicate_Opred__comp(T_b,T_c,T_d,V_r_2,V_s_2,V_a_2,V_c_2) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_wf__empty,axiom, % 19.07/19.00 ! [T_b] : c_Wellfounded_Owf(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) ). % 19.07/19.00 % 19.07/19.00 fof(fact_wf__inv__image,axiom, % 19.07/19.00 ! [V_f_2,T_c,V_r_2,T_b] : % 19.07/19.00 ( c_Wellfounded_Owf(T_b,V_r_2) % 19.07/19.00 => c_Wellfounded_Owf(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_wf__lex__prod,axiom, % 19.07/19.00 ! [V_rb_2,T_c,V_ra_2,T_b] : % 19.07/19.00 ( c_Wellfounded_Owf(T_b,V_ra_2) % 19.07/19.00 => ( c_Wellfounded_Owf(T_c,V_rb_2) % 19.07/19.00 => c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Wellfounded_Olex__prod(T_b,T_c,V_ra_2,V_rb_2)) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_wf__measure,axiom, % 19.07/19.00 ! [V_f_2,T_b] : c_Wellfounded_Owf(T_b,hAPP(c_Wellfounded_Omeasure(T_b),V_f_2)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_wf__union__merge,axiom, % 19.07/19.00 ! [V_S_2,V_R_2,T_b] : % 19.07/19.00 ( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) % 19.07/19.00 <=> c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_S_2),V_R_2))),V_S_2)) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_wf__no__loop,axiom, % 19.07/19.00 ! [V_R_2,T_b] : % 19.07/19.00 ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) % 19.07/19.00 => c_Wellfounded_Owf(T_b,V_R_2) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_wf__comp__self,axiom, % 19.07/19.00 ! [V_R_2,T_b] : % 19.07/19.00 ( c_Wellfounded_Owf(T_b,V_R_2) % 19.07/19.00 <=> c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2)) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_wf__less,axiom, % 19.07/19.00 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)))) ). % 19.07/19.00 % 19.07/19.00 fof(fact_wf__int__ge__less__than2,axiom, % 19.07/19.00 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(V_d_2)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_acc__wfD,axiom, % 19.07/19.00 ! [V_x_2,V_r_2,T_b] : % 19.07/19.00 ( c_Wellfounded_Owf(T_b,V_r_2) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_wf__acc__iff,axiom, % 19.07/19.00 ! [V_r_2,T_b] : % 19.07/19.00 ( c_Wellfounded_Owf(T_b,V_r_2) % 19.07/19.00 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_wf__mlex,axiom, % 19.07/19.00 ! [V_f_2,V_R_2,T_b] : % 19.07/19.00 ( c_Wellfounded_Owf(T_b,V_R_2) % 19.07/19.00 => c_Wellfounded_Owf(T_b,c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2)) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_wf__pair__less,axiom, % 19.07/19.00 c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ). % 19.07/19.00 % 19.07/19.00 fof(fact_max__ext__wf,axiom, % 19.07/19.00 ! [V_r_2,T_b] : % 19.07/19.00 ( c_Wellfounded_Owf(T_b,V_r_2) % 19.07/19.00 => c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omax__ext(T_b,V_r_2)) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_pred__comp_Oequations,axiom, % 19.07/19.00 ! [V_a3_2,V_a1_2,V_s_2,V_r_2,T_d,T_c,T_b] : % 19.07/19.00 ( c_Predicate_Opred__comp(T_b,T_c,T_d,V_r_2,V_s_2,V_a1_2,V_a3_2) % 19.07/19.00 <=> ? [B_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_b)) % 19.07/19.00 & hBOOL(hAPP(hAPP(V_s_2,B_b),V_a3_2)) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_min__ext__wf,axiom, % 19.07/19.00 ! [V_r_2,T_b] : % 19.07/19.00 ( c_Wellfounded_Owf(T_b,V_r_2) % 19.07/19.00 => c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omin__ext(T_b,V_r_2)) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_wf__finite__psubset,axiom, % 19.07/19.00 ! [T_b] : c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_b)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_wf__Int1,axiom, % 19.07/19.00 ! [V_r_H_2,V_r_2,T_b] : % 19.07/19.00 ( c_Wellfounded_Owf(T_b,V_r_2) % 19.07/19.00 => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_r_H_2)) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_wf__Int2,axiom, % 19.07/19.00 ! [V_r_H_2,V_r_2,T_b] : % 19.07/19.00 ( c_Wellfounded_Owf(T_b,V_r_2) % 19.07/19.00 => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_H_2),V_r_2)) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_wf__subset,axiom, % 19.07/19.00 ! [V_p_2,V_r_2,T_b] : % 19.07/19.00 ( c_Wellfounded_Owf(T_b,V_r_2) % 19.07/19.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_p_2),V_r_2)) % 19.07/19.00 => c_Wellfounded_Owf(T_b,V_p_2) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_wf__irrefl,axiom, % 19.07/19.00 ! [V_a_2,V_r_2,T_b] : % 19.07/19.00 ( c_Wellfounded_Owf(T_b,V_r_2) % 19.07/19.00 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),V_r_2)) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_wf__asym,axiom, % 19.07/19.00 ! [V_x_2,V_a_2,V_r_2,T_b] : % 19.07/19.00 ( c_Wellfounded_Owf(T_b,V_r_2) % 19.07/19.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_x_2)),V_r_2)) % 19.07/19.00 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_a_2)),V_r_2)) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_wf__not__sym,axiom, % 19.07/19.00 ! [V_x_2,V_a_2,V_r_2,T_b] : % 19.07/19.00 ( c_Wellfounded_Owf(T_b,V_r_2) % 19.07/19.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_x_2)),V_r_2)) % 19.07/19.00 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_a_2)),V_r_2)) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_wf__not__refl,axiom, % 19.07/19.00 ! [V_a_2,V_r_2,T_b] : % 19.07/19.00 ( c_Wellfounded_Owf(T_b,V_r_2) % 19.07/19.00 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),V_r_2)) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_wf__int__ge__less__than,axiom, % 19.07/19.00 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(V_d_2)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_wf__iff__no__infinite__down__chain,axiom, % 19.07/19.00 ! [V_r_2,T_b] : % 19.07/19.00 ( c_Wellfounded_Owf(T_b,V_r_2) % 19.07/19.00 <=> ~ ? [B_f] : % 19.07/19.00 ! [B_i] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(B_f,hAPP(c_Nat_OSuc,B_i))),hAPP(B_f,B_i))),V_r_2)) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_wfE__pf,axiom, % 19.07/19.00 ! [V_A_2,V_R_2,T_b] : % 19.07/19.00 ( c_Wellfounded_Owf(T_b,V_R_2) % 19.07/19.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Relation_OImage(T_b,T_b,V_R_2),V_A_2))) % 19.07/19.00 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_wf__union__compatible,axiom, % 19.07/19.00 ! [V_S_2,V_R_2,T_b] : % 19.07/19.00 ( c_Wellfounded_Owf(T_b,V_R_2) % 19.07/19.00 => ( c_Wellfounded_Owf(T_b,V_S_2) % 19.07/19.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2)) % 19.07/19.00 => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) ) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_wf,axiom, % 19.07/19.00 ! [T_b] : % 19.07/19.00 ( class_Orderings_Owellorder(T_b) % 19.07/19.00 => c_Wellfounded_Owf(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless(T_b)))) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_reduction__pair__def,axiom, % 19.07/19.00 ! [V_Pa_2,T_b] : % 19.07/19.00 ( c_FunDef_Oreduction__pair(T_b,V_Pa_2) % 19.07/19.00 <=> ( c_Wellfounded_Owf(T_b,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2)) % 19.07/19.00 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2))) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_reduction__pair__lemma,axiom, % 19.07/19.00 ! [V_S_2,V_R_2,V_Pa_2,T_b] : % 19.07/19.00 ( c_FunDef_Oreduction__pair(T_b,V_Pa_2) % 19.07/19.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2))) % 19.07/19.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_S_2),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2))) % 19.07/19.00 => ( c_Wellfounded_Owf(T_b,V_S_2) % 19.07/19.00 => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) ) ) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_wf__map__pair__image,axiom, % 19.07/19.00 ! [V_f_2,T_c,V_r_2,T_b] : % 19.07/19.00 ( c_Wellfounded_Owf(T_b,V_r_2) % 19.07/19.00 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 19.07/19.00 => c_Wellfounded_Owf(T_c,hAPP(c_Set_Oimage(tc_prod(T_b,T_b),tc_prod(T_c,T_c),c_Product__Type_Omap__pair(T_b,T_c,T_b,T_c,V_f_2,V_f_2)),V_r_2)) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_wf__lenlex,axiom, % 19.07/19.00 ! [V_r_2,T_b] : % 19.07/19.00 ( c_Wellfounded_Owf(T_b,V_r_2) % 19.07/19.00 => c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olenlex(T_b,V_r_2)) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_wf__if__measure,axiom, % 19.07/19.00 ! [T_b,V_g_2,V_f_2,V_Pa_2] : % 19.07/19.00 ( ! [B_x] : % 19.07/19.00 ( hBOOL(hAPP(V_Pa_2,B_x)) % 19.07/19.00 => 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))) ) % 19.07/19.00 => c_Wellfounded_Owf(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Pa_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),V_g_2))))) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_pred__nat__def,axiom, % 19.07/19.00 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))) ). % 19.07/19.00 % 19.07/19.00 fof(fact_wf__lex,axiom, % 19.07/19.00 ! [V_r_2,T_b] : % 19.07/19.00 ( c_Wellfounded_Owf(T_b,V_r_2) % 19.07/19.00 => c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olex(T_b,V_r_2)) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_wf__pred__nat,axiom, % 19.07/19.00 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat) ). % 19.07/19.00 % 19.07/19.00 fof(fact_lex__def,axiom, % 19.07/19.00 ! [V_r_2,T_b] : c_List_Olex(T_b,V_r_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(T_b,V_r_2)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_wf__lexn,axiom, % 19.07/19.00 ! [V_n_2,V_r_2,T_b] : % 19.07/19.00 ( c_Wellfounded_Owf(T_b,V_r_2) % 19.07/19.00 => c_Wellfounded_Owf(tc_List_Olist(T_b),hAPP(c_List_Olexn(T_b,V_r_2),V_n_2)) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_lexn_Osimps_I1_J,axiom, % 19.07/19.00 ! [V_r_2,T_b] : hAPP(c_List_Olexn(T_b,V_r_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_wf__same__fst,axiom, % 19.07/19.00 ! [T_b,V_R_2,T_c,V_Pa_2] : % 19.07/19.00 ( ! [B_x] : % 19.07/19.00 ( hBOOL(hAPP(V_Pa_2,B_x)) % 19.07/19.00 => c_Wellfounded_Owf(T_c,hAPP(V_R_2,B_x)) ) % 19.07/19.00 => c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Recdef_Osame__fst(T_b,T_c,V_Pa_2,V_R_2)) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Range__Collect__split,axiom, % 19.07/19.00 ! [V_Pa_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(c_Set_OCollect(tc_prod(T_c,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_HOL_Obool),V_Pa_2))) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c)),hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_Pa_2))) ). % 19.07/19.00 % 19.07/19.00 fof(fact_RangeI,axiom, % 19.07/19.00 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2)) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Range__Id__on,axiom, % 19.07/19.00 ! [V_A_2,T_b] : hAPP(c_Relation_ORange(T_b,T_b),c_Relation_OId__on(T_b,V_A_2)) = V_A_2 ). % 19.07/19.00 % 19.07/19.00 fof(fact_Range__empty,axiom, % 19.07/19.00 ! [T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Range__empty__iff,axiom, % 19.07/19.00 ! [V_r_2,T_b,T_c] : % 19.07/19.00 ( hAPP(c_Relation_ORange(T_c,T_b),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.00 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Range__Un__eq,axiom, % 19.07/19.00 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_c,T_b),V_A_2)),hAPP(c_Relation_ORange(T_c,T_b),V_B_2)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_finite__Range,axiom, % 19.07/19.00 ! [V_r_2,T_c,T_b] : % 19.07/19.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2)) % 19.07/19.00 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_snd__eq__Range,axiom, % 19.07/19.00 ! [V_R_2,T_b,T_c] : hAPP(c_Set_Oimage(tc_prod(T_c,T_b),T_b,c_Product__Type_Osnd(T_c,T_b)),V_R_2) = hAPP(c_Relation_ORange(T_c,T_b),V_R_2) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Range__iff,axiom, % 19.07/19.00 ! [V_r_2,T_c,V_a_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2))) % 19.07/19.00 <=> ? [B_y] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_y),V_a_2)),V_r_2)) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Range__insert,axiom, % 19.07/19.00 ! [V_r_2,V_b_2,V_a_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Range__Int__subset,axiom, % 19.07/19.00 ! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_c,T_b),V_A_2)),hAPP(c_Relation_ORange(T_c,T_b),V_B_2)))) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Range__Diff__subset,axiom, % 19.07/19.00 ! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_c,T_b),V_A_2)),hAPP(c_Relation_ORange(T_c,T_b),V_B_2))),hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_A_2),V_B_2)))) ). % 19.07/19.00 % 19.07/19.00 fof(fact_RangeP__Range__eq,axiom, % 19.07/19.00 ! [V_x_2,V_r_2,T_c,T_b] : % 19.07/19.00 ( hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_r_2)),V_x_2)) % 19.07/19.00 <=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_RangeE,axiom, % 19.07/19.00 ! [V_r_2,T_c,V_b_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2))) % 19.07/19.00 => ~ ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),V_b_2)),V_r_2)) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_RangeP_Ointros,axiom, % 19.07/19.00 ! [T_c,T_b,V_b_2,V_a_2,V_r_2] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 19.07/19.00 => hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_b_2)) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_RangeP_Oequations,axiom, % 19.07/19.00 ! [V_a2_2,V_r_2,T_c,T_b] : % 19.07/19.00 ( hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_a2_2)) % 19.07/19.00 <=> ? [B_a] : hBOOL(hAPP(hAPP(V_r_2,B_a),V_a2_2)) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_wf__Un,axiom, % 19.07/19.00 ! [V_s_2,V_r_2,T_b] : % 19.07/19.00 ( c_Wellfounded_Owf(T_b,V_r_2) % 19.07/19.00 => ( c_Wellfounded_Owf(T_b,V_s_2) % 19.07/19.00 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_b),V_r_2)),hAPP(c_Relation_ORange(T_b,T_b),V_s_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.00 => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_wfP__def,axiom, % 19.07/19.00 ! [V_r_2,T_b] : % 19.07/19.00 ( c_Wellfounded_OwfP(T_b,V_r_2) % 19.07/19.00 <=> c_Wellfounded_Owf(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_wfP__empty,axiom, % 19.07/19.00 ! [T_b] : c_Wellfounded_OwfP(T_b,hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBK(tc_HOL_Obool,T_b),c_fFalse))) ). % 19.07/19.00 % 19.07/19.00 fof(fact_DomainI,axiom, % 19.07/19.00 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2)) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_accp__wfPD,axiom, % 19.07/19.00 ! [V_x_2,V_r_2,T_b] : % 19.07/19.00 ( c_Wellfounded_OwfP(T_b,V_r_2) % 19.07/19.00 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_x_2)) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_wfP__accp__iff,axiom, % 19.07/19.00 ! [V_r_2,T_b] : % 19.07/19.00 ( c_Wellfounded_OwfP(T_b,V_r_2) % 19.07/19.00 <=> ! [B_x1] : hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x1)) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Domain__Id__on,axiom, % 19.07/19.00 ! [V_A_2,T_b] : hAPP(c_Relation_ODomain(T_b,T_b),c_Relation_OId__on(T_b,V_A_2)) = V_A_2 ). % 19.07/19.00 % 19.07/19.00 fof(fact_wfP__subset,axiom, % 19.07/19.00 ! [V_p_2,V_r_2,T_b] : % 19.07/19.00 ( c_Wellfounded_OwfP(T_b,V_r_2) % 19.07/19.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),V_p_2),V_r_2)) % 19.07/19.00 => c_Wellfounded_OwfP(T_b,V_p_2) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Domain__empty,axiom, % 19.07/19.00 ! [T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Domain__empty__iff,axiom, % 19.07/19.00 ! [V_r_2,T_c,T_b] : % 19.07/19.00 ( hAPP(c_Relation_ODomain(T_b,T_c),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.00 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Domain__mono,axiom, % 19.07/19.00 ! [V_s_2,V_r_2,T_c,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_2),V_s_2)) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)),hAPP(c_Relation_ODomain(T_b,T_c),V_s_2))) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Domain__Un__eq,axiom, % 19.07/19.00 ! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),V_A_2)),hAPP(c_Relation_ODomain(T_b,T_c),V_B_2)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_finite__Domain,axiom, % 19.07/19.00 ! [V_r_2,T_c,T_b] : % 19.07/19.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2)) % 19.07/19.00 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_fst__eq__Domain,axiom, % 19.07/19.00 ! [V_R_2,T_c,T_b] : hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_b,c_Product__Type_Ofst(T_b,T_c)),V_R_2) = hAPP(c_Relation_ODomain(T_b,T_c),V_R_2) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Domain__iff,axiom, % 19.07/19.00 ! [V_r_2,T_c,V_a_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) % 19.07/19.00 <=> ? [B_y] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),B_y)),V_r_2)) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Domain__insert,axiom, % 19.07/19.00 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Domain__Int__subset,axiom, % 19.07/19.00 ! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),V_A_2)),hAPP(c_Relation_ODomain(T_b,T_c),V_B_2)))) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Domain__Diff__subset,axiom, % 19.07/19.00 ! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),V_A_2)),hAPP(c_Relation_ODomain(T_b,T_c),V_B_2))),hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_A_2),V_B_2)))) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Field__def,axiom, % 19.07/19.00 ! [V_r_2,T_b] : hAPP(c_Relation_OField(T_b),V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_b),V_r_2)),hAPP(c_Relation_ORange(T_b,T_b),V_r_2)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_wf__in__rel,axiom, % 19.07/19.00 ! [V_R_2,T_b] : % 19.07/19.00 ( c_Wellfounded_Owf(T_b,V_R_2) % 19.07/19.00 => c_Wellfounded_OwfP(T_b,c_FunDef_Oin__rel(T_b,T_b,V_R_2)) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_wfP__wf__eq,axiom, % 19.07/19.00 ! [V_r_2,T_b] : % 19.07/19.00 ( c_Wellfounded_OwfP(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2)) % 19.07/19.00 <=> c_Wellfounded_Owf(T_b,V_r_2) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Domain__Collect__split,axiom, % 19.07/19.00 ! [V_Pa_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_Pa_2))) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c)),V_Pa_2)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_DomainP__Domain__eq,axiom, % 19.07/19.00 ! [V_x_2,V_r_2,T_c,T_b] : % 19.07/19.00 ( hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_r_2)),V_x_2)) % 19.07/19.00 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_DomainE,axiom, % 19.07/19.00 ! [V_r_2,T_c,V_a_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) % 19.07/19.00 => ~ ! [B_y] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),B_y)),V_r_2)) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_DomainP_Ointros,axiom, % 19.07/19.00 ! [T_c,T_b,V_b_2,V_a_2,V_r_2] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 19.07/19.00 => hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a_2)) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_DomainP_Oequations,axiom, % 19.07/19.00 ! [V_a1_2,V_r_2,T_c,T_b] : % 19.07/19.00 ( hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a1_2)) % 19.07/19.00 <=> ? [B_x1] : hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_x1)) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_wfP__acyclicP,axiom, % 19.07/19.00 ! [V_r_2,T_b] : % 19.07/19.00 ( c_Wellfounded_OwfP(T_b,V_r_2) % 19.07/19.00 => c_Wellfounded_Oacyclic(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_neg__map__def,axiom, % 19.07/19.00 ! [V_Pa_2,V_f_2,T_b,T_c] : c_New__Random__Sequence_Oneg__map(T_c,T_b,V_f_2,V_Pa_2) = c_New__Random__Sequence_Oneg__bind(T_c,T_b,V_Pa_2,hAPP(c_Fun_Ocomp(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))))),T_c,c_New__Random__Sequence_Oneg__single(T_b)),V_f_2)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_wf__acyclic,axiom, % 19.07/19.00 ! [V_r_2,T_b] : % 19.07/19.00 ( c_Wellfounded_Owf(T_b,V_r_2) % 19.07/19.00 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_acyclic__subset,axiom, % 19.07/19.00 ! [V_r_2,V_s_2,T_b] : % 19.07/19.00 ( c_Wellfounded_Oacyclic(T_b,V_s_2) % 19.07/19.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) % 19.07/19.00 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_finite__acyclic__wf,axiom, % 19.07/19.00 ! [V_r_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) % 19.07/19.00 => ( c_Wellfounded_Oacyclic(T_b,V_r_2) % 19.07/19.00 => c_Wellfounded_Owf(T_b,V_r_2) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_wf__iff__acyclic__if__finite,axiom, % 19.07/19.00 ! [V_r_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) % 19.07/19.00 => ( c_Wellfounded_Owf(T_b,V_r_2) % 19.07/19.00 <=> c_Wellfounded_Oacyclic(T_b,V_r_2) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_neg__single__def,axiom, % 19.07/19.00 ! [V_seed_2,V_size_2,V_nrandom_2,V_x_2,T_b] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(T_b),V_x_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Oneg__single(T_b,V_x_2) ). % 19.07/19.00 % 19.07/19.00 fof(fact_pos__map__def,axiom, % 19.07/19.00 ! [V_Pa_2,V_f_2,T_b,T_c] : c_New__Random__Sequence_Opos__map(T_c,T_b,V_f_2,V_Pa_2) = c_New__Random__Sequence_Opos__bind(T_c,T_b,V_Pa_2,hAPP(c_Fun_Ocomp(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))))),T_c,c_New__Random__Sequence_Opos__single(T_b)),V_f_2)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_New__DSequence_Oneg__single__def,axiom, % 19.07/19.00 ! [V_i_1,V_x,T_a] : hAPP(c_New__DSequence_Oneg__single(T_a,V_x),V_i_1) = c_Lazy__Sequence_Ohb__single(T_a,V_x) ). % 19.07/19.00 % 19.07/19.00 fof(fact_pos__single__def,axiom, % 19.07/19.00 ! [V_seed_2,V_size_2,V_nrandom_2,V_x_2,T_b] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(T_b),V_x_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Opos__single(T_b,V_x_2) ). % 19.07/19.00 % 19.07/19.00 fof(fact_New__DSequence_Opos__single__def,axiom, % 19.07/19.00 ! [V_i_1,V_x,T_a] : hAPP(c_New__DSequence_Opos__single(T_a,V_x),V_i_1) = c_Lazy__Sequence_Osingle(T_a,V_x) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Nitpick_Owf_H__def,axiom, % 19.07/19.00 ! [V_r_2,T_b] : % 19.07/19.00 ( c_Nitpick_Owf_H(T_b,V_r_2) % 19.07/19.00 <=> ( c_Wellfounded_Oacyclic(T_b,V_r_2) % 19.07/19.00 & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) % 19.07/19.00 | c_Nitpick_Ounknown(tc_HOL_Obool) ) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_pigeonhole__infinite,axiom, % 19.07/19.00 ! [V_f_2,T_c,V_A_2,T_b] : % 19.07/19.00 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) % 19.07/19.00 => ? [B_x] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 19.07/19.00 & ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),hAPP(V_f_2,B_x)))))) ) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_refl__on__def_H,axiom, % 19.07/19.00 ! [V_r_2,V_A_2,T_b] : % 19.07/19.00 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 19.07/19.00 <=> ( ! [B_x] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2)) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),B_x)) ) % 19.07/19.00 & ! [B_x] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) ) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Powp__def,axiom, % 19.07/19.00 ! [V_B_2,V_A_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(c_Predicate_OPowp(T_b,V_A_2),V_B_2)) % 19.07/19.00 <=> ! [B_x] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) % 19.07/19.00 => hBOOL(hAPP(V_A_2,B_x)) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_ball__empty,axiom, % 19.07/19.00 ! [V_Pa_2,T_b,B_x] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) % 19.07/19.00 => hBOOL(hAPP(V_Pa_2,B_x)) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_congruent__def,axiom, % 19.07/19.00 ! [V_f_2,V_r_2,T_c,T_b] : % 19.07/19.00 ( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2) % 19.07/19.00 <=> ! [B_x] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2)) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_c,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2))),V_f_2)),B_x)) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Abs__Integ__induct,axiom, % 19.07/19.00 ! [V_x_2,V_Pa_2] : % 19.07/19.00 ( ! [B_y] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) % 19.07/19.00 => hBOOL(hAPP(V_Pa_2,hAPP(c_Int_OAbs__Integ,B_y))) ) % 19.07/19.00 => hBOOL(hAPP(V_Pa_2,V_x_2)) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Abs__Integ__cases,axiom, % 19.07/19.00 ! [V_x_2] : % 19.07/19.00 ~ ! [B_y] : % 19.07/19.00 ( V_x_2 = hAPP(c_Int_OAbs__Integ,B_y) % 19.07/19.00 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_hoare__valids__def,axiom, % 19.07/19.00 ! [V_ts_2,V_G_2,T_b] : % 19.07/19.00 ( c_Hoare__Mirabelle_Ohoare__valids(T_b,V_G_2,V_ts_2) % 19.07/19.00 <=> ! [B_n] : % 19.07/19.00 ( ! [B_x] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_G_2)) % 19.07/19.00 => c_Hoare__Mirabelle_Otriple__valid(T_b,B_n,B_x) ) % 19.07/19.00 => ! [B_x] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_ts_2)) % 19.07/19.00 => c_Hoare__Mirabelle_Otriple__valid(T_b,B_n,B_x) ) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_finite__UN__I,axiom, % 19.07/19.00 ! [V_B_2,T_c,V_A_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.00 => ( ! [B_a] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2)) % 19.07/19.00 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a))) ) % 19.07/19.00 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_inj__on__diff__nat,axiom, % 19.07/19.00 ! [V_k_2,V_N_2] : % 19.07/19.00 ( ! [B_x] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),B_x)) ) % 19.07/19.00 => 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) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_wfP__SUP,axiom, % 19.07/19.00 ! [T_b,V_r_2,T_c] : % 19.07/19.00 ( ! [B_i] : c_Wellfounded_OwfP(T_c,hAPP(V_r_2,B_i)) % 19.07/19.00 => ( ! [B_i,B_j] : % 19.07/19.00 ( hAPP(V_r_2,B_i) != hAPP(V_r_2,B_j) % 19.07/19.00 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_Predicate_ODomainP(T_c,T_c,hAPP(V_r_2,B_i))),c_Predicate_ORangeP(T_c,T_c,hAPP(V_r_2,B_j))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) % 19.07/19.00 => c_Wellfounded_OwfP(T_c,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2)) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_finite__map__freshness,axiom, % 19.07/19.00 ! [V_f_2,T_c,T_b] : % 19.07/19.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Map_Odom(T_b,T_c,V_f_2))) % 19.07/19.00 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 19.07/19.00 => ? [B_x] : hAPP(V_f_2,B_x) = c_Option_Ooption_ONone(T_c) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_mem__splitI2,axiom, % 19.07/19.00 ! [V_c_2,V_z_2,T_d,T_c,T_b,V_p_2] : % 19.07/19.00 ( ! [B_a,B_b] : % 19.07/19.00 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_member(T_d),V_z_2),hAPP(hAPP(V_c_2,B_a),B_b))) ) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_member(T_d),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_d,tc_HOL_Obool)),V_c_2),V_p_2))) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_mem__splitE,axiom, % 19.07/19.00 ! [V_p_2,V_c_2,T_d,T_c,V_z_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_fun(T_b,tc_HOL_Obool)),V_c_2),V_p_2))) % 19.07/19.00 => ~ ! [B_x,B_y] : % 19.07/19.00 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_x),B_y) % 19.07/19.00 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_c_2,B_x),B_y))) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_setsum__SucD,axiom, % 19.07/19.00 ! [V_n_2,V_A_2,V_f_2,T_b] : % 19.07/19.00 ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Nat_OSuc,V_n_2) % 19.07/19.00 => ? [B_x] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 19.07/19.00 & 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))) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Eps__split,axiom, % 19.07/19.00 ! [V_Pa_2,T_c,T_b] : c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_Pa_2)) = c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(hAPP(c_COMBS(tc_prod(T_b,T_c),T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_HOL_Obool),tc_prod(T_b,T_c)),V_Pa_2),c_Product__Type_Ofst(T_b,T_c))),c_Product__Type_Osnd(T_b,T_c))) ). % 19.07/19.00 % 19.07/19.00 fof(fact_wfI__pf,axiom, % 19.07/19.00 ! [V_R_2,T_b] : % 19.07/19.00 ( ! [B_A] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_A),hAPP(c_Relation_OImage(T_b,T_b,V_R_2),B_A))) % 19.07/19.00 => B_A = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) % 19.07/19.00 => c_Wellfounded_Owf(T_b,V_R_2) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_tfl__some,axiom, % 19.07/19.00 ! [T_b,B_P] : % 19.07/19.00 ( ? [B_x] : hBOOL(hAPP(B_P,B_x)) % 19.07/19.00 => hBOOL(hAPP(B_P,c_Hilbert__Choice_OEps(T_b,B_P))) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_someI,axiom, % 19.07/19.00 ! [T_b,V_x_2,V_Pa_2] : % 19.07/19.00 ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 19.07/19.00 => hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2))) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_some__sym__eq__trivial,axiom, % 19.07/19.00 ! [V_x_2,T_b] : c_Hilbert__Choice_OEps(T_b,hAPP(c_fequal,V_x_2)) = V_x_2 ). % 19.07/19.00 % 19.07/19.00 fof(fact_some__eq__trivial,axiom, % 19.07/19.00 ! [V_x_2,T_b] : c_Hilbert__Choice_OEps(T_b,hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)) = V_x_2 ). % 19.07/19.00 % 19.07/19.00 fof(fact_some__eq__ex,axiom, % 19.07/19.00 ! [T_b,V_Pa_2] : % 19.07/19.00 ( hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2))) % 19.07/19.00 <=> ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_someI__ex,axiom, % 19.07/19.00 ! [T_b,V_Pa_2] : % 19.07/19.00 ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 19.07/19.00 => hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2))) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_exE__some,axiom, % 19.07/19.00 ! [T_b,V_c_2,V_Pa_2] : % 19.07/19.00 ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 19.07/19.00 => ( V_c_2 = c_Hilbert__Choice_OEps(T_b,V_Pa_2) % 19.07/19.00 => hBOOL(hAPP(V_Pa_2,V_c_2)) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_split__paired__Eps,axiom, % 19.07/19.00 ! [V_Pa_2,T_c,T_b] : c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),V_Pa_2) = c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_Pa_2)),c_Product__Type_OPair(T_b,T_c)))) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Eps__split__eq,axiom, % 19.07/19.00 ! [V_y_2,V_x_2,T_c,T_b] : c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_x_2)))),hAPP(c_fequal,V_y_2)))) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Sigma__mono,axiom, % 19.07/19.00 ! [V_D_2,V_B_2,T_c,V_C_2,V_A_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) % 19.07/19.00 => ( ! [B_x] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_B_2,B_x)),hAPP(V_D_2,B_x))) ) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_C_2),V_D_2))) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_not__acc__down,axiom, % 19.07/19.00 ! [V_R_2,V_x_2,T_b] : % 19.07/19.00 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_R_2))) % 19.07/19.00 => ~ ! [B_z] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_z),V_x_2)),V_R_2)) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_member(T_b),B_z),c_Wellfounded_Oacc(T_b,V_R_2))) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_acc_OaccI,axiom, % 19.07/19.00 ! [V_r_2,V_x_2,T_b] : % 19.07/19.00 ( ! [B_y] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_x_2)),V_r_2)) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_member(T_b),B_y),c_Wellfounded_Oacc(T_b,V_r_2))) ) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_fold__image__1,axiom, % 19.07/19.00 ! [V_f_2,V_S_2,T_b,T_c] : % 19.07/19.00 ( class_Groups_Ocomm__monoid__mult(T_c) % 19.07/19.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 19.07/19.00 => ( ! [B_x] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) % 19.07/19.00 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) ) % 19.07/19.00 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_f_2),c_Groups_Oone__class_Oone(T_c)),V_S_2) = c_Groups_Oone__class_Oone(T_c) ) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_card_Oneutral,axiom, % 19.07/19.00 ! [V_A_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.00 => ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 19.07/19.00 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 19.07/19.00 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_max__ext_Osimps,axiom, % 19.07/19.00 ! [V_R_2,V_a2_2,V_a1_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_a1_2),V_a2_2)),c_Wellfounded_Omax__ext(T_b,V_R_2))) % 19.07/19.00 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2)) % 19.07/19.00 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2)) % 19.07/19.00 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.00 & ! [B_x] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2)) % 19.07/19.00 => ? [B_xa] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2)) % 19.07/19.00 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_xa)),V_R_2)) ) ) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_fold__image__cong,axiom, % 19.07/19.00 ! [V_z_2,V_h_2,V_g_2,V_A_2,T_b,T_c] : % 19.07/19.00 ( class_Groups_Oab__semigroup__mult(T_c) % 19.07/19.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.00 => ( ! [B_x] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 19.07/19.00 => hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) ) % 19.07/19.00 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),V_z_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_h_2),V_z_2),V_A_2) ) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_setprod__dvd__setprod__subset2,axiom, % 19.07/19.00 ! [V_g_2,V_f_2,V_A_2,V_B_2,T_b,T_c] : % 19.07/19.00 ( class_Rings_Ocomm__semiring__1(T_c) % 19.07/19.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 19.07/19.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 19.07/19.00 => ( ! [B_x] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2))) ) ) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Max__eqI,axiom, % 19.07/19.00 ! [V_x_2,V_A_2,T_b] : % 19.07/19.00 ( class_Orderings_Olinorder(T_b) % 19.07/19.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.00 => ( ! [B_y] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2)) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_y),V_x_2)) ) % 19.07/19.00 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/19.00 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2 ) ) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Min__eqI,axiom, % 19.07/19.00 ! [V_x_2,V_A_2,T_b] : % 19.07/19.00 ( class_Orderings_Olinorder(T_b) % 19.07/19.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.00 => ( ! [B_y] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2)) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_y)) ) % 19.07/19.00 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/19.00 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2 ) ) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_wf__no__infinite__down__chainE,axiom, % 19.07/19.00 ! [V_f_2,V_r_2,T_b] : % 19.07/19.00 ( c_Wellfounded_Owf(T_b,V_r_2) % 19.07/19.00 => ~ ! [B_k] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_k))),hAPP(V_f_2,B_k))),V_r_2)) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_setsum__reindex__cong,axiom, % 19.07/19.00 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] : % 19.07/19.00 ( class_Groups_Ocomm__monoid__add(T_d) % 19.07/19.00 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 19.07/19.00 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) % 19.07/19.00 => ( ! [B_a] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2)) % 19.07/19.00 => hAPP(V_g_2,B_a) = hAPP(V_h_2,hAPP(V_f_2,B_a)) ) % 19.07/19.00 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),V_g_2),V_A_2) ) ) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_setsum__ivl__cong,axiom, % 19.07/19.00 ! [V_g_2,V_f_2,V_d_2,V_b_2,V_c_2,V_a_2,T_b,T_c] : % 19.07/19.00 ( ( class_Groups_Ocomm__monoid__add(T_c) % 19.07/19.00 & class_Orderings_Oord(T_b) ) % 19.07/19.00 => ( V_a_2 = V_c_2 % 19.07/19.00 => ( V_b_2 = V_d_2 % 19.07/19.00 => ( ! [B_x] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),B_x)) % 19.07/19.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_d_2)) % 19.07/19.00 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) % 19.07/19.00 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)) ) ) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_less__eq,axiom, % 19.07/19.00 ! [V_n_2,V_m_2] : % 19.07/19.00 ( 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))) % 19.07/19.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_wf__trancl,axiom, % 19.07/19.00 ! [V_r_2,T_b] : % 19.07/19.00 ( c_Wellfounded_Owf(T_b,V_r_2) % 19.07/19.00 => c_Wellfounded_Owf(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_less__than__def,axiom, % 19.07/19.00 c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat) ). % 19.07/19.00 % 19.07/19.00 fof(fact_acyclic__def,axiom, % 19.07/19.00 ! [V_r_2,T_b] : % 19.07/19.00 ( c_Wellfounded_Oacyclic(T_b,V_r_2) % 19.07/19.00 <=> ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_trancl_Or__into__trancl,axiom, % 19.07/19.00 ! [V_r_2,V_b_2,V_a_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_trancl__subset__Field2,axiom, % 19.07/19.00 ! [V_r_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),hAPP(c_Relation_OField(T_b),V_r_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_Relation_OField(T_b),V_r_2))))) ). % 19.07/19.00 % 19.07/19.00 fof(fact_r__into__trancl_H,axiom, % 19.07/19.00 ! [V_r_2,V_p_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2)) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_trancl__empty,axiom, % 19.07/19.00 ! [T_b] : c_Transitive__Closure_Otrancl(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_trancl__domain,axiom, % 19.07/19.00 ! [V_r_2,T_b] : hAPP(c_Relation_ODomain(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)) = hAPP(c_Relation_ODomain(T_b,T_b),V_r_2) ). % 19.07/19.00 % 19.07/19.00 fof(fact_trancl__range,axiom, % 19.07/19.00 ! [V_r_2,T_b] : hAPP(c_Relation_ORange(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)) = hAPP(c_Relation_ORange(T_b,T_b),V_r_2) ). % 19.07/19.00 % 19.07/19.00 fof(fact_finite__trancl,axiom, % 19.07/19.00 ! [V_r_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) % 19.07/19.00 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_r__r__into__trancl,axiom, % 19.07/19.00 ! [V_c_2,V_R_2,V_b_2,V_a_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_R_2)) % 19.07/19.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),V_R_2)) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2))) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_trancl__into__trancl2,axiom, % 19.07/19.00 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) % 19.07/19.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Transitive__Closure_Otrancl__into__trancl,axiom, % 19.07/19.00 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) % 19.07/19.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),V_r_2)) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_trancl__trans,axiom, % 19.07/19.00 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) % 19.07/19.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_trancl__mono,axiom, % 19.07/19.00 ! [V_s_2,V_r_2,V_p_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2))) % 19.07/19.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_s_2))) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_trancl__unfold,axiom, % 19.07/19.00 ! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)),V_r_2)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_trancl__subset__Sigma,axiom, % 19.07/19.00 ! [V_A_2,V_r_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_trancl__Int__subset,axiom, % 19.07/19.00 ! [V_s_2,V_r_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) % 19.07/19.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),V_s_2)),V_r_2)),V_s_2)) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),V_s_2)) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_trancl__insert,axiom, % 19.07/19.00 ! [V_r_2,V_x_2,V_y_2,T_b] : c_Transitive__Closure_Otrancl(T_b,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),V_r_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b))),hAPP(hAPP(c_COMBC(T_b,T_b,tc_prod(T_b,T_b)),c_Product__Type_OPair(T_b,T_b)),V_y_2))),c_Transitive__Closure_Ortrancl(T_b,V_r_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b))),hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2))),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))))) ). % 19.07/19.00 % 19.07/19.00 fof(fact_reflcl__set__eq,axiom, % 19.07/19.00 ! [V_y_2,V_x_2,V_r_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2)),c_fequal),V_x_2),V_y_2)) % 19.07/19.00 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b)))) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_r__into__rtrancl,axiom, % 19.07/19.00 ! [V_r_2,V_p_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2)) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_rtrancl_Ortrancl__refl,axiom, % 19.07/19.00 ! [V_r_2,V_a_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ). % 19.07/19.00 % 19.07/19.00 fof(fact_IdI,axiom, % 19.07/19.00 ! [V_a_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),c_Relation_OId(T_b))) ). % 19.07/19.00 % 19.07/19.00 fof(fact_trancl__into__rtrancl,axiom, % 19.07/19.00 ! [V_r_2,V_b_2,V_a_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_trancl__unfold__left,axiom, % 19.07/19.00 ! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,V_r_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_r_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_trancl__unfold__right,axiom, % 19.07/19.00 ! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,V_r_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_r_2) ). % 19.07/19.00 % 19.07/19.00 fof(fact_reflcl__trancl,axiom, % 19.07/19.00 ! [V_r_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),c_Relation_OId(T_b)) = c_Transitive__Closure_Ortrancl(T_b,V_r_2) ). % 19.07/19.00 % 19.07/19.00 fof(fact_trancl__reflcl,axiom, % 19.07/19.00 ! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) = c_Transitive__Closure_Ortrancl(T_b,V_r_2) ). % 19.07/19.00 % 19.07/19.00 fof(fact_rtrancl__trancl__absorb,axiom, % 19.07/19.00 ! [V_R_2,T_b] : c_Transitive__Closure_Otrancl(T_b,c_Transitive__Closure_Ortrancl(T_b,V_R_2)) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ). % 19.07/19.00 % 19.07/19.00 fof(fact_trancl__rtrancl__absorb,axiom, % 19.07/19.00 ! [V_R_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,c_Transitive__Closure_Otrancl(T_b,V_R_2)) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ). % 19.07/19.00 % 19.07/19.00 fof(fact_refl__rtrancl,axiom, % 19.07/19.00 ! [V_r_2,T_b] : c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_rtrancl__idemp,axiom, % 19.07/19.00 ! [V_r_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) = c_Transitive__Closure_Ortrancl(T_b,V_r_2) ). % 19.07/19.00 % 19.07/19.00 fof(fact_converse__rtrancl__into__rtrancl,axiom, % 19.07/19.00 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) % 19.07/19.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_rtrancl_Ortrancl__into__rtrancl,axiom, % 19.07/19.00 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 19.07/19.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),V_r_2)) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_rtrancl__trans,axiom, % 19.07/19.00 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 19.07/19.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_rtrancl__r__diff__Id,axiom, % 19.07/19.00 ! [V_r_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) = c_Transitive__Closure_Ortrancl(T_b,V_r_2) ). % 19.07/19.00 % 19.07/19.00 fof(fact_in__rtrancl__UnI,axiom, % 19.07/19.00 ! [V_S_2,V_R_2,V_x_2,T_b] : % 19.07/19.00 ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) % 19.07/19.00 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_S_2))) ) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)))) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Image__closed__trancl,axiom, % 19.07/19.00 ! [V_X_2,V_r_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),V_X_2)),V_X_2)) % 19.07/19.00 => hAPP(c_Relation_OImage(T_b,T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_X_2) = V_X_2 ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_rtrancl__mono,axiom, % 19.07/19.00 ! [V_s_2,V_r_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),c_Transitive__Closure_Ortrancl(T_b,V_s_2))) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_rtrancl__subset,axiom, % 19.07/19.00 ! [V_S_2,V_R_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) % 19.07/19.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_S_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) % 19.07/19.00 => c_Transitive__Closure_Ortrancl(T_b,V_S_2) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_rtrancl__subset__rtrancl,axiom, % 19.07/19.00 ! [V_s_2,V_r_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Transitive__Closure_Ortrancl(T_b,V_s_2))) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),c_Transitive__Closure_Ortrancl(T_b,V_s_2))) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_rtrancl__reflcl,axiom, % 19.07/19.00 ! [V_R_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),c_Relation_OId(T_b))) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ). % 19.07/19.00 % 19.07/19.00 fof(fact_rtrancl__Un__rtrancl,axiom, % 19.07/19.00 ! [V_S_2,V_R_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Transitive__Closure_Ortrancl(T_b,V_S_2))) = c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_rtrancl__reflcl__absorb,axiom, % 19.07/19.00 ! [V_R_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Relation_OId(T_b)) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ). % 19.07/19.00 % 19.07/19.00 fof(fact_rtrancl__Un__subset,axiom, % 19.07/19.00 ! [V_S_2,V_R_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Transitive__Closure_Ortrancl(T_b,V_S_2))),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)))) ). % 19.07/19.00 % 19.07/19.00 fof(fact_rtrancl__idemp__self__comp,axiom, % 19.07/19.00 ! [V_R_2,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ). % 19.07/19.00 % 19.07/19.00 fof(fact_r__comp__rtrancl__eq,axiom, % 19.07/19.00 ! [V_r_2,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_r_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_r_2) ). % 19.07/19.00 % 19.07/19.00 fof(fact_rtrancl__unfold,axiom, % 19.07/19.00 ! [V_r_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Relation_OId(T_b)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_r_2)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_rtrancl__Int__subset,axiom, % 19.07/19.00 ! [V_r_2,V_s_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Relation_OId(T_b)),V_s_2)) % 19.07/19.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_s_2)),V_r_2)),V_s_2)) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_s_2)) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_rtrancl__empty,axiom, % 19.07/19.00 ! [T_b] : c_Transitive__Closure_Ortrancl(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) = c_Relation_OId(T_b) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Range__rtrancl,axiom, % 19.07/19.00 ! [V_R_2,T_b] : hAPP(c_Relation_ORange(T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_R_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Domain__rtrancl,axiom, % 19.07/19.00 ! [V_R_2,T_b] : hAPP(c_Relation_ODomain(T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_R_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_R__O__Id,axiom, % 19.07/19.00 ! [V_R_2,T_c,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_c),V_R_2),c_Relation_OId(T_c)) = V_R_2 ). % 19.07/19.00 % 19.07/19.00 fof(fact_Id__O__R,axiom, % 19.07/19.00 ! [V_R_2,T_c,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_c),c_Relation_OId(T_b)),V_R_2) = V_R_2 ). % 19.07/19.00 % 19.07/19.00 fof(fact_Image__Id,axiom, % 19.07/19.00 ! [V_A_2,T_b] : hAPP(c_Relation_OImage(T_b,T_b,c_Relation_OId(T_b)),V_A_2) = V_A_2 ). % 19.07/19.00 % 19.07/19.00 fof(fact_pair__in__Id__conv,axiom, % 19.07/19.00 ! [V_b_2,V_a_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Relation_OId(T_b))) % 19.07/19.00 <=> V_a_2 = V_b_2 ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_rtrancl__eq__or__trancl,axiom, % 19.07/19.00 ! [V_R_2,V_y_2,V_x_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) % 19.07/19.00 <=> ( V_x_2 = V_y_2 % 19.07/19.00 | ( V_x_2 != V_y_2 % 19.07/19.00 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2))) ) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_rtrancl__into__trancl2,axiom, % 19.07/19.00 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) % 19.07/19.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_rtranclD,axiom, % 19.07/19.00 ! [V_R_2,V_b_2,V_a_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) % 19.07/19.00 => ( V_a_2 = V_b_2 % 19.07/19.00 | ( V_a_2 != V_b_2 % 19.07/19.00 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2))) ) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_rtrancl__into__trancl1,axiom, % 19.07/19.00 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 19.07/19.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),V_r_2)) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_trancl__rtrancl__trancl,axiom, % 19.07/19.00 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) % 19.07/19.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_rtrancl__trancl__trancl,axiom, % 19.07/19.00 ! [V_z_2,V_r_2,V_y_2,V_x_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 19.07/19.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Domain__Id,axiom, % 19.07/19.00 ! [T_b] : hAPP(c_Relation_ODomain(T_b,T_b),c_Relation_OId(T_b)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Range__Id,axiom, % 19.07/19.00 ! [T_b] : hAPP(c_Relation_ORange(T_b,T_b),c_Relation_OId(T_b)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_refl__Id,axiom, % 19.07/19.00 ! [T_b] : c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Relation_OId(T_b)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_pair__leq__def,axiom, % 19.07/19.00 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))) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Not__Domain__rtrancl,axiom, % 19.07/19.00 ! [V_y_2,V_R_2,V_x_2,T_b] : % 19.07/19.00 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_b),V_R_2))) % 19.07/19.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) % 19.07/19.00 <=> V_x_2 = V_y_2 ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_acc__downwards,axiom, % 19.07/19.00 ! [V_b_2,V_r_2,V_a_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2))) % 19.07/19.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_acc__downwards__aux,axiom, % 19.07/19.00 ! [V_r_2,V_a_2,V_b_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 19.07/19.00 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2))) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_wf__insert,axiom, % 19.07/19.00 ! [V_r_2,V_x_2,V_y_2,T_b] : % 19.07/19.00 ( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),V_r_2)) % 19.07/19.00 <=> ( c_Wellfounded_Owf(T_b,V_r_2) % 19.07/19.00 & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_acyclic__insert,axiom, % 19.07/19.00 ! [V_r_2,V_x_2,V_y_2,T_b] : % 19.07/19.00 ( c_Wellfounded_Oacyclic(T_b,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),V_r_2)) % 19.07/19.00 <=> ( c_Wellfounded_Oacyclic(T_b,V_r_2) % 19.07/19.00 & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_refl__reflcl,axiom, % 19.07/19.00 ! [V_r_2,T_b] : c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Id__def,axiom, % 19.07/19.00 ! [T_b] : c_Relation_OId(T_b) = hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_prod(T_b,T_b)),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(tc_prod(T_b,T_b),tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_HOL_Obool)),tc_prod(T_b,T_b)),c_COMBB(tc_prod(T_b,T_b),tc_HOL_Obool,T_b)),c_fequal)),hAPP(hAPP(c_COMBS(T_b,T_b,tc_prod(T_b,T_b)),c_Product__Type_OPair(T_b,T_b)),c_COMBI(T_b))))) ). % 19.07/19.00 % 19.07/19.00 fof(fact_irrefl__diff__Id,axiom, % 19.07/19.00 ! [V_r_2,T_b] : c_Relation_Oirrefl(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) ). % 19.07/19.00 % 19.07/19.00 fof(fact_pred__nat__trancl__eq__le,axiom, % 19.07/19.00 ! [V_n_2,V_m_2] : % 19.07/19.00 ( 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))) % 19.07/19.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_trancl__subset__Sigma__aux,axiom, % 19.07/19.00 ! [V_A_2,V_r_2,V_b_2,V_a_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 19.07/19.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) % 19.07/19.00 => ( V_a_2 = V_b_2 % 19.07/19.00 | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_irrefl__tranclI,axiom, % 19.07/19.00 ! [V_x_2,V_r_2,T_b] : % 19.07/19.00 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) % 19.07/19.00 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_x_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_sequence__trans,axiom, % 19.07/19.00 ! [V_k_2,V_i_2,V_r_2,V_f_2,T_b] : % 19.07/19.00 ( ! [B_i] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_i))),hAPP(V_f_2,B_i))),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2))),hAPP(V_f_2,V_i_2))),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_rtrancl__converse,axiom, % 19.07/19.00 ! [V_r_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) = hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_converse__Id,axiom, % 19.07/19.00 ! [T_b] : hAPP(c_Relation_Oconverse(T_b,T_b),c_Relation_OId(T_b)) = c_Relation_OId(T_b) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Range__converse,axiom, % 19.07/19.00 ! [V_r_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2)) = hAPP(c_Relation_ODomain(T_b,T_c),V_r_2) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Domain__converse,axiom, % 19.07/19.00 ! [V_r_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)) = hAPP(c_Relation_ORange(T_c,T_b),V_r_2) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Range__def,axiom, % 19.07/19.00 ! [V_r_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),V_r_2) = hAPP(c_Relation_ODomain(T_b,T_c),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_equiv__comp__eq,axiom, % 19.07/19.00 ! [V_r_2,V_A_2,T_b] : % 19.07/19.00 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 19.07/19.00 => hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),V_r_2) = V_r_2 ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_converse__UNION,axiom, % 19.07/19.00 ! [V_r_2,V_S_2,T_d,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_S_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_S_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_d),c_Relation_Oconverse(T_c,T_b)),V_r_2)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_refl__on__converse,axiom, % 19.07/19.00 ! [V_r_2,V_A_2,T_b] : % 19.07/19.00 ( c_Relation_Orefl__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) % 19.07/19.00 <=> c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_converse__Id__on,axiom, % 19.07/19.00 ! [V_A_2,T_b] : hAPP(c_Relation_Oconverse(T_b,T_b),c_Relation_OId__on(T_b,V_A_2)) = c_Relation_OId__on(T_b,V_A_2) ). % 19.07/19.00 % 19.07/19.00 fof(fact_converse__inv__image,axiom, % 19.07/19.00 ! [V_f_2,V_R_2,T_c,T_b] : hAPP(c_Relation_Oconverse(T_b,T_b),hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),V_R_2),V_f_2)) = hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),hAPP(c_Relation_Oconverse(T_c,T_c),V_R_2)),V_f_2) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Field__converse,axiom, % 19.07/19.00 ! [V_r_2,T_b] : hAPP(c_Relation_OField(T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) = hAPP(c_Relation_OField(T_b),V_r_2) ). % 19.07/19.00 % 19.07/19.00 fof(fact_converse__converse,axiom, % 19.07/19.00 ! [V_r_2,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2)) = V_r_2 ). % 19.07/19.00 % 19.07/19.00 fof(fact_converse__Int,axiom, % 19.07/19.00 ! [V_s_2,V_r_2,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_s_2)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_finite__converse,axiom, % 19.07/19.00 ! [V_r_2,T_c,T_b] : % 19.07/19.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2))) % 19.07/19.00 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_b)),V_r_2)) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_converseD,axiom, % 19.07/19.00 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2))) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_b_2),V_a_2)),V_r_2)) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_converseI,axiom, % 19.07/19.00 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2)) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_b_2),V_a_2)),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2))) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_converse__iff,axiom, % 19.07/19.00 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2))) % 19.07/19.00 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_b_2),V_a_2)),V_r_2)) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_converse__Un,axiom, % 19.07/19.00 ! [V_s_2,V_r_2,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_s_2)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_converse__rel__comp,axiom, % 19.07/19.00 ! [V_s_2,V_r_2,T_d,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_d,T_b),V_r_2),V_s_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(c_Relation_Oconverse(T_d,T_b),V_s_2)),hAPP(c_Relation_Oconverse(T_c,T_d),V_r_2)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_acyclic__converse,axiom, % 19.07/19.00 ! [V_r_2,T_b] : % 19.07/19.00 ( c_Wellfounded_Oacyclic(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) % 19.07/19.00 <=> c_Wellfounded_Oacyclic(T_b,V_r_2) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_wf__converse__trancl,axiom, % 19.07/19.00 ! [V_r_2,T_b] : % 19.07/19.00 ( c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) % 19.07/19.00 => c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_trancl__converse,axiom, % 19.07/19.00 ! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) = hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_rtrancl__converseD,axiom, % 19.07/19.00 ! [V_r_2,V_y_2,V_x_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)))) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_rtrancl__converseI,axiom, % 19.07/19.00 ! [V_r_2,V_x_2,V_y_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)))) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_trancl__converseD,axiom, % 19.07/19.00 ! [V_r_2,V_y_2,V_x_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)))) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)))) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_trancl__converseI,axiom, % 19.07/19.00 ! [V_r_2,V_y_2,V_x_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)))) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)))) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_Image__subset__eq,axiom, % 19.07/19.00 ! [V_B_2,V_A_2,V_r_2,T_c,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)),V_B_2)) % 19.07/19.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2))))) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_refl__on__comp__subset,axiom, % 19.07/19.00 ! [V_r_2,V_A_2,T_b] : % 19.07/19.00 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),V_r_2))) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_comp__equivI,axiom, % 19.07/19.00 ! [V_A_2,V_r_2,T_b] : % 19.07/19.00 ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),V_r_2) = V_r_2 % 19.07/19.00 => ( hAPP(c_Relation_ODomain(T_b,T_b),V_r_2) = V_A_2 % 19.07/19.00 => c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_finite__acyclic__wf__converse,axiom, % 19.07/19.00 ! [V_r_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) % 19.07/19.00 => ( c_Wellfounded_Oacyclic(T_b,V_r_2) % 19.07/19.00 => c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_converse__def,axiom, % 19.07/19.00 ! [V_r_2,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_c,T_b)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_c,T_b),tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_c,T_b)))),hAPP(c_COMBC(T_c,T_b,tc_prod(T_c,T_b)),c_Product__Type_OPair(T_c,T_b))))),V_r_2))) ). % 19.07/19.00 % 19.07/19.00 fof(fact_total__on__diff__Id,axiom, % 19.07/19.00 ! [V_r_2,V_A_2,T_b] : % 19.07/19.00 ( c_Relation_Ototal__on(T_b,V_A_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) % 19.07/19.00 <=> c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_rtrancl__imp__UN__rel__pow,axiom, % 19.07/19.00 ! [V_R_2,V_p_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2)))) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_relpow_Osimps_I1_J,axiom, % 19.07/19.00 ! [V_R_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2) = c_Relation_OId(T_b) ). % 19.07/19.00 % 19.07/19.00 fof(fact_rtrancl__power,axiom, % 19.07/19.00 ! [V_R_2,V_p_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) % 19.07/19.00 <=> ? [B_n] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_n),V_R_2))) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_rel__pow__imp__rtrancl,axiom, % 19.07/19.00 ! [V_R_2,V_n_2,V_p_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_rel__pow__1,axiom, % 19.07/19.00 ! [V_R_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_R_2) = V_R_2 ). % 19.07/19.00 % 19.07/19.00 fof(fact_rel__pow__commute,axiom, % 19.07/19.00 ! [V_n_2,V_R_2,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)),V_R_2) ). % 19.07/19.00 % 19.07/19.00 fof(fact_relpow_Osimps_I2_J,axiom, % 19.07/19.00 ! [V_R_2,V_n_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)),V_R_2) ). % 19.07/19.00 % 19.07/19.00 fof(fact_rel__pow__add,axiom, % 19.07/19.00 ! [V_R_2,V_n_2,V_m_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)),V_R_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_m_2),V_R_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_funpow__mult,axiom, % 19.07/19.00 ! [V_f_2,V_m_2,V_n_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_m_2),V_f_2)) = hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)),V_f_2) ). % 19.07/19.00 % 19.07/19.00 fof(fact_funpow__swap1,axiom, % 19.07/19.00 ! [V_x_2,V_n_2,T_b,V_f_2] : hAPP(V_f_2,hAPP(hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2),V_x_2)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2),hAPP(V_f_2,V_x_2)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_wf__exp,axiom, % 19.07/19.00 ! [V_R_2,V_n_2,T_b] : % 19.07/19.00 ( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)) % 19.07/19.00 => c_Wellfounded_Owf(T_b,V_R_2) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_comp__funpow,axiom, % 19.07/19.00 ! [V_f_2,V_n_2,T_c,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_fun(T_b,T_c),tc_fun(T_b,T_c)),V_n_2),c_Fun_Ocomp(T_c,T_c,T_b,V_f_2)) = c_Fun_Ocomp(T_c,T_c,T_b,hAPP(hAPP(c_Nat_Ocompow(T_c,T_c),V_n_2),V_f_2)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_total__on__empty,axiom, % 19.07/19.00 ! [V_r_2,T_b] : c_Relation_Ototal__on(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_r_2) ). % 19.07/19.00 % 19.07/19.00 fof(fact_total__on__converse,axiom, % 19.07/19.00 ! [V_r_2,V_A_2,T_b] : % 19.07/19.00 ( c_Relation_Ototal__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) % 19.07/19.00 <=> c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_rel__pow__0__I,axiom, % 19.07/19.00 ! [V_R_2,V_x_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2))) ). % 19.07/19.00 % 19.07/19.00 fof(fact_rel__pow__0__E,axiom, % 19.07/19.00 ! [V_R_2,V_y_2,V_x_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2))) % 19.07/19.00 => V_x_2 = V_y_2 ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_rel__pow__Suc__I2,axiom, % 19.07/19.00 ! [V_n_2,V_z_2,V_R_2,V_y_2,V_x_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_R_2)) % 19.07/19.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_rel__pow__Suc__I,axiom, % 19.07/19.00 ! [V_z_2,V_R_2,V_n_2,V_y_2,V_x_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))) % 19.07/19.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),V_R_2)) % 19.07/19.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_funpow_Osimps_I2_J,axiom, % 19.07/19.00 ! [V_f_2,V_n_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),hAPP(c_Nat_OSuc,V_n_2)),V_f_2) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,V_f_2),hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_funpow__add,axiom, % 19.07/19.00 ! [V_f_2,V_n_2,V_m_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)),V_f_2) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_m_2),V_f_2)),hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_funpow_Osimps_I1_J,axiom, % 19.07/19.00 ! [V_f_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_f_2) = c_Fun_Oid(T_b) ). % 19.07/19.00 % 19.07/19.00 fof(fact_trancl__power,axiom, % 19.07/19.00 ! [V_R_2,V_p_2,T_b] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_R_2))) % 19.07/19.00 <=> ? [B_n] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)) % 19.07/19.00 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_n),V_R_2))) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_total__on__def,axiom, % 19.07/19.00 ! [V_r_2,V_A_2,T_b] : % 19.07/19.00 ( c_Relation_Ototal__on(T_b,V_A_2,V_r_2) % 19.07/19.00 <=> ! [B_x] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 19.07/19.00 => ! [B_xa] : % 19.07/19.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2)) % 19.07/19.00 => ( B_x != B_xa % 19.07/19.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_xa)),V_r_2)) % 19.07/19.00 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_xa),B_x)),V_r_2)) ) ) ) ) ) ). % 19.07/19.00 % 19.07/19.00 fof(fact_rtrancl__is__UN__rel__pow,axiom, % 19.07/19.00 ! [V_R_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,V_R_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2)) ). % 19.07/19.00 % 19.07/19.00 fof(fact_funpow__code__def,axiom, % 19.07/19.00 ! [T_b] : c_Nat_Ofunpow(T_b) = c_Nat_Ocompow(T_b,T_b) ). % 19.07/19.00 % 19.07/19.00 fof(fact_rel__pow__E2,axiom, % 19.07/19.01 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))) % 19.07/19.01 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 19.07/19.01 => V_x_2 != V_z_2 ) % 19.07/19.01 => ~ ! [B_y,B_m] : % 19.07/19.01 ( V_n_2 = hAPP(c_Nat_OSuc,B_m) % 19.07/19.01 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),V_R_2)) % 19.07/19.01 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_m),V_R_2))) ) ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_rel__pow__E,axiom, % 19.07/19.01 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))) % 19.07/19.01 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 19.07/19.01 => V_x_2 != V_z_2 ) % 19.07/19.01 => ~ ! [B_y,B_m] : % 19.07/19.01 ( V_n_2 = hAPP(c_Nat_OSuc,B_m) % 19.07/19.01 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_m),V_R_2))) % 19.07/19.01 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),V_R_2)) ) ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_acyclicI,axiom, % 19.07/19.01 ! [V_r_2,T_b] : % 19.07/19.01 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) % 19.07/19.01 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Image__Int__eq,axiom, % 19.07/19.01 ! [V_B_2,V_A_2,V_R_2,T_c,T_b] : % 19.07/19.01 ( c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_R_2)) % 19.07/19.01 => hAPP(c_Relation_OImage(T_c,T_b,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_B_2)) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_rtrancl__Un__separatorE,axiom, % 19.07/19.01 ! [V_Qa_2,V_Pa_2,V_b_2,V_a_2,T_b] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2),V_Qa_2)))) % 19.07/19.01 => ( ! [B_x] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),B_x)),c_Transitive__Closure_Ortrancl(T_b,V_Pa_2))) % 19.07/19.01 => ! [B_y] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_Qa_2)) % 19.07/19.01 => B_x = B_y ) ) % 19.07/19.01 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_Pa_2))) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_single__valued__Id__on,axiom, % 19.07/19.01 ! [V_A_2,T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId__on(T_b,V_A_2)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_single__valued__subset,axiom, % 19.07/19.01 ! [V_s_2,V_r_2,T_c,T_b] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_2),V_s_2)) % 19.07/19.01 => ( c_Relation_Osingle__valued(T_b,T_c,V_s_2) % 19.07/19.01 => c_Relation_Osingle__valued(T_b,T_c,V_r_2) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_single__valued__rel__comp,axiom, % 19.07/19.01 ! [V_s_2,T_d,V_r_2,T_c,T_b] : % 19.07/19.01 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2) % 19.07/19.01 => ( c_Relation_Osingle__valued(T_c,T_d,V_s_2) % 19.07/19.01 => c_Relation_Osingle__valued(T_b,T_d,hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2)) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_single__valued__Id,axiom, % 19.07/19.01 ! [T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId(T_b)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_single__valued__rel__pow,axiom, % 19.07/19.01 ! [V_n_2,V_R_2,T_b] : % 19.07/19.01 ( c_Relation_Osingle__valued(T_b,T_b,V_R_2) % 19.07/19.01 => c_Relation_Osingle__valued(T_b,T_b,hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_single__valued__def,axiom, % 19.07/19.01 ! [V_r_2,T_c,T_b] : % 19.07/19.01 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2) % 19.07/19.01 <=> ! [B_x,B_y] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y)),V_r_2)) % 19.07/19.01 => ! [B_z] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_z)),V_r_2)) % 19.07/19.01 => B_y = B_z ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_single__valuedD,axiom, % 19.07/19.01 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_c,T_b] : % 19.07/19.01 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2) % 19.07/19.01 => ( 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)),V_r_2)) % 19.07/19.01 => ( 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_z_2)),V_r_2)) % 19.07/19.01 => V_y_2 = V_z_2 ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_single__valued__confluent,axiom, % 19.07/19.01 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b] : % 19.07/19.01 ( c_Relation_Osingle__valued(T_b,T_b,V_r_2) % 19.07/19.01 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 19.07/19.01 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 19.07/19.01 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 19.07/19.01 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_z_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_rtrancl__Un__separator__converseE,axiom, % 19.07/19.01 ! [V_Qa_2,V_Pa_2,V_b_2,V_a_2,T_b] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2),V_Qa_2)))) % 19.07/19.01 => ( ! [B_x] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_Pa_2))) % 19.07/19.01 => ! [B_y] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_x)),V_Qa_2)) % 19.07/19.01 => B_y = B_x ) ) % 19.07/19.01 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_Pa_2))) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_rel__pow__Suc__D2,axiom, % 19.07/19.01 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) % 19.07/19.01 => ? [B_y] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),V_R_2)) % 19.07/19.01 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_rel__pow__Suc__E,axiom, % 19.07/19.01 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) % 19.07/19.01 => ~ ! [B_y] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))) % 19.07/19.01 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),V_R_2)) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_rel__pow__Suc__E2,axiom, % 19.07/19.01 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) % 19.07/19.01 => ~ ! [B_y] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),V_R_2)) % 19.07/19.01 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_tranclD,axiom, % 19.07/19.01 ! [V_R_2,V_y_2,V_x_2,T_b] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2))) % 19.07/19.01 => ? [B_z] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_z)),V_R_2)) % 19.07/19.01 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_z),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_tranclD2,axiom, % 19.07/19.01 ! [V_R_2,V_y_2,V_x_2,T_b] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2))) % 19.07/19.01 => ? [B_z] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_z)),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) % 19.07/19.01 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_z),V_y_2)),V_R_2)) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_IdE,axiom, % 19.07/19.01 ! [V_p_2,T_b] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Relation_OId(T_b))) % 19.07/19.01 => ~ ! [B_x] : V_p_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_min__max_OSup__fin_Oeq__fold_H,axiom, % 19.07/19.01 ! [V_x_2,V_A_2,T_b] : % 19.07/19.01 ( class_Orderings_Olinorder(T_b) % 19.07/19.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.01 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/19.01 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_x_2),V_A_2) ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_folding_Oeq__fold,axiom, % 19.07/19.01 ! [V_s_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 19.07/19.01 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 19.07/19.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.01 => hAPP(hAPP(V_F_2,V_A_2),V_s_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_s_2),V_A_2) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_fold__image__def,axiom, % 19.07/19.01 ! [V_g_2,V_f_2,T_c,T_b] : hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2) = c_Finite__Set_Ofold(T_c,T_b,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),V_f_2),V_g_2)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_fold__empty,axiom, % 19.07/19.01 ! [V_z_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_b,V_f_2),V_z_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2 ). % 19.07/19.01 % 19.07/19.01 fof(fact_fold__def,axiom, % 19.07/19.01 ! [V_A_2,V_z_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_b,V_f_2),V_z_2),V_A_2) = c_HOL_OThe(T_b,c_Finite__Set_Ofold__graph(T_c,T_b,V_f_2,V_z_2,V_A_2)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_union__fold__insert,axiom, % 19.07/19.01 ! [V_B_2,V_A_2,T_b] : % 19.07/19.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.01 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,tc_fun(T_b,tc_HOL_Obool),c_Set_Oinsert(T_b)),V_B_2),V_A_2) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_fold__sup__insert,axiom, % 19.07/19.01 ! [V_a_2,V_b_2,V_A_2,T_b] : % 19.07/19.01 ( class_Lattices_Osemilattice__sup(T_b) % 19.07/19.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.01 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_b_2),V_A_2)) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_fold__inf__insert,axiom, % 19.07/19.01 ! [V_a_2,V_b_2,V_A_2,T_b] : % 19.07/19.01 ( class_Lattices_Osemilattice__inf(T_b) % 19.07/19.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.01 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_b_2),V_A_2)) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_min__max_Ofold__inf__insert,axiom, % 19.07/19.01 ! [V_a_2,V_b_2,V_A_2,T_b] : % 19.07/19.01 ( class_Orderings_Olinorder(T_b) % 19.07/19.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.01 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_b_2),V_A_2)) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_min__max_Ofold__sup__insert,axiom, % 19.07/19.01 ! [V_a_2,V_b_2,V_A_2,T_b] : % 19.07/19.01 ( class_Orderings_Olinorder(T_b) % 19.07/19.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.01 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_b_2),V_A_2)) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_fun__left__comm__idem_Ofold__insert__idem,axiom, % 19.07/19.01 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] : % 19.07/19.01 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) % 19.07/19.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.01 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2)) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_fun__left__comm__idem_Ofold__insert__idem2,axiom, % 19.07/19.01 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] : % 19.07/19.01 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) % 19.07/19.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.01 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_sup__SUPR__fold__sup,axiom, % 19.07/19.01 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] : % 19.07/19.01 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 19.07/19.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.01 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),V_f_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Lattices_Osemilattice__sup__class_Osup(T_c)),V_f_2)),V_B_2),V_A_2) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_folding__one__idem_Oeq__fold__idem_H,axiom, % 19.07/19.01 ! [V_a_2,V_A_2,V_F_2,V_f_2,T_b] : % 19.07/19.01 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) % 19.07/19.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.01 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,V_f_2),V_a_2),V_A_2) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_sup__le__fold__sup,axiom, % 19.07/19.01 ! [V_b_2,V_a_2,V_A_2,T_b] : % 19.07/19.01 ( class_Lattices_Osemilattice__sup(T_b) % 19.07/19.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.01 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 19.07/19.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_b_2),V_A_2))) ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_fold__inf__le__inf,axiom, % 19.07/19.01 ! [V_b_2,V_a_2,V_A_2,T_b] : % 19.07/19.01 ( class_Lattices_Osemilattice__inf(T_b) % 19.07/19.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.01 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 19.07/19.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_b_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),V_b_2))) ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_min__max_Ofold__inf__le__inf,axiom, % 19.07/19.01 ! [V_b_2,V_a_2,V_A_2,T_b] : % 19.07/19.01 ( class_Orderings_Olinorder(T_b) % 19.07/19.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.01 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 19.07/19.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_b_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_a_2),V_b_2))) ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_min__max_Osup__le__fold__sup,axiom, % 19.07/19.01 ! [V_b_2,V_a_2,V_A_2,T_b] : % 19.07/19.01 ( class_Orderings_Olinorder(T_b) % 19.07/19.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.01 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 19.07/19.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_b_2),V_A_2))) ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_fold1__eq__fold__idem,axiom, % 19.07/19.01 ! [V_a_2,V_A_2,T_b] : % 19.07/19.01 ( class_Lattices_Oab__semigroup__idem__mult(T_b) % 19.07/19.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.01 => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)),V_a_2),V_A_2) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Sup__fin_Oeq__fold__idem_H,axiom, % 19.07/19.01 ! [V_a_2,V_A_2,T_b] : % 19.07/19.01 ( class_Lattices_Olattice(T_b) % 19.07/19.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.01 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_a_2),V_A_2) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Inf__fin_Oeq__fold__idem_H,axiom, % 19.07/19.01 ! [V_a_2,V_A_2,T_b] : % 19.07/19.01 ( class_Lattices_Olattice(T_b) % 19.07/19.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.01 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_a_2),V_A_2) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Min_Oeq__fold__idem_H,axiom, % 19.07/19.01 ! [V_a_2,V_A_2,T_b] : % 19.07/19.01 ( class_Orderings_Olinorder(T_b) % 19.07/19.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.01 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_a_2),V_A_2) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Max_Oeq__fold__idem_H,axiom, % 19.07/19.01 ! [V_a_2,V_A_2,T_b] : % 19.07/19.01 ( class_Orderings_Olinorder(T_b) % 19.07/19.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.01 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_a_2),V_A_2) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_min__max_OInf__fin_Oeq__fold__idem_H,axiom, % 19.07/19.01 ! [V_a_2,V_A_2,T_b] : % 19.07/19.01 ( class_Orderings_Olinorder(T_b) % 19.07/19.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.01 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_a_2),V_A_2) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_min__max_OSup__fin_Oeq__fold__idem_H,axiom, % 19.07/19.01 ! [V_a_2,V_A_2,T_b] : % 19.07/19.01 ( class_Orderings_Olinorder(T_b) % 19.07/19.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.01 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_a_2),V_A_2) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_minus__fold__remove,axiom, % 19.07/19.01 ! [V_B_2,V_A_2,T_b] : % 19.07/19.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.01 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2),V_A_2) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_folding__one_Oeq__fold_H,axiom, % 19.07/19.01 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] : % 19.07/19.01 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 19.07/19.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.01 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/19.01 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,V_f_2),V_x_2),V_A_2) ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_SUPR__fold__sup,axiom, % 19.07/19.01 ! [V_f_2,V_A_2,T_b,T_c] : % 19.07/19.01 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 19.07/19.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.01 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),V_f_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Lattices_Osemilattice__sup__class_Osup(T_c)),V_f_2)),c_Orderings_Obot__class_Obot(T_c)),V_A_2) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_fold1__eq__fold,axiom, % 19.07/19.01 ! [V_a_2,V_A_2,T_b] : % 19.07/19.01 ( class_Groups_Oab__semigroup__mult(T_b) % 19.07/19.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.01 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 19.07/19.01 => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)),V_a_2),V_A_2) ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Sup__fin_Oeq__fold_H,axiom, % 19.07/19.01 ! [V_x_2,V_A_2,T_b] : % 19.07/19.01 ( class_Lattices_Olattice(T_b) % 19.07/19.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.01 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/19.01 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_x_2),V_A_2) ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Inf__fin_Oeq__fold_H,axiom, % 19.07/19.01 ! [V_x_2,V_A_2,T_b] : % 19.07/19.01 ( class_Lattices_Olattice(T_b) % 19.07/19.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.01 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/19.01 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_x_2),V_A_2) ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Min_Oeq__fold_H,axiom, % 19.07/19.01 ! [V_x_2,V_A_2,T_b] : % 19.07/19.01 ( class_Orderings_Olinorder(T_b) % 19.07/19.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.01 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/19.01 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_x_2),V_A_2) ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Max_Oeq__fold_H,axiom, % 19.07/19.01 ! [V_x_2,V_A_2,T_b] : % 19.07/19.01 ( class_Orderings_Olinorder(T_b) % 19.07/19.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.01 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/19.01 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_x_2),V_A_2) ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_min__max_OInf__fin_Oeq__fold_H,axiom, % 19.07/19.01 ! [V_x_2,V_A_2,T_b] : % 19.07/19.01 ( class_Orderings_Olinorder(T_b) % 19.07/19.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.01 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/19.01 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_x_2),V_A_2) ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_fun__left__comm_Ofold__rec,axiom, % 19.07/19.01 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 19.07/19.01 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 19.07/19.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.01 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/19.01 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_fun__left__comm_Ofold__insert__remove,axiom, % 19.07/19.01 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] : % 19.07/19.01 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 19.07/19.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.01 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_fun__left__comm,axiom, % 19.07/19.01 ! [T_b] : % 19.07/19.01 ( class_Groups_Oab__semigroup__mult(T_b) % 19.07/19.01 => c_Finite__Set_Ofun__left__comm(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_fun__left__comm_Ofun__left__comm__apply,axiom, % 19.07/19.01 ! [V_g_2,T_d,V_f_2,T_c,T_b] : % 19.07/19.01 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 19.07/19.01 => c_Finite__Set_Ofun__left__comm(T_d,T_c,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,T_c),T_d),V_f_2),V_g_2)) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_fun__left__comm_Ofun__left__comm,axiom, % 19.07/19.01 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_c,T_b] : % 19.07/19.01 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 19.07/19.01 => hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(V_f_2,V_y_2),V_z_2)) = hAPP(hAPP(V_f_2,V_y_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_fun__left__comm_Ofold__graph__determ,axiom, % 19.07/19.01 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] : % 19.07/19.01 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 19.07/19.01 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2)) % 19.07/19.01 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2)) % 19.07/19.01 => V_y_2 = V_x_2 ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_fun__left__comm_Ofun__comp__comm,axiom, % 19.07/19.01 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] : % 19.07/19.01 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 19.07/19.01 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_y_2)),hAPP(V_f_2,V_x_2)) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_fun__left__comm_Ofold__fun__comm,axiom, % 19.07/19.01 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 19.07/19.01 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 19.07/19.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.01 => hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_fun__left__comm_Ofold__equality,axiom, % 19.07/19.01 ! [V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] : % 19.07/19.01 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 19.07/19.01 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2)) % 19.07/19.01 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2) = V_y_2 ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_fun__left__comm_Ofold__graph__fold,axiom, % 19.07/19.01 ! [V_z_2,V_A_2,V_f_2,T_c,T_b] : % 19.07/19.01 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 19.07/19.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.01 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2))) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_fun__left__comm_Ofold__insert2,axiom, % 19.07/19.01 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 19.07/19.01 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 19.07/19.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.01 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/19.01 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2) ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_fun__left__comm_Ofold__insert,axiom, % 19.07/19.01 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 19.07/19.01 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 19.07/19.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.01 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/19.01 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2)) ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_fun__left__comm_Ofold__graph__insertE__aux,axiom, % 19.07/19.01 ! [V_a_2,V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] : % 19.07/19.01 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 19.07/19.01 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2)) % 19.07/19.01 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 19.07/19.01 => ? [B_y_H] : % 19.07/19.01 ( V_y_2 = hAPP(hAPP(V_f_2,V_a_2),B_y_H) % 19.07/19.01 & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),B_y_H)) ) ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_INFI__fold__inf,axiom, % 19.07/19.01 ! [V_f_2,V_A_2,T_b,T_c] : % 19.07/19.01 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 19.07/19.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.01 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),V_f_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Lattices_Osemilattice__inf__class_Oinf(T_c)),V_f_2)),c_Orderings_Otop__class_Otop(T_c)),V_A_2) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_INF2__E,axiom, % 19.07/19.01 ! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) % 19.07/19.01 => ( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2)) % 19.07/19.01 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_INF2__D,axiom, % 19.07/19.01 ! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) % 19.07/19.01 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 19.07/19.01 => hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2)) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_INT__E,axiom, % 19.07/19.01 ! [V_a_2,V_B_2,V_A_2,T_c,V_b_2,T_b] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 19.07/19.01 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) % 19.07/19.01 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_INT__D,axiom, % 19.07/19.01 ! [V_a_2,V_B_2,V_A_2,T_c,V_b_2,T_b] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 19.07/19.01 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) % 19.07/19.01 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_INF1__E,axiom, % 19.07/19.01 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_c,T_b] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) % 19.07/19.01 => ( ~ hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) % 19.07/19.01 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_INF1__D,axiom, % 19.07/19.01 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_c,T_b] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) % 19.07/19.01 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 19.07/19.01 => hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_finite__INT,axiom, % 19.07/19.01 ! [V_A_2,T_c,V_I_2,T_b] : % 19.07/19.01 ( ? [B_x] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2)) % 19.07/19.01 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_A_2,B_x))) ) % 19.07/19.01 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2))) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_UN__simps_I7_J,axiom, % 19.07/19.01 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_UN__extend__simps_I7_J,axiom, % 19.07/19.01 ! [V_B_2,V_C_2,T_c,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_INT__simps_I9_J,axiom, % 19.07/19.01 ! [V_C_2,V_B_2,V_A_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_d),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_INT__extend__simps_I9_J,axiom, % 19.07/19.01 ! [V_C_2,V_B_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Compl__INT,axiom, % 19.07/19.01 ! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool))),V_B_2)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Compl__UN,axiom, % 19.07/19.01 ! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool))),V_B_2)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Pow__INT__eq,axiom, % 19.07/19.01 ! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_c),c_Set_OPow(T_b)),V_B_2)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_INF__commute,axiom, % 19.07/19.01 ! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] : % 19.07/19.01 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 19.07/19.01 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),T_b,T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,T_b),V_B_2)),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,T_b),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),T_b,T_d),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2)),hAPP(c_COMBC(T_c,T_d,T_b),V_f_2))) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_INFI__apply,axiom, % 19.07/19.01 ! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] : % 19.07/19.01 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 19.07/19.01 => hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,T_b)),V_A_2),V_f_2),V_x_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),hAPP(hAPP(c_COMBC(T_c,T_d,T_b),V_f_2),V_x_2)) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_INT__Int__distrib,axiom, % 19.07/19.01 ! [V_B_2,V_A_2,V_I_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_B_2)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_INF__less__iff,axiom, % 19.07/19.01 ! [V_a_2,V_f_2,V_A_2,T_c,T_b] : % 19.07/19.01 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 19.07/19.01 & class_Orderings_Olinorder(T_b) ) % 19.07/19.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),V_f_2)),V_a_2)) % 19.07/19.01 <=> ? [B_x] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 19.07/19.01 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),V_a_2)) ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_INTER__UNIV__conv_I1_J,axiom, % 19.07/19.01 ! [V_B_2,V_A_2,T_c,T_b] : % 19.07/19.01 ( c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) % 19.07/19.01 <=> ! [B_x] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 19.07/19.01 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_INTER__UNIV__conv_I2_J,axiom, % 19.07/19.01 ! [V_B_2,V_A_2,T_b,T_c] : % 19.07/19.01 ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.01 <=> ! [B_x] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 19.07/19.01 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_INT__absorb,axiom, % 19.07/19.01 ! [V_A_2,T_c,V_I_2,V_k_2,T_b] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2)) % 19.07/19.01 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_A_2,V_k_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_INF__INT__eq2,axiom, % 19.07/19.01 ! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),T_b),hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_c,T_d)))),c_Product__Type_OPair(T_c,T_d))))),V_r_2)),V_x_2),V_y_2)) % 19.07/19.01 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_INF__INT__eq,axiom, % 19.07/19.01 ! [V_x_2,V_r_2,T_c,T_b] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c))),V_r_2)),V_x_2)) % 19.07/19.01 <=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_INT__iff,axiom, % 19.07/19.01 ! [V_B_2,V_A_2,T_c,V_b_2,T_b] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 19.07/19.01 <=> ! [B_x] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 19.07/19.01 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x))) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_vimage__INT,axiom, % 19.07/19.01 ! [V_B_2,V_A_2,T_d,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Set_Ovimage(T_b,T_c,V_f_2)),V_B_2)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_INT__extend__simps_I10_J,axiom, % 19.07/19.01 ! [V_f_2,V_B_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),V_B_2) ). % 19.07/19.01 % 19.07/19.01 fof(fact_INT__simps_I10_J,axiom, % 19.07/19.01 ! [V_B_2,V_A_2,V_f_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_b,tc_HOL_Obool),T_d),V_B_2),V_f_2)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_INT__insert,axiom, % 19.07/19.01 ! [V_B_2,V_A_2,V_a_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_INT__lower,axiom, % 19.07/19.01 ! [V_B_2,T_c,V_A_2,V_a_2,T_b] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 19.07/19.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(V_B_2,V_a_2))) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_INT__insert__distrib,axiom, % 19.07/19.01 ! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2)) % 19.07/19.01 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_INT__simps_I5_J,axiom, % 19.07/19.01 ! [V_B_2,V_a_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Set_Oinsert(T_b),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_INT__extend__simps_I5_J,axiom, % 19.07/19.01 ! [V_B_2,V_C_2,T_c,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Set_Oinsert(T_b),V_a_2)),V_B_2)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_le__INF__iff,axiom, % 19.07/19.01 ! [V_M_2,V_A_2,T_c,V_u_2,T_b] : % 19.07/19.01 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 19.07/19.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_u_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),V_M_2))) % 19.07/19.01 <=> ! [B_x] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 19.07/19.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_u_2),hAPP(V_M_2,B_x))) ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_INT__subset__iff,axiom, % 19.07/19.01 ! [V_A_2,V_I_2,T_c,V_B_2,T_b] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2))) % 19.07/19.01 <=> ! [B_x] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2)) % 19.07/19.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(V_A_2,B_x))) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Image__INT__subset,axiom, % 19.07/19.01 ! [V_B_2,V_A_2,T_d,V_r_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Relation_OImage(T_c,T_b,V_r_2)),V_B_2)))) ). % 19.07/19.01 % 19.07/19.01 fof(fact_INT__constant,axiom, % 19.07/19.01 ! [V_c_2,T_c,T_b,V_A_2] : % 19.07/19.01 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.01 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_c_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) % 19.07/19.01 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.01 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_c_2)) = V_c_2 ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_INT__empty,axiom, % 19.07/19.01 ! [V_B_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_INT__extend__simps_I1_J,axiom, % 19.07/19.01 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 19.07/19.01 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.01 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = V_B_2 ) % 19.07/19.01 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.01 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_INT__extend__simps_I2_J,axiom, % 19.07/19.01 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 19.07/19.01 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.01 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2 ) % 19.07/19.01 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.01 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_INF__const,axiom, % 19.07/19.01 ! [V_M_2,T_b,V_A_2,T_c] : % 19.07/19.01 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 19.07/19.01 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.01 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),hAPP(c_COMBK(T_c,T_b),V_M_2)) = V_M_2 ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_INFI__bool__eq,axiom, % 19.07/19.01 ! [T_b] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_HOL_Obool) = c_Set_OBall(T_b) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Collect__ball__eq,axiom, % 19.07/19.01 ! [V_Pa_2,V_A_2,T_c,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fimplies),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),V_Pa_2))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Set_OCollect(T_b)),hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_Pa_2))) ). % 19.07/19.01 % 19.07/19.01 fof(fact_INT__simps_I7_J,axiom, % 19.07/19.01 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_INT__simps_I6_J,axiom, % 19.07/19.01 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ). % 19.07/19.01 % 19.07/19.01 fof(fact_INT__extend__simps_I7_J,axiom, % 19.07/19.01 ! [V_B_2,V_C_2,T_c,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Un__INT__distrib,axiom, % 19.07/19.01 ! [V_A_2,V_I_2,T_c,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),V_A_2)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_INT__extend__simps_I6_J,axiom, % 19.07/19.01 ! [V_B_2,V_A_2,V_C_2,T_c,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Un__INT__distrib2,axiom, % 19.07/19.01 ! [V_B_2,V_J_2,T_d,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_J_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_J_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool))),T_c),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2))),V_B_2))) ). % 19.07/19.01 % 19.07/19.01 fof(fact_INT__Un,axiom, % 19.07/19.01 ! [V_M_2,V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_M_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_M_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_M_2)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_converse__INTER,axiom, % 19.07/19.01 ! [V_r_2,V_S_2,T_d,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_S_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_S_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_d),c_Relation_Oconverse(T_c,T_b)),V_r_2)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_INF__subset,axiom, % 19.07/19.01 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] : % 19.07/19.01 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 19.07/19.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 19.07/19.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_B_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),V_f_2))) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_INTER__def,axiom, % 19.07/19.01 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fimplies),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c)),c_member(T_b))),V_B_2)))) ). % 19.07/19.01 % 19.07/19.01 fof(fact_INT__simps_I2_J,axiom, % 19.07/19.01 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 19.07/19.01 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.01 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) % 19.07/19.01 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.01 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_INT__simps_I1_J,axiom, % 19.07/19.01 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 19.07/19.01 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.01 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) % 19.07/19.01 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.01 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_INT__simps_I3_J,axiom, % 19.07/19.01 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 19.07/19.01 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.01 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) % 19.07/19.01 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.01 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_INT__extend__simps_I3_J,axiom, % 19.07/19.01 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 19.07/19.01 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.01 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))),V_B_2) ) % 19.07/19.01 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.01 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_INT__extend__simps_I4_J,axiom, % 19.07/19.01 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 19.07/19.01 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.01 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2 ) % 19.07/19.01 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.01 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_INF__leI,axiom, % 19.07/19.01 ! [V_M_2,V_A_2,V_i_2,T_b,T_c] : % 19.07/19.01 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 19.07/19.01 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2)) % 19.07/19.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),V_M_2)),hAPP(V_M_2,V_i_2))) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_INT__greaterThan__UNIV,axiom, % 19.07/19.01 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)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_INT__simps_I4_J,axiom, % 19.07/19.01 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 19.07/19.01 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.01 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) % 19.07/19.01 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.01 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Image__INT__eq,axiom, % 19.07/19.01 ! [V_B_2,T_d,V_A_2,V_r_2,T_c,T_b] : % 19.07/19.01 ( c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)) % 19.07/19.01 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)) % 19.07/19.01 => hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Relation_OImage(T_c,T_b,V_r_2)),V_B_2)) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_inf__INFI__fold__inf,axiom, % 19.07/19.01 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] : % 19.07/19.01 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 19.07/19.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.01 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),V_f_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Lattices_Osemilattice__inf__class_Oinf(T_c)),V_f_2)),V_B_2),V_A_2) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Inf__fold__inf,axiom, % 19.07/19.01 ! [V_A_2,T_b] : % 19.07/19.01 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 19.07/19.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.01 => c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),c_Orderings_Otop__class_Otop(T_b)),V_A_2) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Sup__fold__sup,axiom, % 19.07/19.01 ! [V_A_2,T_b] : % 19.07/19.01 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 19.07/19.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.01 => c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),c_Orderings_Obot__class_Obot(T_b)),V_A_2) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_finite__Inter,axiom, % 19.07/19.01 ! [V_M_2,T_b] : % 19.07/19.01 ( ? [B_x] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_M_2)) % 19.07/19.01 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_x)) ) % 19.07/19.01 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_M_2))) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_UnionI,axiom, % 19.07/19.01 ! [V_A_2,V_C_2,V_X_2,T_b] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2)) % 19.07/19.01 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) % 19.07/19.01 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2))) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_InterD,axiom, % 19.07/19.01 ! [V_X_2,V_C_2,V_A_2,T_b] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_C_2))) % 19.07/19.01 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2)) % 19.07/19.01 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_InterE,axiom, % 19.07/19.01 ! [V_X_2,V_C_2,V_A_2,T_b] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_C_2))) % 19.07/19.01 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2)) % 19.07/19.01 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_INF1__iff,axiom, % 19.07/19.01 ! [V_b_2,V_B_2,V_A_2,T_c,T_b] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) % 19.07/19.01 <=> ! [B_x] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 19.07/19.01 => hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_INF2__iff,axiom, % 19.07/19.01 ! [V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) % 19.07/19.01 <=> ! [B_x] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 19.07/19.01 => hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_INT__extend__simps_I8_J,axiom, % 19.07/19.01 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2) ). % 19.07/19.01 % 19.07/19.01 fof(fact_INT__simps_I8_J,axiom, % 19.07/19.01 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Inter__image__eq,axiom, % 19.07/19.01 ! [V_A_2,V_B_2,T_c,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ). % 19.07/19.01 % 19.07/19.01 fof(fact_INTER__eq__Inter__image,axiom, % 19.07/19.01 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Un__Inter,axiom, % 19.07/19.01 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Inter__anti__mono,axiom, % 19.07/19.01 ! [V_A_2,V_B_2,T_b] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_B_2),V_A_2)) % 19.07/19.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2))) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Inter__empty,axiom, % 19.07/19.01 ! [T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Union__insert,axiom, % 19.07/19.01 ! [V_B_2,V_a_2,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_a_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_subset__Pow__Union,axiom, % 19.07/19.01 ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)))) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Sup__Inf,axiom, % 19.07/19.01 ! [V_A_2,T_b] : % 19.07/19.01 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 19.07/19.01 => c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_b)))))) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Inf__Sup,axiom, % 19.07/19.01 ! [V_A_2,T_b] : % 19.07/19.01 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 19.07/19.01 => c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),c_Orderings_Oord__class_Oless__eq(T_b))))) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Union__empty,axiom, % 19.07/19.01 ! [T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Union__disjoint,axiom, % 19.07/19.01 ! [V_A_2,V_C_2,T_b] : % 19.07/19.01 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.01 <=> ! [B_x] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_C_2)) % 19.07/19.01 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),B_x),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Sup__le__iff,axiom, % 19.07/19.01 ! [V_b_2,V_A_2,T_b] : % 19.07/19.01 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 19.07/19.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2)),V_b_2)) % 19.07/19.01 <=> ! [B_x] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 19.07/19.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_le__Inf__iff,axiom, % 19.07/19.01 ! [V_A_2,V_b_2,T_b] : % 19.07/19.01 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 19.07/19.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2))) % 19.07/19.01 <=> ! [B_x] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 19.07/19.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Union__upper,axiom, % 19.07/19.01 ! [V_A_2,V_B_2,T_b] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 19.07/19.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2))) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Inter__lower,axiom, % 19.07/19.01 ! [V_A_2,V_B_2,T_b] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 19.07/19.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2)) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Union__mono,axiom, % 19.07/19.01 ! [V_B_2,V_A_2,T_b] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) % 19.07/19.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2))) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Field__Union,axiom, % 19.07/19.01 ! [V_R_2,T_b] : hAPP(c_Relation_OField(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),V_R_2)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),c_Relation_OField(T_b)),V_R_2)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_less__Sup__iff,axiom, % 19.07/19.01 ! [V_S_2,V_a_2,T_b] : % 19.07/19.01 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 19.07/19.01 & class_Orderings_Olinorder(T_b) ) % 19.07/19.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_S_2))) % 19.07/19.01 <=> ? [B_x] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) % 19.07/19.01 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),B_x)) ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Inf__less__iff,axiom, % 19.07/19.01 ! [V_a_2,V_S_2,T_b] : % 19.07/19.01 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 19.07/19.01 & class_Orderings_Olinorder(T_b) ) % 19.07/19.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Complete__Lattice_OInf__class_OInf(T_b,V_S_2)),V_a_2)) % 19.07/19.01 <=> ? [B_x] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) % 19.07/19.01 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_a_2)) ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Union__Pow__eq,axiom, % 19.07/19.01 ! [V_A_2,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_OPow(T_b),V_A_2)) = V_A_2 ). % 19.07/19.01 % 19.07/19.01 fof(fact_Union__quotient,axiom, % 19.07/19.01 ! [V_r_2,V_A_2,T_b] : % 19.07/19.01 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 19.07/19.01 => c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)) = V_A_2 ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_finite__UnionD,axiom, % 19.07/19.01 ! [V_A_2,T_b] : % 19.07/19.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2))) % 19.07/19.01 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_image__Union,axiom, % 19.07/19.01 ! [V_S_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_Set_Oimage(T_c,T_b,V_f_2)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Sigma__Union,axiom, % 19.07/19.01 ! [V_B_2,V_X_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_X_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),c_Product__Type_OSigma(T_b,T_c)),V_B_2)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_UN__extend__simps_I8_J,axiom, % 19.07/19.01 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2) ). % 19.07/19.01 % 19.07/19.01 fof(fact_UN__simps_I8_J,axiom, % 19.07/19.01 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Int__Union,axiom, % 19.07/19.01 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Int__Union2,axiom, % 19.07/19.01 ! [V_A_2,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_vimage__Union,axiom, % 19.07/19.01 ! [V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Set_Ovimage(T_b,T_c,V_f_2)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Range__Union,axiom, % 19.07/19.01 ! [V_S_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_Relation_ORange(T_c,T_b)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Domain__Union,axiom, % 19.07/19.01 ! [V_S_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_Relation_ODomain(T_b,T_c)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Inter__eq,axiom, % 19.07/19.01 ! [V_A_2,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_b,tc_HOL_Obool))),V_A_2)))),c_member(T_b)))) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Union__Un__distrib,axiom, % 19.07/19.01 ! [V_B_2,V_A_2,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Inter__insert,axiom, % 19.07/19.01 ! [V_B_2,V_a_2,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_a_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Union__UNIV,axiom, % 19.07/19.01 ! [T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_UNION__eq__Union__image,axiom, % 19.07/19.01 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Union__image__eq,axiom, % 19.07/19.01 ! [V_A_2,V_B_2,T_c,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Sup__upper,axiom, % 19.07/19.01 ! [V_A_2,V_x_2,T_b] : % 19.07/19.01 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 19.07/19.01 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/19.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2))) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Inter__UNIV,axiom, % 19.07/19.01 ! [T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Inf__lower,axiom, % 19.07/19.01 ! [V_A_2,V_x_2,T_b] : % 19.07/19.01 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 19.07/19.01 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/19.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2)),V_x_2)) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Inter__Un__distrib,axiom, % 19.07/19.01 ! [V_B_2,V_A_2,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Sup__empty,axiom, % 19.07/19.01 ! [T_b] : % 19.07/19.01 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 19.07/19.01 => c_Complete__Lattice_OSup__class_OSup(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(T_b) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Sup__singleton,axiom, % 19.07/19.01 ! [V_a_2,T_b] : % 19.07/19.01 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 19.07/19.01 => c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_a_2 ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Sup__insert,axiom, % 19.07/19.01 ! [V_A_2,V_a_2,T_b] : % 19.07/19.01 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 19.07/19.01 => c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2)) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Int__Inter__image,axiom, % 19.07/19.01 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_A_2),V_C_2))),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_C_2))) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Sup__UNIV,axiom, % 19.07/19.01 ! [T_b] : % 19.07/19.01 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 19.07/19.01 => c_Complete__Lattice_OSup__class_OSup(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(T_b) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Inf__singleton,axiom, % 19.07/19.01 ! [V_a_2,T_b] : % 19.07/19.01 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 19.07/19.01 => c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_a_2 ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Inf__empty,axiom, % 19.07/19.01 ! [T_b] : % 19.07/19.01 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 19.07/19.01 => c_Complete__Lattice_OInf__class_OInf(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(T_b) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Inf__UNIV,axiom, % 19.07/19.01 ! [T_b] : % 19.07/19.01 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 19.07/19.01 => c_Complete__Lattice_OInf__class_OInf(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(T_b) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Inf__insert,axiom, % 19.07/19.01 ! [V_A_2,V_a_2,T_b] : % 19.07/19.01 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 19.07/19.01 => c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2)) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Un__eq__Union,axiom, % 19.07/19.01 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_B_2),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))))) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Un__Union__image,axiom, % 19.07/19.01 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_A_2),V_C_2))),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_C_2))) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Union__Int__subset,axiom, % 19.07/19.01 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)))) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Int__eq__Inter,axiom, % 19.07/19.01 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_B_2),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))))) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Inter__Un__subset,axiom, % 19.07/19.01 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2))),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)))) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Sup__binary,axiom, % 19.07/19.01 ! [V_b_2,V_a_2,T_b] : % 19.07/19.01 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 19.07/19.01 => c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),V_b_2) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Inf__binary,axiom, % 19.07/19.01 ! [V_b_2,V_a_2,T_b] : % 19.07/19.01 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 19.07/19.01 => c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),V_b_2) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_sup__Sup__fold__sup,axiom, % 19.07/19.01 ! [V_B_2,V_A_2,T_b] : % 19.07/19.01 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 19.07/19.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.01 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_B_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_B_2),V_A_2) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Sup__fin__Sup,axiom, % 19.07/19.01 ! [V_A_2,T_b] : % 19.07/19.01 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 19.07/19.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.01 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.01 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_inf__Inf__fold__inf,axiom, % 19.07/19.01 ! [V_B_2,V_A_2,T_b] : % 19.07/19.01 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 19.07/19.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.01 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_B_2),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_B_2),V_A_2) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Inf__fin__Inf,axiom, % 19.07/19.01 ! [V_A_2,T_b] : % 19.07/19.01 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 19.07/19.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.01 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.01 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_image__INT,axiom, % 19.07/19.01 ! [V_j_2,V_B_2,V_A_2,T_d,V_C_2,V_f_2,T_c,T_b] : % 19.07/19.01 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2) % 19.07/19.01 => ( ! [B_x] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2)) % 19.07/19.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_B_2,B_x)),V_C_2)) ) % 19.07/19.01 => ( hBOOL(hAPP(hAPP(c_member(T_d),V_j_2),V_A_2)) % 19.07/19.01 => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_d),c_Set_Oimage(T_b,T_c,V_f_2)),V_B_2)) ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_card__partition,axiom, % 19.07/19.01 ! [V_k_2,V_C_2,T_b] : % 19.07/19.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_C_2)) % 19.07/19.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2))) % 19.07/19.01 => ( ! [B_c] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c),V_C_2)) % 19.07/19.01 => hAPP(c_Finite__Set_Ocard(T_b),B_c) = V_k_2 ) % 19.07/19.01 => ( ! [B_c1] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c1),V_C_2)) % 19.07/19.01 => ! [B_c2] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c2),V_C_2)) % 19.07/19.01 => ( B_c1 != B_c2 % 19.07/19.01 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),B_c1),B_c2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ) % 19.07/19.01 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(tc_fun(T_b,tc_HOL_Obool)),V_C_2)) = hAPP(c_Finite__Set_Ocard(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)) ) ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Inter__def,axiom, % 19.07/19.01 ! [V_S_2,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_S_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_COMBI(tc_fun(T_b,tc_HOL_Obool))) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Union__def,axiom, % 19.07/19.01 ! [V_S_2,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_S_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_COMBI(tc_fun(T_b,tc_HOL_Obool))) ). % 19.07/19.01 % 19.07/19.01 fof(fact_finite__Union,axiom, % 19.07/19.01 ! [V_A_2,T_b] : % 19.07/19.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) % 19.07/19.01 => ( ! [B_M] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_M),V_A_2)) % 19.07/19.01 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_M)) ) % 19.07/19.01 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2))) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_insert__partition,axiom, % 19.07/19.01 ! [V_F_2,V_x_2,T_b] : % 19.07/19.01 ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2)) % 19.07/19.01 => ( ! [B_x] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2))) % 19.07/19.01 => ! [B_xa] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_xa),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2))) % 19.07/19.01 => ( B_x != B_xa % 19.07/19.01 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),B_x),B_xa) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ) % 19.07/19.01 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_x_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_F_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_inj__on__Inter,axiom, % 19.07/19.01 ! [V_f_2,T_c,T_b,V_S_2] : % 19.07/19.01 ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) % 19.07/19.01 => ( ! [B_A] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_A),V_S_2)) % 19.07/19.01 => c_Fun_Oinj__on(T_b,T_c,V_f_2,B_A) ) % 19.07/19.01 => c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_S_2)) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Inter__subset,axiom, % 19.07/19.01 ! [V_B_2,V_A_2,T_b] : % 19.07/19.01 ( ! [B_X] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_A_2)) % 19.07/19.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_X),V_B_2)) ) % 19.07/19.01 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) % 19.07/19.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2)) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_inj__on__INTER,axiom, % 19.07/19.01 ! [V_A_2,V_f_2,T_d,T_c,T_b,V_I_2] : % 19.07/19.01 ( V_I_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.01 => ( ! [B_i] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_I_2)) % 19.07/19.01 => c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(V_A_2,B_i)) ) % 19.07/19.01 => c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_fun__left__comm_Ofold__graph__insertE,axiom, % 19.07/19.01 ! [V_v_2,V_A_2,V_x_2,V_z_2,V_f_2,T_c,T_b] : % 19.07/19.01 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 19.07/19.01 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_v_2)) % 19.07/19.01 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/19.01 => ~ ! [B_y] : % 19.07/19.01 ( V_v_2 = hAPP(hAPP(V_f_2,V_x_2),B_y) % 19.07/19.01 => ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),B_y)) ) ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_min__max_Ofold__sup__le__sup,axiom, % 19.07/19.01 ! [V_c_2,V_b_2,V_A_2,T_b] : % 19.07/19.01 ( class_Orderings_Olinorder(T_b) % 19.07/19.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.01 => ( ! [B_x] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 19.07/19.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) ) % 19.07/19.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_c_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_b_2),V_c_2))) ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_min__max_Oinf__le__fold__inf,axiom, % 19.07/19.01 ! [V_c_2,V_b_2,V_A_2,T_b] : % 19.07/19.01 ( class_Orderings_Olinorder(T_b) % 19.07/19.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.01 => ( ! [B_x] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 19.07/19.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) ) % 19.07/19.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_c_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_c_2),V_A_2))) ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_InterI,axiom, % 19.07/19.01 ! [V_A_2,V_C_2,T_b] : % 19.07/19.01 ( ! [B_X] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2)) % 19.07/19.01 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X)) ) % 19.07/19.01 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_C_2))) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_inf__le__fold__inf,axiom, % 19.07/19.01 ! [V_c_2,V_b_2,V_A_2,T_b] : % 19.07/19.01 ( class_Lattices_Osemilattice__inf(T_b) % 19.07/19.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.01 => ( ! [B_x] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 19.07/19.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) ) % 19.07/19.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_b_2),V_c_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_c_2),V_A_2))) ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_fold__sup__le__sup,axiom, % 19.07/19.01 ! [V_c_2,V_b_2,V_A_2,T_b] : % 19.07/19.01 ( class_Lattices_Osemilattice__sup(T_b) % 19.07/19.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.01 => ( ! [B_x] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 19.07/19.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) ) % 19.07/19.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_c_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_b_2),V_c_2))) ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_wf__eq__minimal,axiom, % 19.07/19.01 ! [V_r_2,T_b] : % 19.07/19.01 ( c_Wellfounded_Owf(T_b,V_r_2) % 19.07/19.01 <=> ! [B_Q] : % 19.07/19.01 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q)) % 19.07/19.01 => ? [B_x] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q)) % 19.07/19.01 & ! [B_y] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_x)),V_r_2)) % 19.07/19.01 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_y),B_Q)) ) ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_folding__image__simple__idem_Ounion__idem,axiom, % 19.07/19.01 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 19.07/19.01 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 19.07/19.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 19.07/19.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 19.07/19.01 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_transfer__nat__int__set__cong,axiom, % 19.07/19.01 ! [V_P_H_2,V_Pa_2] : % 19.07/19.01 ( ! [B_x] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 19.07/19.01 => ( hBOOL(hAPP(V_Pa_2,B_x)) % 19.07/19.01 <=> hBOOL(hAPP(V_P_H_2,B_x)) ) ) % 19.07/19.01 => hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_Pa_2)) = hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_H_2)) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_folding__image__simple__idem_Oidem,axiom, % 19.07/19.01 ! [V_x_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 19.07/19.01 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 19.07/19.01 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_folding__image__simple__idem_Oin__idem,axiom, % 19.07/19.01 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 19.07/19.01 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 19.07/19.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 19.07/19.01 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 19.07/19.01 => hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_folding__image__simple__idem_Oinsert__idem,axiom, % 19.07/19.01 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 19.07/19.01 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 19.07/19.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 19.07/19.01 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,V_A_2)) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_folding__image__simple__idem_Osubset__idem,axiom, % 19.07/19.01 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 19.07/19.01 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 19.07/19.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 19.07/19.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2)) % 19.07/19.01 => 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) ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Int__Collect__mono,axiom, % 19.07/19.01 ! [V_Qa_2,V_Pa_2,V_B_2,V_A_2,T_b] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 19.07/19.01 => ( ! [B_x] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 19.07/19.01 => ( hBOOL(hAPP(V_Pa_2,B_x)) % 19.07/19.01 => hBOOL(hAPP(V_Qa_2,B_x)) ) ) % 19.07/19.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_OCollect(T_b),V_Qa_2)))) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_UnionE,axiom, % 19.07/19.01 ! [V_C_2,V_A_2,T_b] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2))) % 19.07/19.01 => ~ ! [B_X] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X)) % 19.07/19.01 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2)) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_map__add__upd__left,axiom, % 19.07/19.01 ! [V_u1_2,V_e1_2,V_e2_2,T_c,V_m_2,T_b] : % 19.07/19.01 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_m_2),c_Map_Odom(T_b,T_c,V_e2_2))) % 19.07/19.01 => c_Map_Omap__add(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_e1_2),V_m_2),hAPP(c_Option_Ooption_OSome(T_c),V_u1_2)),V_e2_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Omap__add(T_b,T_c,V_e1_2,V_e2_2)),V_m_2),hAPP(c_Option_Ooption_OSome(T_c),V_u1_2)) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_converseE,axiom, % 19.07/19.01 ! [V_r_2,V_yx_2,T_c,T_b] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_yx_2),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2))) % 19.07/19.01 => ~ ! [B_x,B_y] : % 19.07/19.01 ( V_yx_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_y),B_x) % 19.07/19.01 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),B_y)),V_r_2)) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_map__add__Some__iff,axiom, % 19.07/19.01 ! [V_x_2,V_k_2,V_n_2,V_m_2,T_b,T_c] : % 19.07/19.01 ( hAPP(c_Map_Omap__add(T_c,T_b,V_m_2,V_n_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2) % 19.07/19.01 <=> ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2) % 19.07/19.01 | ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_b) % 19.07/19.01 & hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2) ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_map__add__SomeD,axiom, % 19.07/19.01 ! [V_x_2,V_k_2,V_n_2,V_m_2,T_b,T_c] : % 19.07/19.01 ( hAPP(c_Map_Omap__add(T_c,T_b,V_m_2,V_n_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2) % 19.07/19.01 => ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2) % 19.07/19.01 | ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_b) % 19.07/19.01 & hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2) ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_map__add__def,axiom, % 19.07/19.01 ! [V_x_2,V_m2_2,V_m1_2,T_b,T_c] : hAPP(c_Map_Omap__add(T_c,T_b,V_m1_2,V_m2_2),V_x_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_b),T_b,hAPP(V_m1_2,V_x_2),c_Option_Ooption_OSome(T_b)),hAPP(V_m2_2,V_x_2)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_empty__map__add,axiom, % 19.07/19.01 ! [V_m_2,T_c,T_b] : c_Map_Omap__add(T_b,T_c,hAPP(c_COMBK(tc_Option_Ooption(T_c),T_b),c_Option_Ooption_ONone(T_c)),V_m_2) = V_m_2 ). % 19.07/19.01 % 19.07/19.01 fof(fact_map__add__empty,axiom, % 19.07/19.01 ! [V_m_2,T_c,T_b] : c_Map_Omap__add(T_b,T_c,V_m_2,hAPP(c_COMBK(tc_Option_Ooption(T_c),T_b),c_Option_Ooption_ONone(T_c))) = V_m_2 ). % 19.07/19.01 % 19.07/19.01 fof(fact_map__add__None,axiom, % 19.07/19.01 ! [V_k_2,V_n_2,V_m_2,T_b,T_c] : % 19.07/19.01 ( hAPP(c_Map_Omap__add(T_c,T_b,V_m_2,V_n_2),V_k_2) = c_Option_Ooption_ONone(T_b) % 19.07/19.01 <=> ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_b) % 19.07/19.01 & hAPP(V_m_2,V_k_2) = c_Option_Ooption_ONone(T_b) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_map__add__find__right,axiom, % 19.07/19.01 ! [V_m_2,T_c,V_xx_2,T_b,V_k_2,V_n_2] : % 19.07/19.01 ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_xx_2) % 19.07/19.01 => hAPP(c_Map_Omap__add(T_c,T_b,V_m_2,V_n_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_xx_2) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_map__add__assoc,axiom, % 19.07/19.01 ! [V_m3_2,V_m2_2,V_m1_2,T_c,T_b] : c_Map_Omap__add(T_b,T_c,V_m1_2,c_Map_Omap__add(T_b,T_c,V_m2_2,V_m3_2)) = c_Map_Omap__add(T_b,T_c,c_Map_Omap__add(T_b,T_c,V_m1_2,V_m2_2),V_m3_2) ). % 19.07/19.01 % 19.07/19.01 fof(fact_map__add__dom__app__simps_I2_J,axiom, % 19.07/19.01 ! [V_l2_2,V_l1_2,T_c,V_m_2,T_b] : % 19.07/19.01 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_m_2),c_Map_Odom(T_b,T_c,V_l1_2))) % 19.07/19.01 => hAPP(c_Map_Omap__add(T_b,T_c,V_l1_2,V_l2_2),V_m_2) = hAPP(V_l2_2,V_m_2) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_map__add__dom__app__simps_I3_J,axiom, % 19.07/19.01 ! [V_l1_2,V_l2_2,T_c,V_m_2,T_b] : % 19.07/19.01 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_m_2),c_Map_Odom(T_b,T_c,V_l2_2))) % 19.07/19.01 => hAPP(c_Map_Omap__add(T_b,T_c,V_l1_2,V_l2_2),V_m_2) = hAPP(V_l1_2,V_m_2) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_map__add__dom__app__simps_I1_J,axiom, % 19.07/19.01 ! [V_l1_2,V_l2_2,T_c,V_m_2,T_b] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(T_b),V_m_2),c_Map_Odom(T_b,T_c,V_l2_2))) % 19.07/19.01 => hAPP(c_Map_Omap__add(T_b,T_c,V_l1_2,V_l2_2),V_m_2) = hAPP(V_l2_2,V_m_2) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_dom__map__add,axiom, % 19.07/19.01 ! [V_n_2,V_m_2,T_c,T_b] : c_Map_Odom(T_b,T_c,c_Map_Omap__add(T_b,T_c,V_m_2,V_n_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_c,V_n_2)),c_Map_Odom(T_b,T_c,V_m_2)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_map__add__upd,axiom, % 19.07/19.01 ! [V_y_2,V_x_2,V_g_2,V_f_2,T_c,T_b] : c_Map_Omap__add(T_b,T_c,V_f_2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_g_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Omap__add(T_b,T_c,V_f_2,V_g_2)),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_inj__on__map__add__dom,axiom, % 19.07/19.01 ! [V_m_H_2,V_m_2,T_c,T_b] : % 19.07/19.01 ( c_Fun_Oinj__on(T_b,tc_Option_Ooption(T_c),c_Map_Omap__add(T_b,T_c,V_m_2,V_m_H_2),c_Map_Odom(T_b,T_c,V_m_H_2)) % 19.07/19.01 <=> c_Fun_Oinj__on(T_b,tc_Option_Ooption(T_c),V_m_H_2,c_Map_Odom(T_b,T_c,V_m_H_2)) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_map__add__comm,axiom, % 19.07/19.01 ! [V_m2_2,V_m1_2,T_c,T_b] : % 19.07/19.01 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_c,V_m1_2)),c_Map_Odom(T_b,T_c,V_m2_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.01 => c_Map_Omap__add(T_b,T_c,V_m1_2,V_m2_2) = c_Map_Omap__add(T_b,T_c,V_m2_2,V_m1_2) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_finite__range__map__of__map__add,axiom, % 19.07/19.01 ! [V_l_2,V_f_2,T_c,T_b] : % 19.07/19.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_b)),hAPP(c_Set_Oimage(T_c,tc_Option_Ooption(T_b),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) % 19.07/19.01 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_b)),hAPP(c_Set_Oimage(T_c,tc_Option_Ooption(T_b),c_Map_Omap__add(T_c,T_b,V_f_2,c_Map_Omap__of(T_c,T_b,V_l_2))),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_rel__compE,axiom, % 19.07/19.01 ! [V_s_2,V_r_2,T_d,V_xz_2,T_c,T_b] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_xz_2),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_r_2),V_s_2))) % 19.07/19.01 => ~ ! [B_x,B_y,B_z] : % 19.07/19.01 ( V_xz_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_z) % 19.07/19.01 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),B_x),B_y)),V_r_2)) % 19.07/19.01 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_c),B_y),B_z)),V_s_2)) ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_finite__dom__map__of,axiom, % 19.07/19.01 ! [V_l_2,T_c,T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Map_Odom(T_b,T_c,c_Map_Omap__of(T_b,T_c,V_l_2)))) ). % 19.07/19.01 % 19.07/19.01 fof(fact_finite__range__map__of,axiom, % 19.07/19.01 ! [V_xys_2,T_c,T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_b)),hAPP(c_Set_Oimage(T_c,tc_Option_Ooption(T_b),c_Map_Omap__of(T_c,T_b,V_xys_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ). % 19.07/19.01 % 19.07/19.01 fof(fact_map__add__map__of__foldr,axiom, % 19.07/19.01 ! [V_ps_2,V_m_2,T_c,T_b] : c_Map_Omap__add(T_b,T_c,V_m_2,c_Map_Omap__of(T_b,T_c,V_ps_2)) = c_List_Ofoldr(tc_prod(T_b,T_c),tc_fun(T_b,tc_Option_Ooption(T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,tc_Option_Ooption(T_c)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_fun(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,tc_Option_Ooption(T_c))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(T_c),tc_fun(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,tc_Option_Ooption(T_c)))),tc_fun(tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_fun(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,tc_Option_Ooption(T_c))))),T_b),c_COMBB(tc_Option_Ooption(T_c),tc_fun(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,tc_Option_Ooption(T_c))),T_c)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(tc_Option_Ooption(T_c),tc_fun(T_b,tc_Option_Ooption(T_c)))),tc_fun(tc_Option_Ooption(T_c),tc_fun(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,tc_Option_Ooption(T_c)))),T_b),c_COMBC(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_Option_Ooption(T_c),tc_fun(T_b,tc_Option_Ooption(T_c)))),hAPP(c_COMBC(tc_fun(T_b,tc_Option_Ooption(T_c)),T_b,tc_fun(tc_Option_Ooption(T_c),tc_fun(T_b,tc_Option_Ooption(T_c)))),c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)))))),c_Option_Ooption_OSome(T_c))),V_ps_2,V_m_2) ). % 19.07/19.01 % 19.07/19.01 fof(fact_,axiom, % 19.07/19.01 ! [V_y_2,V_x_2,T_b] : c_Smallcheck_Oorelse(T_b,V_x_2,V_y_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_b),T_b,V_y_2,c_Option_Ooption_OSome(T_b)),V_x_2) ). % 19.07/19.01 % 19.07/19.01 fof(fact_full__small__int__def,axiom, % 19.07/19.01 ! [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))) ). % 19.07/19.01 % 19.07/19.01 fof(fact_small_H_Osimps,axiom, % 19.07/19.01 ! [V_f_2,V_i_2,V_d_2] : % 19.07/19.01 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 19.07/19.01 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) ) % 19.07/19.01 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 19.07/19.01 => 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)) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_small_H_Opsimps,axiom, % 19.07/19.01 ! [V_i_2,V_d_2,V_f_2] : % 19.07/19.01 ( 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)))) % 19.07/19.01 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 19.07/19.01 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) ) % 19.07/19.01 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 19.07/19.01 => 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)) ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_small__int__def,axiom, % 19.07/19.01 ! [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))) ). % 19.07/19.01 % 19.07/19.01 fof(fact_small__prod__def,axiom, % 19.07/19.01 ! [V_d_2,V_f_2,T_b,T_c] : % 19.07/19.01 ( ( class_Smallcheck_Osmall(T_c) % 19.07/19.01 & class_Smallcheck_Osmall(T_b) ) % 19.07/19.01 => hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_prod(T_b,T_c)),V_f_2),V_d_2) = hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(T_b),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),T_b),c_Smallcheck_Osmall__class_Osmall(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),T_c),V_f_2)),c_Product__Type_OPair(T_b,T_c)))),V_d_2)),V_d_2) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_small_H_Opinduct,axiom, % 19.07/19.01 ! [V_Pa_2,V_a2_2,V_a1_2,V_a0_2] : % 19.07/19.01 ( 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)))) % 19.07/19.01 => ( ! [B_f,B_d,B_i] : % 19.07/19.01 ( 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)))) % 19.07/19.01 => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_d),B_i)) % 19.07/19.01 => ( hAPP(B_f,B_i) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) % 19.07/19.01 => hBOOL(hAPP(hAPP(hAPP(V_Pa_2,B_f),B_d),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_i),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ) % 19.07/19.01 => hBOOL(hAPP(hAPP(hAPP(V_Pa_2,B_f),B_d),B_i)) ) ) % 19.07/19.01 => hBOOL(hAPP(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2),V_a2_2)) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_body__def,axiom, % 19.07/19.01 c_Com_Obody = c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom,c_Com_Obodies) ). % 19.07/19.01 % 19.07/19.01 fof(fact_map__of__mapk__SomeI,axiom, % 19.07/19.01 ! [V_x_2,V_k_2,V_t_2,T_d,V_f_2,T_c,T_b] : % 19.07/19.01 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 19.07/19.01 => ( hAPP(c_Map_Omap__of(T_b,T_d,V_t_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_d),V_x_2) % 19.07/19.01 => hAPP(c_Map_Omap__of(T_c,T_d,hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_d),tc_prod(T_c,T_d)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_d,tc_prod(T_c,T_d)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_d,tc_prod(T_c,T_d)),T_b),c_Product__Type_OPair(T_c,T_d)),V_f_2))),V_t_2)),hAPP(V_f_2,V_k_2)) = hAPP(c_Option_Ooption_OSome(T_d),V_x_2) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_map__comp__def,axiom, % 19.07/19.01 ! [V_k_2,V_g_2,V_f_2,T_d,T_b,T_c] : c_Map_Omap__comp(T_c,T_b,T_d,V_f_2,V_g_2,V_k_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_b),T_c,c_Option_Ooption_ONone(T_b),V_f_2),hAPP(V_g_2,V_k_2)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_inj__mapI,axiom, % 19.07/19.01 ! [V_f_2,T_c,T_b] : % 19.07/19.01 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 19.07/19.01 => c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_map__comp__simps_I2_J,axiom, % 19.07/19.01 ! [V_m1_2,T_c,T_d,V_k_H_2,T_b,V_k_2,V_m2_2] : % 19.07/19.01 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_k_H_2) % 19.07/19.01 => c_Map_Omap__comp(T_b,T_d,T_c,V_m1_2,V_m2_2,V_k_2) = hAPP(V_m1_2,V_k_H_2) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_map__comp__Some__iff,axiom, % 19.07/19.01 ! [V_v_2,V_k_2,V_m2_2,V_m1_2,T_d,T_b,T_c] : % 19.07/19.01 ( c_Map_Omap__comp(T_c,T_b,T_d,V_m1_2,V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_v_2) % 19.07/19.01 <=> ? [B_k_H] : % 19.07/19.01 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_c),B_k_H) % 19.07/19.01 & hAPP(V_m1_2,B_k_H) = hAPP(c_Option_Ooption_OSome(T_b),V_v_2) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_map__comp__simps_I1_J,axiom, % 19.07/19.01 ! [V_m1_2,T_c,T_d,T_b,V_k_2,V_m2_2] : % 19.07/19.01 ( hAPP(V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_b) % 19.07/19.01 => c_Map_Omap__comp(T_b,T_d,T_c,V_m1_2,V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_d) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_inj__map,axiom, % 19.07/19.01 ! [V_f_2,T_c,T_b] : % 19.07/19.01 ( c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))) % 19.07/19.01 <=> c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_inj__map__eq__map,axiom, % 19.07/19.01 ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] : % 19.07/19.01 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 19.07/19.01 => ( hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2) % 19.07/19.01 <=> V_xs_2 = V_ys_2 ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_inj__mapD,axiom, % 19.07/19.01 ! [V_f_2,T_c,T_b] : % 19.07/19.01 ( c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))) % 19.07/19.01 => c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_map__injective,axiom, % 19.07/19.01 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] : % 19.07/19.01 ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_ys_2) % 19.07/19.01 => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 19.07/19.01 => V_xs_2 = V_ys_2 ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_map__ident,axiom, % 19.07/19.01 ! [V_xs_2,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)),V_xs_2) = V_xs_2 ). % 19.07/19.01 % 19.07/19.01 fof(fact_List_Omap_Oidentity,axiom, % 19.07/19.01 ! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_List_Omap_Oid,axiom, % 19.07/19.01 ! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_Fun_Oid(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_List_Omap_Ocomp,axiom, % 19.07/19.01 ! [V_g_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(tc_List_Olist(T_d),tc_List_Olist(T_c),tc_List_Olist(T_b),hAPP(c_List_Omap(T_d,T_c),V_f_2)),hAPP(c_List_Omap(T_b,T_d),V_g_2)) = hAPP(c_List_Omap(T_b,T_c),hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),V_g_2)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_map__comp__map,axiom, % 19.07/19.01 ! [V_g_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(tc_List_Olist(T_d),tc_List_Olist(T_c),tc_List_Olist(T_b),hAPP(c_List_Omap(T_d,T_c),V_f_2)),hAPP(c_List_Omap(T_b,T_d),V_g_2)) = hAPP(c_List_Omap(T_b,T_c),hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),V_g_2)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_List_Omap_Ocompositionality,axiom, % 19.07/19.01 ! [V_list_2,V_g_2,T_d,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_g_2),V_list_2)) = hAPP(hAPP(c_List_Omap(T_d,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2)),V_list_2) ). % 19.07/19.01 % 19.07/19.01 fof(fact_map__map,axiom, % 19.07/19.01 ! [V_xs_2,V_g_2,T_d,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_g_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_d,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2)),V_xs_2) ). % 19.07/19.01 % 19.07/19.01 fof(fact_foldr__map,axiom, % 19.07/19.01 ! [V_a_2,V_xs_2,V_f_2,T_d,V_g_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_g_2,hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2),V_a_2) = c_List_Ofoldr(T_d,T_b,hAPP(c_Fun_Ocomp(T_c,tc_fun(T_b,T_b),T_d,V_g_2),V_f_2),V_xs_2,V_a_2) ). % 19.07/19.01 % 19.07/19.01 fof(fact_map__comp__empty_I2_J,axiom, % 19.07/19.01 ! [V_x_2,V_m_2,T_d,T_b,T_c] : c_Map_Omap__comp(T_c,T_b,T_d,hAPP(c_COMBK(tc_Option_Ooption(T_b),T_c),c_Option_Ooption_ONone(T_b)),V_m_2,V_x_2) = c_Option_Ooption_ONone(T_b) ). % 19.07/19.01 % 19.07/19.01 fof(fact_map__comp__empty_I1_J,axiom, % 19.07/19.01 ! [V_x_2,V_m_2,T_d,T_b,T_c] : c_Map_Omap__comp(T_c,T_b,T_d,V_m_2,hAPP(c_COMBK(tc_Option_Ooption(T_c),T_d),c_Option_Ooption_ONone(T_c)),V_x_2) = c_Option_Ooption_ONone(T_b) ). % 19.07/19.01 % 19.07/19.01 fof(fact_map__comp__None__iff,axiom, % 19.07/19.01 ! [V_k_2,V_m2_2,V_m1_2,T_d,T_b,T_c] : % 19.07/19.01 ( c_Map_Omap__comp(T_c,T_b,T_d,V_m1_2,V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_b) % 19.07/19.01 <=> ( hAPP(V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_c) % 19.07/19.01 | ? [B_k_H] : % 19.07/19.01 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_c),B_k_H) % 19.07/19.01 & hAPP(V_m1_2,B_k_H) = c_Option_Ooption_ONone(T_b) ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_map__of__map,axiom, % 19.07/19.01 ! [V_xs_2,V_f_2,T_d,T_c,T_b] : c_Map_Omap__of(T_b,T_c,hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_d),tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_d,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,T_c),tc_fun(T_d,tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(tc_fun(T_d,T_c),tc_fun(T_d,tc_prod(T_b,T_c))),T_b),c_COMBB(T_c,tc_prod(T_b,T_c),T_d)),c_Product__Type_OPair(T_b,T_c))),V_f_2))),V_xs_2)) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_d),tc_Option_Ooption(T_c),T_b,hAPP(c_Option_Omap(T_d,T_c),V_f_2)),c_Map_Omap__of(T_b,T_d,V_xs_2)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_map__of__map__keys,axiom, % 19.07/19.01 ! [V_m_2,T_c,V_xs_2,T_b] : % 19.07/19.01 ( hAPP(c_List_Oset(T_b),V_xs_2) = c_Map_Odom(T_b,T_c,V_m_2) % 19.07/19.01 => c_Map_Omap__of(T_b,T_c,hAPP(hAPP(c_List_Omap(T_b,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBS(T_b,T_c,tc_prod(T_b,T_c)),c_Product__Type_OPair(T_b,T_c)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_c),T_c,T_b),c_Option_Othe(T_c)),V_m_2))),V_xs_2)) = V_m_2 ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_finite__set,axiom, % 19.07/19.01 ! [V_xs_2,T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_List_Oset(T_b),V_xs_2))) ). % 19.07/19.01 % 19.07/19.01 fof(fact_set__map,axiom, % 19.07/19.01 ! [V_xs_2,V_f_2,T_c,T_b] : hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_List_Oset(T_c),V_xs_2)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_map__eq__conv,axiom, % 19.07/19.01 ! [V_g_2,V_xs_2,V_f_2,T_b,T_c] : % 19.07/19.01 ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2) % 19.07/19.01 <=> ! [B_x] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2))) % 19.07/19.01 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_option__map__comp,axiom, % 19.07/19.01 ! [V_opt_2,V_g_2,T_d,V_f_2,T_b,T_c] : hAPP(hAPP(c_Option_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_Option_Omap(T_d,T_c),V_g_2),V_opt_2)) = hAPP(hAPP(c_Option_Omap(T_d,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2)),V_opt_2) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Option_Omap_Ocompositionality,axiom, % 19.07/19.01 ! [V_option_2,V_g_2,T_d,V_f_2,T_b,T_c] : hAPP(hAPP(c_Option_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_Option_Omap(T_d,T_c),V_g_2),V_option_2)) = hAPP(hAPP(c_Option_Omap(T_d,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2)),V_option_2) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Option_Omap_Ocomp,axiom, % 19.07/19.01 ! [V_g_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_d),tc_Option_Ooption(T_c),tc_Option_Ooption(T_b),hAPP(c_Option_Omap(T_d,T_c),V_f_2)),hAPP(c_Option_Omap(T_b,T_d),V_g_2)) = hAPP(c_Option_Omap(T_b,T_c),hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),V_g_2)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_option__map__o__sum__case,axiom, % 19.07/19.01 ! [V_h_2,V_g_2,V_f_2,T_c,T_b,T_d,T_e] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_e),tc_Option_Ooption(T_d),tc_sum(T_b,T_c),hAPP(c_Option_Omap(T_e,T_d),V_f_2)),c_Sum__Type_Osum_Osum__case(T_b,tc_Option_Ooption(T_e),T_c,V_g_2,V_h_2)) = c_Sum__Type_Osum_Osum__case(T_b,tc_Option_Ooption(T_d),T_c,hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_e),tc_Option_Ooption(T_d),T_b,hAPP(c_Option_Omap(T_e,T_d),V_f_2)),V_g_2),hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_e),tc_Option_Ooption(T_d),T_c,hAPP(c_Option_Omap(T_e,T_d),V_f_2)),V_h_2)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Option_Omap_Oidentity,axiom, % 19.07/19.01 ! [T_b] : hAPP(c_Option_Omap(T_b,T_b),c_COMBI(T_b)) = c_Fun_Oid(tc_Option_Ooption(T_b)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Option_Omap_Oid,axiom, % 19.07/19.01 ! [T_b] : hAPP(c_Option_Omap(T_b,T_b),c_Fun_Oid(T_b)) = c_Fun_Oid(tc_Option_Ooption(T_b)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_dom__option__map,axiom, % 19.07/19.01 ! [V_m_2,V_f_2,T_d,T_c,T_b] : c_Map_Odom(T_b,T_c,hAPP(hAPP(c_COMBS(T_b,tc_Option_Ooption(T_d),tc_Option_Ooption(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_c),tc_fun(tc_Option_Ooption(T_d),tc_Option_Ooption(T_c)),T_b),c_Option_Omap(T_d,T_c)),V_f_2)),V_m_2)) = c_Map_Odom(T_b,T_d,V_m_2) ). % 19.07/19.01 % 19.07/19.01 fof(fact_infinite__UNIV__listI,axiom, % 19.07/19.01 ! [T_b] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))) ). % 19.07/19.01 % 19.07/19.01 fof(fact_option__map__eq__Some,axiom, % 19.07/19.01 ! [V_y_2,V_xo_2,V_f_2,T_b,T_c] : % 19.07/19.01 ( hAPP(hAPP(c_Option_Omap(T_c,T_b),V_f_2),V_xo_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2) % 19.07/19.01 <=> ? [B_z] : % 19.07/19.01 ( V_xo_2 = hAPP(c_Option_Ooption_OSome(T_c),B_z) % 19.07/19.01 & hAPP(V_f_2,B_z) = V_y_2 ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_option__map__Some,axiom, % 19.07/19.01 ! [V_x_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_Option_Omap(T_c,T_b),V_f_2),hAPP(c_Option_Ooption_OSome(T_c),V_x_2)) = hAPP(c_Option_Ooption_OSome(T_b),hAPP(V_f_2,V_x_2)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_option__map__is__None,axiom, % 19.07/19.01 ! [V_opt_2,V_f_2,T_b,T_c] : % 19.07/19.01 ( hAPP(hAPP(c_Option_Omap(T_c,T_b),V_f_2),V_opt_2) = c_Option_Ooption_ONone(T_b) % 19.07/19.01 <=> V_opt_2 = c_Option_Ooption_ONone(T_c) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_option__map__None,axiom, % 19.07/19.01 ! [V_f_2,T_b,T_c] : hAPP(hAPP(c_Option_Omap(T_c,T_b),V_f_2),c_Option_Ooption_ONone(T_c)) = c_Option_Ooption_ONone(T_b) ). % 19.07/19.01 % 19.07/19.01 fof(fact_option__map__o__empty,axiom, % 19.07/19.01 ! [V_x_2,V_f_2,T_d,T_b,T_c] : hAPP(hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_c),tc_Option_Ooption(T_b),T_d,hAPP(c_Option_Omap(T_c,T_b),V_f_2)),hAPP(c_COMBK(tc_Option_Ooption(T_c),T_d),c_Option_Ooption_ONone(T_c))),V_x_2) = c_Option_Ooption_ONone(T_b) ). % 19.07/19.01 % 19.07/19.01 fof(fact_option__map__o__map__upd,axiom, % 19.07/19.01 ! [V_b_2,V_a_2,V_m_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_d),tc_Option_Ooption(T_c),T_b,hAPP(c_Option_Omap(T_d,T_c),V_f_2)),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_d)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_d),V_b_2))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_d),tc_Option_Ooption(T_c),T_b,hAPP(c_Option_Omap(T_d,T_c),V_f_2)),V_m_2)),V_a_2),hAPP(c_Option_Ooption_OSome(T_c),hAPP(V_f_2,V_b_2))) ). % 19.07/19.01 % 19.07/19.01 fof(fact_map__inj__on,axiom, % 19.07/19.01 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] : % 19.07/19.01 ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_ys_2) % 19.07/19.01 => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_List_Oset(T_c),V_xs_2)),hAPP(c_List_Oset(T_c),V_ys_2))) % 19.07/19.01 => V_xs_2 = V_ys_2 ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_inj__on__map__eq__map,axiom, % 19.07/19.01 ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] : % 19.07/19.01 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_ys_2))) % 19.07/19.01 => ( hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2) % 19.07/19.01 <=> V_xs_2 = V_ys_2 ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_map__fun__upd,axiom, % 19.07/19.01 ! [V_v_2,V_f_2,T_c,V_xs_2,V_y_2,T_b] : % 19.07/19.01 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 19.07/19.01 => hAPP(hAPP(c_List_Omap(T_b,T_c),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_y_2),V_v_2)),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_inj__on__mapI,axiom, % 19.07/19.01 ! [V_A_2,V_f_2,T_c,T_b] : % 19.07/19.01 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),c_List_Oset(T_b)),V_A_2))) % 19.07/19.01 => c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),V_A_2) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_map__of__eq__dom,axiom, % 19.07/19.01 ! [V_ys_2,V_xs_2,T_c,T_b] : % 19.07/19.01 ( c_Map_Omap__of(T_b,T_c,V_xs_2) = c_Map_Omap__of(T_b,T_c,V_ys_2) % 19.07/19.01 => hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_b,c_Product__Type_Ofst(T_b,T_c)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_xs_2)) = hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_b,c_Product__Type_Ofst(T_b,T_c)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_ys_2)) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_map__of__is__SomeD,axiom, % 19.07/19.01 ! [V_y_2,V_x_2,V_xys_2,T_b,T_c] : % 19.07/19.01 ( hAPP(c_Map_Omap__of(T_c,T_b,V_xys_2),V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2) % 19.07/19.01 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_c,T_b)),V_xys_2))) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_map__of__SomeD,axiom, % 19.07/19.01 ! [V_y_2,V_k_2,V_xs_2,T_b,T_c] : % 19.07/19.01 ( hAPP(c_Map_Omap__of(T_c,T_b,V_xs_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2) % 19.07/19.01 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_k_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_c,T_b)),V_xs_2))) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_dom__map__of__conv__image__fst,axiom, % 19.07/19.01 ! [V_xys_2,T_c,T_b] : c_Map_Odom(T_b,T_c,c_Map_Omap__of(T_b,T_c,V_xys_2)) = hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_b,c_Product__Type_Ofst(T_b,T_c)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_xys_2)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_map__of__eq__None__iff,axiom, % 19.07/19.01 ! [V_x_2,V_xys_2,T_b,T_c] : % 19.07/19.01 ( hAPP(c_Map_Omap__of(T_c,T_b,V_xys_2),V_x_2) = c_Option_Ooption_ONone(T_b) % 19.07/19.01 <=> ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(tc_prod(T_c,T_b),T_c,c_Product__Type_Ofst(T_c,T_b)),hAPP(c_List_Oset(tc_prod(T_c,T_b)),V_xys_2)))) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Option_Omap__def,axiom, % 19.07/19.01 ! [V_f_2,T_c,T_b] : hAPP(c_Option_Omap(T_b,T_c),V_f_2) = c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_c),T_b,c_Option_Ooption_ONone(T_c),hAPP(hAPP(c_COMBB(T_c,tc_Option_Ooption(T_c),T_b),c_Option_Ooption_OSome(T_c)),V_f_2)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_WT__bodies__def,axiom, % 19.07/19.01 ( c_Com_OWT__bodies % 19.07/19.01 <=> ! [B_x] : % 19.07/19.01 ( 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))) % 19.07/19.01 => 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)) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_map__of__map__restrict,axiom, % 19.07/19.01 ! [V_ks_2,V_f_2,T_c,T_b] : c_Map_Omap__of(T_b,T_c,hAPP(hAPP(c_List_Omap(T_b,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBS(T_b,T_c,tc_prod(T_b,T_c)),c_Product__Type_OPair(T_b,T_c)),V_f_2)),V_ks_2)) = c_Map_Orestrict__map(T_b,T_c,hAPP(c_Fun_Ocomp(T_c,tc_Option_Ooption(T_c),T_b,c_Option_Ooption_OSome(T_c)),V_f_2),hAPP(c_List_Oset(T_b),V_ks_2)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_ran__distinct,axiom, % 19.07/19.01 ! [V_al_2,T_c,T_b] : % 19.07/19.01 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_al_2))) % 19.07/19.01 => c_Map_Oran(T_b,T_c,c_Map_Omap__of(T_b,T_c,V_al_2)) = hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_c,c_Product__Type_Osnd(T_b,T_c)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_al_2)) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_set__map__of__compr,axiom, % 19.07/19.01 ! [V_xs_2,T_c,T_b] : % 19.07/19.01 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_xs_2))) % 19.07/19.01 => hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_xs_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(T_c),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_Option_Ooption(T_c),tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_c),tc_fun(tc_Option_Ooption(T_c),tc_HOL_Obool),T_b),c_fequal),c_Map_Omap__of(T_b,T_c,V_xs_2)))),c_Option_Ooption_OSome(T_c)))) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_distinct__map,axiom, % 19.07/19.01 ! [V_xs_2,V_f_2,T_c,T_b] : % 19.07/19.01 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) % 19.07/19.01 <=> ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2)) % 19.07/19.01 & c_Fun_Oinj__on(T_c,T_b,V_f_2,hAPP(c_List_Oset(T_c),V_xs_2)) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_map__of__inject__set,axiom, % 19.07/19.01 ! [V_ys_2,V_xs_2,T_c,T_b] : % 19.07/19.01 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_xs_2))) % 19.07/19.01 => ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_ys_2))) % 19.07/19.01 => ( c_Map_Omap__of(T_b,T_c,V_xs_2) = c_Map_Omap__of(T_b,T_c,V_ys_2) % 19.07/19.01 <=> hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_xs_2) = hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_ys_2) ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Some__eq__map__of__iff,axiom, % 19.07/19.01 ! [V_x_2,V_y_2,V_xys_2,T_c,T_b] : % 19.07/19.01 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_xys_2))) % 19.07/19.01 => ( hAPP(c_Option_Ooption_OSome(T_c),V_y_2) = hAPP(c_Map_Omap__of(T_b,T_c,V_xys_2),V_x_2) % 19.07/19.01 <=> 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(c_List_Oset(tc_prod(T_b,T_c)),V_xys_2))) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_map__of__eq__Some__iff,axiom, % 19.07/19.01 ! [V_y_2,V_x_2,V_xys_2,T_c,T_b] : % 19.07/19.01 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_xys_2))) % 19.07/19.01 => ( hAPP(c_Map_Omap__of(T_b,T_c,V_xys_2),V_x_2) = hAPP(c_Option_Ooption_OSome(T_c),V_y_2) % 19.07/19.01 <=> 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(c_List_Oset(tc_prod(T_b,T_c)),V_xys_2))) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_map__of__is__SomeI,axiom, % 19.07/19.01 ! [V_y_2,V_x_2,V_xys_2,T_c,T_b] : % 19.07/19.01 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_xys_2))) % 19.07/19.01 => ( 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(c_List_Oset(tc_prod(T_b,T_c)),V_xys_2))) % 19.07/19.01 => hAPP(c_Map_Omap__of(T_b,T_c,V_xys_2),V_x_2) = hAPP(c_Option_Ooption_OSome(T_c),V_y_2) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_greaterThanLessThan__upto,axiom, % 19.07/19.01 ! [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)))) ). % 19.07/19.01 % 19.07/19.01 fof(fact_weak__map__of__SomeI,axiom, % 19.07/19.01 ! [V_l_2,V_x_2,V_k_2,T_c,T_b] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_k_2),V_x_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_l_2))) % 19.07/19.01 => ? [B_x] : hAPP(c_Map_Omap__of(T_b,T_c,V_l_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_c),B_x) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_set__upto,axiom, % 19.07/19.01 ! [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) ). % 19.07/19.01 % 19.07/19.01 fof(fact_atLeastAtMost__upto,axiom, % 19.07/19.01 ! [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)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_distinct__upto,axiom, % 19.07/19.01 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(V_i,V_j))) ). % 19.07/19.01 % 19.07/19.01 fof(fact_atLeastLessThan__upto,axiom, % 19.07/19.01 ! [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)))) ). % 19.07/19.01 % 19.07/19.01 fof(fact_greaterThanAtMost__upto,axiom, % 19.07/19.01 ! [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)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_nat__list__def,axiom, % 19.07/19.01 ! [V_l_2] : % 19.07/19.01 ( c_List_Onat__list(V_l_2) % 19.07/19.01 <=> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),V_l_2)) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_set__remove1__eq,axiom, % 19.07/19.01 ! [V_x_2,V_xs_2,T_b] : % 19.07/19.01 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 19.07/19.01 => hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_x_2,V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_remove1__idem,axiom, % 19.07/19.01 ! [V_xs_2,V_x_2,T_b] : % 19.07/19.01 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 19.07/19.01 => c_List_Oremove1(T_b,V_x_2,V_xs_2) = V_xs_2 ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_notin__set__remove1,axiom, % 19.07/19.01 ! [V_y_2,V_xs_2,V_x_2,T_b] : % 19.07/19.01 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 19.07/19.01 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_y_2,V_xs_2)))) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_in__set__remove1,axiom, % 19.07/19.01 ! [V_xs_2,T_b,V_b_2,V_a_2] : % 19.07/19.01 ( V_a_2 != V_b_2 % 19.07/19.01 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_b_2,V_xs_2)))) % 19.07/19.01 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_set__remove1__subset,axiom, % 19.07/19.01 ! [V_xs_2,V_x_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_x_2,V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ). % 19.07/19.01 % 19.07/19.01 fof(fact_remove1__commute,axiom, % 19.07/19.01 ! [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)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_distinct__remove1,axiom, % 19.07/19.01 ! [V_x,V_xs,T_a] : % 19.07/19.01 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 19.07/19.01 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremove1(T_a,V_x,V_xs))) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_sorted__list__of__set__remove,axiom, % 19.07/19.01 ! [V_x_2,V_A_2,T_b] : % 19.07/19.01 ( class_Orderings_Olinorder(T_b) % 19.07/19.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.01 => c_List_Olinorder__class_Osorted__list__of__set(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = c_List_Oremove1(T_b,V_x_2,c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_map__of__zip__map,axiom, % 19.07/19.01 ! [V_f_2,T_c,V_xs_2,V_x_2,T_b] : % 19.07/19.01 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 19.07/19.01 => hAPP(c_Map_Omap__of(T_b,T_c,hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))),V_x_2) = hAPP(c_Option_Ooption_OSome(T_c),hAPP(V_f_2,V_x_2)) ) % 19.07/19.01 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 19.07/19.01 => hAPP(c_Map_Omap__of(T_b,T_c,hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))),V_x_2) = c_Option_Ooption_ONone(T_c) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_distinct__zipI1,axiom, % 19.07/19.01 ! [V_ys,T_b,V_xs,T_a] : % 19.07/19.01 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 19.07/19.01 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys))) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_distinct__zipI2,axiom, % 19.07/19.01 ! [V_xs,T_b,V_ys,T_a] : % 19.07/19.01 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys)) % 19.07/19.01 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_b,T_a)),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs),V_ys))) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_zip__same__conv__map,axiom, % 19.07/19.01 ! [V_xs_2,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,tc_prod(T_b,T_b)),hAPP(hAPP(c_COMBS(T_b,T_b,tc_prod(T_b,T_b)),c_Product__Type_OPair(T_b,T_b)),c_COMBI(T_b))),V_xs_2) ). % 19.07/19.01 % 19.07/19.01 fof(fact_zip__map__fst__snd,axiom, % 19.07/19.01 ! [V_zs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_zs_2)),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_c),c_Product__Type_Osnd(T_b,T_c)),V_zs_2)) = V_zs_2 ). % 19.07/19.01 % 19.07/19.01 fof(fact_map__zip__map,axiom, % 19.07/19.01 ! [V_ys_2,V_xs_2,V_g_2,T_e,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_d),T_b),V_f_2),hAPP(hAPP(c_List_Ozip(T_c,T_d),hAPP(hAPP(c_List_Omap(T_e,T_c),V_g_2),V_xs_2)),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_e,T_d),T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_e,T_d,T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,T_b),T_e),hAPP(c_COMBB(tc_prod(T_c,T_d),T_b,T_d),V_f_2)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_d,tc_prod(T_c,T_d)),T_e),c_Product__Type_OPair(T_c,T_d)),V_g_2)))),hAPP(hAPP(c_List_Ozip(T_e,T_d),V_xs_2),V_ys_2)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_map__zip__map2,axiom, % 19.07/19.01 ! [V_ys_2,V_g_2,T_e,V_xs_2,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_d),T_b),V_f_2),hAPP(hAPP(c_List_Ozip(T_c,T_d),V_xs_2),hAPP(hAPP(c_List_Omap(T_e,T_d),V_g_2),V_ys_2))) = hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_e),T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_e,T_b),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_prod(T_c,T_d)),tc_fun(T_e,T_b),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),T_b,T_e),V_f_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_e,T_d),tc_fun(T_e,tc_prod(T_c,T_d))),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(tc_fun(T_e,T_d),tc_fun(T_e,tc_prod(T_c,T_d))),T_c),c_COMBB(T_d,tc_prod(T_c,T_d),T_e)),c_Product__Type_OPair(T_c,T_d))),V_g_2)))),hAPP(hAPP(c_List_Ozip(T_c,T_e),V_xs_2),V_ys_2)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_zip__same,axiom, % 19.07/19.01 ! [V_xs_2,V_b_2,V_a_2,T_b] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),hAPP(c_List_Oset(tc_prod(T_b,T_b)),hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_xs_2)))) % 19.07/19.01 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 19.07/19.01 & V_a_2 = V_b_2 ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_set__zip__leftD,axiom, % 19.07/19.01 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] : % 19.07/19.01 ( 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(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)))) % 19.07/19.01 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_set__zip__rightD,axiom, % 19.07/19.01 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] : % 19.07/19.01 ( 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(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)))) % 19.07/19.01 => hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_in__set__zipE,axiom, % 19.07/19.01 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] : % 19.07/19.01 ( 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(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)))) % 19.07/19.01 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 19.07/19.01 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_zip__map__map,axiom, % 19.07/19.01 ! [V_ys_2,V_g_2,T_e,V_xs_2,V_f_2,T_d,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Omap(T_d,T_b),V_f_2),V_xs_2)),hAPP(hAPP(c_List_Omap(T_e,T_c),V_g_2),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_d,T_e),tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_e,T_c),tc_fun(T_e,tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(tc_fun(T_e,T_c),tc_fun(T_e,tc_prod(T_b,T_c))),T_d),c_COMBB(T_c,tc_prod(T_b,T_c),T_e)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),T_d),c_Product__Type_OPair(T_b,T_c)),V_f_2))),V_g_2))),hAPP(hAPP(c_List_Ozip(T_d,T_e),V_xs_2),V_ys_2)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_zip__map1,axiom, % 19.07/19.01 ! [V_ys_2,V_xs_2,V_f_2,T_d,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Omap(T_d,T_b),V_f_2),V_xs_2)),V_ys_2) = hAPP(hAPP(c_List_Omap(tc_prod(T_d,T_c),tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_c,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),T_d),c_Product__Type_OPair(T_b,T_c)),V_f_2))),hAPP(hAPP(c_List_Ozip(T_d,T_c),V_xs_2),V_ys_2)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_zip__map2,axiom, % 19.07/19.01 ! [V_ys_2,V_f_2,T_d,V_xs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_d),tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_d,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,T_c),tc_fun(T_d,tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(tc_fun(T_d,T_c),tc_fun(T_d,tc_prod(T_b,T_c))),T_b),c_COMBB(T_c,tc_prod(T_b,T_c),T_d)),c_Product__Type_OPair(T_b,T_c))),V_f_2))),hAPP(hAPP(c_List_Ozip(T_b,T_d),V_xs_2),V_ys_2)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_sorted__list__of__set__insert,axiom, % 19.07/19.01 ! [V_x_2,V_A_2,T_b] : % 19.07/19.01 ( class_Orderings_Olinorder(T_b) % 19.07/19.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.01 => c_List_Olinorder__class_Osorted__list__of__set(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),c_List_Olinorder__class_Osorted__list__of__set(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_map__of__zip__upd,axiom, % 19.07/19.01 ! [V_z_2,V_y_2,V_x_2,V_zs_2,V_xs_2,T_c,V_ys_2,T_b] : % 19.07/19.01 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2) % 19.07/19.01 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_zs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2) % 19.07/19.01 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2))) % 19.07/19.01 => ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),c_Map_Omap__of(T_c,T_b,hAPP(hAPP(c_List_Ozip(T_c,T_b),V_xs_2),V_ys_2))),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),c_Map_Omap__of(T_c,T_b,hAPP(hAPP(c_List_Ozip(T_c,T_b),V_xs_2),V_zs_2))),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_z_2)) % 19.07/19.01 => c_Map_Omap__of(T_c,T_b,hAPP(hAPP(c_List_Ozip(T_c,T_b),V_xs_2),V_ys_2)) = c_Map_Omap__of(T_c,T_b,hAPP(hAPP(c_List_Ozip(T_c,T_b),V_xs_2),V_zs_2)) ) ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_length__zip,axiom, % 19.07/19.01 ! [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)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_set__insort,axiom, % 19.07/19.01 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] : % 19.07/19.01 ( class_Orderings_Olinorder(T_c) % 19.07/19.01 => hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_insort__left__comm,axiom, % 19.07/19.01 ! [V_xs_2,V_y_2,V_x_2,T_b] : % 19.07/19.01 ( class_Orderings_Olinorder(T_b) % 19.07/19.01 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_y_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2)) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_insort__key__left__comm,axiom, % 19.07/19.01 ! [V_xs_2,T_c,V_y_2,V_x_2,V_f_2,T_b] : % 19.07/19.01 ( class_Orderings_Olinorder(T_b) % 19.07/19.01 => ( hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) % 19.07/19.01 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_y_2),V_xs_2)) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_neq__if__length__neq,axiom, % 19.07/19.01 ! [V_ys,V_xs,T_a] : % 19.07/19.01 ( 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) % 19.07/19.01 => V_xs != V_ys ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_length__insort,axiom, % 19.07/19.01 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] : % 19.07/19.01 ( class_Orderings_Olinorder(T_c) % 19.07/19.01 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2)) = hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_fun__left__comm__insort,axiom, % 19.07/19.01 ! [T_b] : % 19.07/19.01 ( class_Orderings_Olinorder(T_b) % 19.07/19.01 => c_Finite__Set_Ofun__left__comm(T_b,tc_List_Olist(T_b),c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b))) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_lexn__length,axiom, % 19.07/19.01 ! [V_n_2,V_r_2,V_ys_2,V_xs_2,T_b] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),hAPP(c_List_Olexn(T_b,V_r_2),V_n_2))) % 19.07/19.01 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = V_n_2 % 19.07/19.01 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = V_n_2 ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_length__map,axiom, % 19.07/19.01 ! [V_xs_2,V_f_2,T_c,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2) ). % 19.07/19.01 % 19.07/19.01 fof(fact_map__eq__imp__length__eq,axiom, % 19.07/19.01 ! [V_ys_2,V_g_2,T_d,V_xs_2,V_f_2,T_b,T_c] : % 19.07/19.01 ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_d,T_b),V_g_2),V_ys_2) % 19.07/19.01 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_d)),V_ys_2) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_remove1__insort,axiom, % 19.07/19.01 ! [V_xs_2,V_x_2,T_b] : % 19.07/19.01 ( class_Orderings_Olinorder(T_b) % 19.07/19.01 => c_List_Oremove1(T_b,V_x_2,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2)) = V_xs_2 ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_card__length,axiom, % 19.07/19.01 ! [V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ). % 19.07/19.01 % 19.07/19.01 fof(fact_distinct__card,axiom, % 19.07/19.01 ! [V_xs_2,T_b] : % 19.07/19.01 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 19.07/19.01 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_card__distinct,axiom, % 19.07/19.01 ! [V_xs_2,T_b] : % 19.07/19.01 ( hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) % 19.07/19.01 => hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_map__of__zip__inject,axiom, % 19.07/19.01 ! [V_zs_2,V_xs_2,T_c,V_ys_2,T_b] : % 19.07/19.01 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2) % 19.07/19.01 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_zs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2) % 19.07/19.01 => ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2)) % 19.07/19.01 => ( c_Map_Omap__of(T_c,T_b,hAPP(hAPP(c_List_Ozip(T_c,T_b),V_xs_2),V_ys_2)) = c_Map_Omap__of(T_c,T_b,hAPP(hAPP(c_List_Ozip(T_c,T_b),V_xs_2),V_zs_2)) % 19.07/19.01 => V_ys_2 = V_zs_2 ) ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_map__fst__zip,axiom, % 19.07/19.01 ! [V_ys_2,T_c,V_xs_2,T_b] : % 19.07/19.01 ( 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) % 19.07/19.01 => hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) = V_xs_2 ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_map__snd__zip,axiom, % 19.07/19.01 ! [V_ys_2,T_c,V_xs_2,T_b] : % 19.07/19.01 ( 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) % 19.07/19.01 => hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_c),c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) = V_ys_2 ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_distinct__insort,axiom, % 19.07/19.01 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] : % 19.07/19.01 ( class_Orderings_Olinorder(T_c) % 19.07/19.01 => ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2))) % 19.07/19.01 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 19.07/19.01 & hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_length__pos__if__in__set,axiom, % 19.07/19.01 ! [V_xs_2,V_x_2,T_b] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 19.07/19.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_zip__eq__conv,axiom, % 19.07/19.01 ! [V_zs_2,V_ys_2,T_c,V_xs_2,T_b] : % 19.07/19.01 ( 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) % 19.07/19.01 => ( hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2) = V_zs_2 % 19.07/19.01 <=> ( hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_zs_2) = V_xs_2 % 19.07/19.01 & hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_c),c_Product__Type_Osnd(T_b,T_c)),V_zs_2) = V_ys_2 ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_lenlex__conv,axiom, % 19.07/19.01 ! [V_r_2,T_b] : c_List_Olenlex(T_b,V_r_2) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBC(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))))),c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b))))),c_List_Olex(T_b,V_r_2)))))) ). % 19.07/19.01 % 19.07/19.01 fof(fact_lenlex__def,axiom, % 19.07/19.01 ! [V_r_2,T_b] : c_List_Olenlex(T_b,V_r_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(T_b)),tc_List_Olist(T_b)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(T_b),c_Wellfounded_Oless__than,c_List_Olex(T_b,V_r_2))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_prod(tc_Nat_Onat,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(T_b),tc_prod(tc_Nat_Onat,tc_List_Olist(T_b))),tc_List_Olist(T_b)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(T_b))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),c_COMBI(tc_List_Olist(T_b)))) ). % 19.07/19.01 % 19.07/19.01 fof(fact_finite__lists__length__eq,axiom, % 19.07/19.01 ! [V_n_2,V_A_2,T_b] : % 19.07/19.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.01 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),c_List_Oset(T_b))),V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_n_2))))) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_list__eq__iff__zip__eq,axiom, % 19.07/19.01 ! [T_b,V_ys_2,V_xs_2] : % 19.07/19.01 ( V_xs_2 = V_ys_2 % 19.07/19.01 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 19.07/19.01 & ! [B_x] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),hAPP(c_List_Oset(tc_prod(T_b,T_b)),hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_ys_2)))) % 19.07/19.01 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_fequal),B_x)) ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_map__of__zip__is__None,axiom, % 19.07/19.01 ! [V_x_2,V_ys_2,T_c,V_xs_2,T_b] : % 19.07/19.01 ( 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) % 19.07/19.01 => ( hAPP(c_Map_Omap__of(T_b,T_c,hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)),V_x_2) = c_Option_Ooption_ONone(T_c) % 19.07/19.01 <=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_map__of__zip__is__Some,axiom, % 19.07/19.01 ! [V_x_2,V_ys_2,T_c,V_xs_2,T_b] : % 19.07/19.01 ( 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) % 19.07/19.01 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 19.07/19.01 <=> ? [B_y] : hAPP(c_Map_Omap__of(T_b,T_c,hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)),V_x_2) = hAPP(c_Option_Ooption_OSome(T_c),B_y) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_length__remove1,axiom, % 19.07/19.01 ! [V_xs_2,V_x_2,T_b] : % 19.07/19.01 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 19.07/19.01 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremove1(T_b,V_x_2,V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) % 19.07/19.01 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 19.07/19.01 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremove1(T_b,V_x_2,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_dom__map__of__zip,axiom, % 19.07/19.01 ! [V_ys_2,T_c,V_xs_2,T_b] : % 19.07/19.01 ( 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) % 19.07/19.01 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 19.07/19.01 => c_Map_Odom(T_b,T_c,c_Map_Omap__of(T_b,T_c,hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))) = hAPP(c_List_Oset(T_b),V_xs_2) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_finite__lists__length__le,axiom, % 19.07/19.01 ! [V_n_2,V_A_2,T_b] : % 19.07/19.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.01 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),c_List_Oset(T_b))),V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_n_2))))) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Nitpick_Ocard_H__def,axiom, % 19.07/19.01 ! [V_A_2,T_b] : % 19.07/19.01 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.01 => c_Nitpick_Ocard_H(T_b,V_A_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_Hilbert__Choice_OEps(tc_List_Olist(T_b),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_List_Oset(T_b))),V_A_2))),c_List_Odistinct(T_b)))) ) % 19.07/19.01 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.01 => c_Nitpick_Ocard_H(T_b,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_listrel__iff__zip,axiom, % 19.07/19.01 ! [V_r_2,V_ys_2,V_xs_2,T_b] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2))) % 19.07/19.01 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 19.07/19.01 & ! [B_x] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),hAPP(c_List_Oset(tc_prod(T_b,T_b)),hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_ys_2)))) % 19.07/19.01 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2)),B_x)) ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_listrel__rtrancl__refl,axiom, % 19.07/19.01 ! [V_r_2,V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_xs_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)))) ). % 19.07/19.01 % 19.07/19.01 fof(fact_listrel__eq__len,axiom, % 19.07/19.01 ! [V_r_2,V_ys_2,V_xs_2,T_b] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2))) % 19.07/19.01 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_listrel__rtrancl__trans,axiom, % 19.07/19.01 ! [V_zs_2,V_r_2,V_ys_2,V_xs_2,T_b] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)))) % 19.07/19.01 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_ys_2),V_zs_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)))) % 19.07/19.01 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_zs_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)))) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_listrel__mono,axiom, % 19.07/19.01 ! [V_s_2,V_r_2,T_b] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) % 19.07/19.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel(T_b,V_r_2)),c_List_Olistrel(T_b,V_s_2))) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_listrelp__listrel__eq,axiom, % 19.07/19.01 ! [V_xa_2,V_x_2,V_r_2,T_b] : % 19.07/19.01 ( c_List_Olistrelp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2),V_x_2,V_xa_2) % 19.07/19.01 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_xa_2)),c_List_Olistrel(T_b,V_r_2))) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_lexn_Osimps_I2_J,axiom, % 19.07/19.01 ! [V_n_2,V_r_2,T_b] : hAPP(c_List_Olexn(T_b,V_r_2),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(T_b,tc_List_Olist(T_b)),tc_prod(T_b,tc_List_Olist(T_b))),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_Product__Type_Omap__pair(tc_prod(T_b,tc_List_Olist(T_b)),tc_List_Olist(T_b),tc_prod(T_b,tc_List_Olist(T_b)),tc_List_Olist(T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)))),c_Wellfounded_Olex__prod(T_b,tc_List_Olist(T_b),V_r_2,hAPP(c_List_Olexn(T_b,V_r_2),V_n_2)))),hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),hAPP(c_Nat_OSuc,V_n_2))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),hAPP(c_Nat_OSuc,V_n_2)))))) ). % 19.07/19.01 % 19.07/19.01 fof(fact_impossible__Cons,axiom, % 19.07/19.01 ! [V_x,V_ys,V_xs,T_a] : % 19.07/19.01 ( 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))) % 19.07/19.01 => V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_set__ConsD,axiom, % 19.07/19.01 ! [V_xs_2,V_x_2,V_y_2,T_b] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)))) % 19.07/19.01 => ( V_y_2 = V_x_2 % 19.07/19.01 | hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_zip__Cons__Cons,axiom, % 19.07/19.01 ! [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)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_List_Oset_Osimps_I2_J,axiom, % 19.07/19.01 ! [V_xs_2,V_x_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_set__subset__Cons,axiom, % 19.07/19.01 ! [V_x_2,V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)))) ). % 19.07/19.01 % 19.07/19.01 fof(fact_foldr_Osimps_I2_J,axiom, % 19.07/19.01 ! [V_a_2,V_xs_2,V_x_2,V_f_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2),V_a_2) = hAPP(hAPP(V_f_2,V_x_2),c_List_Ofoldr(T_c,T_b,V_f_2,V_xs_2,V_a_2)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_listrelp_OCons,axiom, % 19.07/19.01 ! [V_ys_2,V_xs_2,T_b,V_y_2,V_x_2,V_r_2] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2)) % 19.07/19.01 => ( c_List_Olistrelp(T_b,V_r_2,V_xs_2,V_ys_2) % 19.07/19.01 => c_List_Olistrelp(T_b,V_r_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_listrelp_Oequations_I2_J,axiom, % 19.07/19.01 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_r_2,T_b] : % 19.07/19.01 ( c_List_Olistrelp(T_b,V_r_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a1_2),V_a3_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a2_2),V_a4_2)) % 19.07/19.01 <=> ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) % 19.07/19.01 & c_List_Olistrelp(T_b,V_r_2,V_a3_2,V_a4_2) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_list_Oinject,axiom, % 19.07/19.01 ! [V_list_H_2,V_a_H_2,V_list_2,V_a_2,T_b] : % 19.07/19.01 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_list_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_H_2),V_list_H_2) % 19.07/19.01 <=> ( V_a_2 = V_a_H_2 % 19.07/19.01 & V_list_2 = V_list_H_2 ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_not__Cons__self2,axiom, % 19.07/19.01 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) != V_xs ). % 19.07/19.01 % 19.07/19.01 fof(fact_not__Cons__self,axiom, % 19.07/19.01 ! [V_x,T_a,V_xs] : V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) ). % 19.07/19.01 % 19.07/19.01 fof(fact_map_Osimps_I2_J,axiom, % 19.07/19.01 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_remove1_Osimps_I2_J,axiom, % 19.07/19.01 ! [V_xs,T_a,V_y,V_x] : % 19.07/19.01 ( ( V_x = V_y % 19.07/19.01 => c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = V_xs ) % 19.07/19.01 & ( V_x != V_y % 19.07/19.01 => 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)) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_insort__key_Osimps_I2_J,axiom, % 19.07/19.01 ! [V_ys_2,T_c,V_y_2,V_x_2,V_f_2,T_b] : % 19.07/19.01 ( class_Orderings_Olinorder(T_b) % 19.07/19.01 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) % 19.07/19.01 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) = hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) ) % 19.07/19.01 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) % 19.07/19.01 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) = hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_ys_2)) ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_distinct_Osimps_I2_J,axiom, % 19.07/19.01 ! [V_xs_2,V_x_2,T_b] : % 19.07/19.01 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) % 19.07/19.01 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 19.07/19.01 & hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_map__of__Cons__code_I2_J,axiom, % 19.07/19.01 ! [V_ps,V_v,T_c,T_b,V_k,V_l] : % 19.07/19.01 ( ( V_l = V_k % 19.07/19.01 => 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) ) % 19.07/19.01 & ( V_l != V_k % 19.07/19.01 => 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_Map_Omap__of(T_b,T_c,V_ps),V_k) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_list_Osize_I4_J,axiom, % 19.07/19.01 ! [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))) ). % 19.07/19.01 % 19.07/19.01 fof(fact_listrel_OCons,axiom, % 19.07/19.01 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) % 19.07/19.01 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2))) % 19.07/19.01 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olistrel(T_b,V_r_2))) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_map__of_Osimps_I2_J,axiom, % 19.07/19.01 ! [V_ps_2,V_p_2,T_c,T_b] : c_Map_Omap__of(T_b,T_c,hAPP(hAPP(c_List_Olist_OCons(tc_prod(T_b,T_c)),V_p_2),V_ps_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Omap__of(T_b,T_c,V_ps_2)),hAPP(c_Product__Type_Ofst(T_b,T_c),V_p_2)),hAPP(c_Option_Ooption_OSome(T_c),hAPP(c_Product__Type_Osnd(T_b,T_c),V_p_2))) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Cons__in__lex,axiom, % 19.07/19.01 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olex(T_b,V_r_2))) % 19.07/19.01 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) % 19.07/19.01 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ) % 19.07/19.01 | ( V_x_2 = V_y_2 % 19.07/19.01 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olex(T_b,V_r_2))) ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_listrel__Cons,axiom, % 19.07/19.01 ! [V_xs_2,V_x_2,V_r_2,T_b] : hAPP(c_Relation_OImage(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))) = c_List_Oset__Cons(T_b,hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),V_xs_2),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))))) ). % 19.07/19.01 % 19.07/19.01 fof(fact_set__Cons__def,axiom, % 19.07/19.01 ! [V_XS_2,V_A_2,T_b] : c_List_Oset__Cons(T_b,V_A_2,V_XS_2) = hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(T_b)),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_List_Olist(T_b)),c_COMBS(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),T_b),c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_List_Olist(T_b)),c_COMBB(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_List_Olist(T_b),tc_HOL_Obool,tc_List_Olist(T_b))),c_fequal))),c_List_Olist_OCons(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_b))),V_XS_2)))))) ). % 19.07/19.01 % 19.07/19.01 fof(fact_listrel__Cons2,axiom, % 19.07/19.01 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,T_b] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olistrel(T_b,V_r_2))) % 19.07/19.01 => ~ ! [B_x,B_xs] : % 19.07/19.01 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_xs) % 19.07/19.01 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),V_y_2)),V_r_2)) % 19.07/19.01 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),B_xs),V_ys_2)),c_List_Olistrel(T_b,V_r_2))) ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_listrel__Cons1,axiom, % 19.07/19.01 ! [V_r_2,V_xs_2,V_ys_2,V_y_2,T_b] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)),V_xs_2)),c_List_Olistrel(T_b,V_r_2))) % 19.07/19.01 => ~ ! [B_y,B_ys] : % 19.07/19.01 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_ys) % 19.07/19.01 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),B_y)),V_r_2)) % 19.07/19.01 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_ys_2),B_ys)),c_List_Olistrel(T_b,V_r_2))) ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_length__sublist,axiom, % 19.07/19.01 ! [V_I_2,V_xs_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Osublist(T_b,V_xs_2,V_I_2)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_I_2)))) ). % 19.07/19.01 % 19.07/19.01 fof(fact_pick_Osimps,axiom, % 19.07/19.01 ! [V_xs,V_x,T_a,V_i] : % 19.07/19.01 ( ( 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))) % 19.07/19.01 => 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) ) % 19.07/19.01 & ( ~ 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))) % 19.07/19.01 => 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))) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_distinct__sublistI,axiom, % 19.07/19.01 ! [V_I_2,V_xs_2,T_b] : % 19.07/19.01 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 19.07/19.01 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2))) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_in__set__sublistD,axiom, % 19.07/19.01 ! [V_I_2,V_xs_2,V_x_2,T_b] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2)))) % 19.07/19.01 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_notin__set__sublistI,axiom, % 19.07/19.01 ! [V_I_2,V_xs_2,V_x_2,T_b] : % 19.07/19.01 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 19.07/19.01 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2)))) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_set__sublist__subset,axiom, % 19.07/19.01 ! [V_I_2,V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ). % 19.07/19.01 % 19.07/19.01 fof(fact_select__weight__cons__zero,axiom, % 19.07/19.01 ! [V_xs_2,V_x_2,T_b] : c_Random_Oselect__weight(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_b),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),V_x_2)),V_xs_2)) = c_Random_Oselect__weight(T_b,V_xs_2) ). % 19.07/19.01 % 19.07/19.01 fof(fact_pick__member,axiom, % 19.07/19.01 ! [V_xs_2,T_b,V_i_2] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i_2),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2)))) % 19.07/19.01 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Random_Opick(T_b,V_xs_2),V_i_2)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),T_b),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2)))) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_listsum__simps_I2_J,axiom, % 19.07/19.01 ! [V_xs,V_x,T_a] : % 19.07/19.01 ( class_Groups_Omonoid__add(T_a) % 19.07/19.01 => 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)) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_listsum__subtractf,axiom, % 19.07/19.01 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] : % 19.07/19.01 ( class_Groups_Oab__group__add(T_b) % 19.07/19.01 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),V_g_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2))) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_listsum__const__mult,axiom, % 19.07/19.01 ! [V_xs_2,V_f_2,V_c_2,T_c,T_b] : % 19.07/19.01 ( class_Rings_Osemiring__0(T_b) % 19.07/19.01 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2)),V_f_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_listsum__mult__const,axiom, % 19.07/19.01 ! [V_xs_2,V_c_2,V_f_2,T_c,T_b] : % 19.07/19.01 ( class_Rings_Osemiring__0(T_b) % 19.07/19.01 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2)),V_c_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))),V_c_2) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_listsum__addf,axiom, % 19.07/19.01 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] : % 19.07/19.01 ( class_Groups_Ocomm__monoid__add(T_b) % 19.07/19.01 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Oplus__class_Oplus(T_b)),V_f_2)),V_g_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2))) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_listsum__0,axiom, % 19.07/19.01 ! [V_xs_2,T_c,T_b] : % 19.07/19.01 ( class_Groups_Omonoid__add(T_b) % 19.07/19.01 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_COMBK(T_b,T_c),c_Groups_Ozero__class_Ozero(T_b))),V_xs_2)) = c_Groups_Ozero__class_Ozero(T_b) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_listsum__abs,axiom, % 19.07/19.01 ! [V_xs_2,T_b] : % 19.07/19.01 ( class_Groups_Oordered__ab__group__add__abs(T_b) % 19.07/19.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_b,T_b),c_Groups_Oabs__class_Oabs(T_b)),V_xs_2)))) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_uminus__listsum__map,axiom, % 19.07/19.01 ! [V_xs_2,V_f_2,T_c,T_b] : % 19.07/19.01 ( class_Groups_Oab__group__add(T_b) % 19.07/19.01 => hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,c_Groups_Ouminus__class_Ouminus(T_b)),V_f_2)),V_xs_2)) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_distinct__listsum__conv__Setsum,axiom, % 19.07/19.01 ! [V_xs_2,T_b] : % 19.07/19.01 ( class_Groups_Ocomm__monoid__add(T_b) % 19.07/19.01 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 19.07/19.01 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),V_xs_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_b),c_COMBI(T_b)),hAPP(c_List_Oset(T_b),V_xs_2)) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_select__weight__def,axiom, % 19.07/19.01 ! [V_xs_2,T_b] : c_Random_Oselect__weight(T_b,V_xs_2) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Opick(T_b,V_xs_2))) ). % 19.07/19.01 % 19.07/19.01 fof(fact_listsum__distinct__conv__setsum__set,axiom, % 19.07/19.01 ! [V_f_2,V_xs_2,T_b,T_c] : % 19.07/19.01 ( class_Groups_Ocomm__monoid__add(T_c) % 19.07/19.01 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 19.07/19.01 => hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(c_List_Oset(T_b),V_xs_2)) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_setsum__set__upto__conv__listsum__int,axiom, % 19.07/19.01 ! [V_j_2,V_i_2,V_f_2,T_b] : % 19.07/19.01 ( class_Groups_Ocomm__monoid__add(T_b) % 19.07/19.01 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_f_2),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_i_2,V_j_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(tc_Int_Oint,T_b),V_f_2),c_List_Oupto(V_i_2,V_j_2))) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_interv__listsum__conv__setsum__set__int,axiom, % 19.07/19.01 ! [V_l_2,V_k_2,V_f_2,T_b] : % 19.07/19.01 ( class_Groups_Ocomm__monoid__add(T_b) % 19.07/19.01 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(tc_Int_Oint,T_b),V_f_2),c_List_Oupto(V_k_2,V_l_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_f_2),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_k_2,V_l_2))) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_listsum__triv,axiom, % 19.07/19.01 ! [V_xs_2,V_r_2,T_c,T_b] : % 19.07/19.01 ( class_Rings_Osemiring__1(T_b) % 19.07/19.01 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_COMBK(T_b,T_c),V_r_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2))),V_r_2) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_listsum__map__remove1,axiom, % 19.07/19.01 ! [V_f_2,V_xs_2,V_x_2,T_b,T_c] : % 19.07/19.01 ( class_Groups_Ocomm__monoid__add(T_c) % 19.07/19.01 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 19.07/19.01 => hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_f_2,V_x_2)),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),c_List_Oremove1(T_b,V_x_2,V_xs_2)))) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_select__weight__member,axiom, % 19.07/19.01 ! [V_s_2,V_xs_2,T_b] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2)))) % 19.07/19.01 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Product__Type_Ofst(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect__weight(T_b,V_xs_2),V_s_2))),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),T_b),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2)))) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Nitpick_Osetsum_H__def,axiom, % 19.07/19.01 ! [V_f_2,V_A_2,T_b,T_c] : % 19.07/19.01 ( class_Groups_Ocomm__monoid__add(T_c) % 19.07/19.01 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.01 => c_Nitpick_Osetsum_H(T_b,T_c,V_f_2,V_A_2) = hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Hilbert__Choice_OEps(tc_List_Olist(T_b),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_List_Oset(T_b))),V_A_2))),c_List_Odistinct(T_b))))) ) % 19.07/19.01 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.01 => c_Nitpick_Osetsum_H(T_b,T_c,V_f_2,V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_insort__insert__insort__key,axiom, % 19.07/19.01 ! [V_xs_2,T_c,V_x_2,V_f_2,T_b] : % 19.07/19.01 ( class_Orderings_Olinorder(T_b) % 19.07/19.01 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_List_Oset(T_c),V_xs_2)))) % 19.07/19.01 => c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_listsum__eq__0__nat__iff__nat,axiom, % 19.07/19.01 ! [V_ns_2] : % 19.07/19.01 ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 19.07/19.01 <=> ! [B_x] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) % 19.07/19.01 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_distinct__insort__insert,axiom, % 19.07/19.01 ! [V_x_2,V_f_2,V_xs_2,T_b,T_c] : % 19.07/19.01 ( class_Orderings_Olinorder(T_c) % 19.07/19.01 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 19.07/19.01 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Oinsort__insert__key(T_b,T_c,V_f_2,V_x_2,V_xs_2))) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_insort__insert__triv,axiom, % 19.07/19.01 ! [V_xs_2,V_x_2,T_b] : % 19.07/19.01 ( class_Orderings_Olinorder(T_b) % 19.07/19.01 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 19.07/19.01 => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2) = V_xs_2 ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_set__insort__insert,axiom, % 19.07/19.01 ! [V_xs_2,V_x_2,T_b] : % 19.07/19.01 ( class_Orderings_Olinorder(T_b) % 19.07/19.01 => hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_insort__insert__key__triv,axiom, % 19.07/19.01 ! [V_xs_2,T_c,V_x_2,V_f_2,T_b] : % 19.07/19.01 ( class_Orderings_Olinorder(T_b) % 19.07/19.01 => ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_List_Oset(T_c),V_xs_2)))) % 19.07/19.01 => c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2) = V_xs_2 ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_insort__insert__insort,axiom, % 19.07/19.01 ! [V_xs_2,V_x_2,T_b] : % 19.07/19.01 ( class_Orderings_Olinorder(T_b) % 19.07/19.01 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 19.07/19.01 => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_lexord__cons__cons,axiom, % 19.07/19.01 ! [V_r_2,V_y_2,V_b_2,V_x_2,V_a_2,T_b] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_x_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_b_2),V_y_2))),c_List_Olexord(T_b,V_r_2))) % 19.07/19.01 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) % 19.07/19.01 | ( V_a_2 = V_b_2 % 19.07/19.01 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2))) ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_set__zip,axiom, % 19.07/19.01 ! [V_ys_2,V_xs_2,T_c,T_b] : hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(T_b,T_c)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(T_b,T_c),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(T_b,T_c)),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_prod(T_b,T_c)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(tc_prod(T_b,T_c),tc_fun(tc_Nat_Onat,tc_prod(T_b,T_c)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(T_b,T_c)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(T_b,T_c)),c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_c,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),tc_Nat_Onat),c_Product__Type_OPair(T_b,T_c)),hAPP(c_List_Onth(T_b),V_xs_2))),hAPP(c_List_Onth(T_c),V_ys_2)))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)))))) ). % 19.07/19.01 % 19.07/19.01 fof(fact_nth__zip,axiom, % 19.07/19.01 ! [V_ys,T_b,V_xs,T_a,V_i] : % 19.07/19.01 ( 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))) % 19.07/19.01 => ( 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))) % 19.07/19.01 => 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)) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_nth__map,axiom, % 19.07/19.01 ! [V_f_2,T_c,V_xs_2,T_b,V_n_2] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 19.07/19.01 => hAPP(hAPP(c_List_Onth(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)),V_n_2) = hAPP(V_f_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2)) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_elem__le__listsum__nat,axiom, % 19.07/19.01 ! [V_ns,V_k] : % 19.07/19.01 ( 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))) % 19.07/19.01 => 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))) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_nth__Cons__Suc,axiom, % 19.07/19.01 ! [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) ). % 19.07/19.01 % 19.07/19.01 fof(fact_nth__Cons__0,axiom, % 19.07/19.01 ! [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 ). % 19.07/19.01 % 19.07/19.01 fof(fact_nth_Osimps,axiom, % 19.07/19.01 ! [V_n_2,V_xs_2,V_x_2,T_b] : hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_n_2) = c_Nat_Onat_Onat__case(T_b,V_x_2,hAPP(c_List_Onth(T_b),V_xs_2),V_n_2) ). % 19.07/19.01 % 19.07/19.01 fof(fact_all__set__conv__all__nth,axiom, % 19.07/19.01 ! [V_Pa_2,V_xs_2,T_b] : % 19.07/19.01 ( ! [B_x] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 19.07/19.01 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 19.07/19.01 <=> ! [B_i] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 19.07/19.01 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_list__eq__iff__nth__eq,axiom, % 19.07/19.01 ! [T_b,V_ys_2,V_xs_2] : % 19.07/19.01 ( V_xs_2 = V_ys_2 % 19.07/19.01 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 19.07/19.01 & ! [B_i] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 19.07/19.01 => hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = hAPP(hAPP(c_List_Onth(T_b),V_ys_2),B_i) ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_distinct__conv__nth,axiom, % 19.07/19.01 ! [V_xs_2,T_b] : % 19.07/19.01 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 19.07/19.01 <=> ! [B_i] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 19.07/19.01 => ! [B_j] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 19.07/19.01 => ( B_i != B_j % 19.07/19.01 => hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) != hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_j) ) ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_nth__eq__iff__index__eq,axiom, % 19.07/19.01 ! [V_j_2,V_i_2,V_xs_2,T_b] : % 19.07/19.01 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 19.07/19.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 19.07/19.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 19.07/19.01 => ( hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_j_2) % 19.07/19.01 <=> V_i_2 = V_j_2 ) ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_nth__mem,axiom, % 19.07/19.01 ! [V_xs_2,T_b,V_n_2] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 19.07/19.01 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2)),hAPP(c_List_Oset(T_b),V_xs_2))) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_in__set__conv__nth,axiom, % 19.07/19.01 ! [V_xs_2,V_x_2,T_b] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 19.07/19.01 <=> ? [B_i] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 19.07/19.01 & hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = V_x_2 ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_nth__Cons_H,axiom, % 19.07/19.01 ! [V_xs,V_x,T_a,V_n] : % 19.07/19.01 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 19.07/19.01 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_n) = V_x ) % 19.07/19.01 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 19.07/19.01 => 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))) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_set__conv__nth,axiom, % 19.07/19.01 ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_b),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(T_b),V_xs_2))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))))) ). % 19.07/19.01 % 19.07/19.01 fof(fact_nth__Cons__number__of,axiom, % 19.07/19.01 ! [V_xs,V_x,T_a,V_v] : % 19.07/19.01 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 19.07/19.01 => 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 ) % 19.07/19.01 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 19.07/19.01 => 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))) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_listsum__setsum__nth,axiom, % 19.07/19.01 ! [V_xs_2,T_b] : % 19.07/19.01 ( class_Groups_Ocomm__monoid__add(T_b) % 19.07/19.01 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),V_xs_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(c_List_Onth(T_b),V_xs_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_set__sublist,axiom, % 19.07/19.01 ! [V_I_2,V_xs_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_b),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(T_b),V_xs_2))))),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_I_2))))) ). % 19.07/19.01 % 19.07/19.01 fof(fact_lexord__lex,axiom, % 19.07/19.01 ! [V_r_2,V_y_2,V_x_2,T_b] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olex(T_b,V_r_2))) % 19.07/19.01 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2))) % 19.07/19.01 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_listrel__iff__nth,axiom, % 19.07/19.01 ! [V_r_2,V_ys_2,V_xs_2,T_b] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2))) % 19.07/19.01 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 19.07/19.01 & ! [B_n] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 19.07/19.01 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n)),hAPP(hAPP(c_List_Onth(T_b),V_ys_2),B_n))),V_r_2)) ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_pick__same,axiom, % 19.07/19.01 ! [V_xs_2,T_b,V_l_2] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_l_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 19.07/19.01 => hAPP(c_Random_Opick(T_b,hAPP(hAPP(c_List_Omap(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,T_b)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_b),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),V_xs_2)),hAPP(c_Code__Numeral_Oof__nat,V_l_2)) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_l_2) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_select__def,axiom, % 19.07/19.01 ! [V_xs_2,T_b] : c_Random_Oselect(T_b,V_xs_2) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Onth(T_b),V_xs_2)),c_Code__Numeral_Onat__of))) ). % 19.07/19.01 % 19.07/19.01 fof(fact_lexord__take__index__conv,axiom, % 19.07/19.01 ! [V_r_2,V_y_2,V_x_2,T_b] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2))) % 19.07/19.01 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2))) % 19.07/19.01 & hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2)),V_y_2) = V_x_2 ) % 19.07/19.01 | ? [B_i] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2)))) % 19.07/19.01 & hAPP(hAPP(c_List_Otake(T_b),B_i),V_x_2) = hAPP(hAPP(c_List_Otake(T_b),B_i),V_y_2) % 19.07/19.01 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(hAPP(c_List_Onth(T_b),V_x_2),B_i)),hAPP(hAPP(c_List_Onth(T_b),V_y_2),B_i))),V_r_2)) ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_in__set__takeD,axiom, % 19.07/19.01 ! [V_xs_2,V_n_2,V_x_2,T_b] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2)))) % 19.07/19.01 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_set__take__subset__set__take,axiom, % 19.07/19.01 ! [V_xs_2,T_b,V_n_2,V_m_2] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 19.07/19.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),V_m_2),V_xs_2))),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2)))) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_nth__take,axiom, % 19.07/19.01 ! [V_xs,T_a,V_n,V_i] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n)) % 19.07/19.01 => 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) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_set__take__subset,axiom, % 19.07/19.01 ! [V_xs_2,V_n_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ). % 19.07/19.01 % 19.07/19.01 fof(fact_take__all,axiom, % 19.07/19.01 ! [V_n,V_xs,T_a] : % 19.07/19.01 ( 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)) % 19.07/19.01 => hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs) = V_xs ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_distinct__take,axiom, % 19.07/19.01 ! [V_i,V_xs,T_a] : % 19.07/19.01 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 19.07/19.01 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs))) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_take__take,axiom, % 19.07/19.01 ! [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) ). % 19.07/19.01 % 19.07/19.01 fof(fact_take__zip,axiom, % 19.07/19.01 ! [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)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_length__take,axiom, % 19.07/19.01 ! [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) ). % 19.07/19.01 % 19.07/19.01 fof(fact_take__Suc__Cons,axiom, % 19.07/19.01 ! [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)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_sublist__upt__eq__take,axiom, % 19.07/19.01 ! [V_n_2,V_l_2,T_b] : c_List_Osublist(T_b,V_l_2,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2)) = hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_l_2) ). % 19.07/19.01 % 19.07/19.01 fof(fact_take__map,axiom, % 19.07/19.01 ! [V_xs_2,V_f_2,T_c,V_n_2,T_b] : hAPP(hAPP(c_List_Otake(T_b),V_n_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Otake(T_c),V_n_2),V_xs_2)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_listsum__update__nat,axiom, % 19.07/19.01 ! [V_n,V_ns,V_k] : % 19.07/19.01 ( 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))) % 19.07/19.01 => 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)) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_select__weigth__select,axiom, % 19.07/19.01 ! [T_b,V_xs_2] : % 19.07/19.01 ( V_xs_2 != c_List_Olist_ONil(T_b) % 19.07/19.01 => c_Random_Oselect__weight(T_b,hAPP(hAPP(c_List_Omap(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,T_b)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_b),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),V_xs_2)) = c_Random_Oselect(T_b,V_xs_2) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_listrel__Nil2,axiom, % 19.07/19.01 ! [V_r_2,V_xs_2,T_b] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),c_List_Olist_ONil(T_b))),c_List_Olistrel(T_b,V_r_2))) % 19.07/19.01 => V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_listrel__Nil1,axiom, % 19.07/19.01 ! [V_r_2,V_xs_2,T_b] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xs_2)),c_List_Olistrel(T_b,V_r_2))) % 19.07/19.01 => V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_nth__list__update__neq,axiom, % 19.07/19.01 ! [V_x,V_xs,T_a,V_j,V_i] : % 19.07/19.01 ( V_i != V_j % 19.07/19.01 => 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) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_list__update__id,axiom, % 19.07/19.01 ! [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 ). % 19.07/19.01 % 19.07/19.01 fof(fact_list__update__beyond,axiom, % 19.07/19.01 ! [V_x,V_i,V_xs,T_a] : % 19.07/19.01 ( 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)) % 19.07/19.01 => hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x) = V_xs ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_take__Nil,axiom, % 19.07/19.01 ! [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) ). % 19.07/19.01 % 19.07/19.01 fof(fact_take__eq__Nil,axiom, % 19.07/19.01 ! [V_xs_2,V_n_2,T_b] : % 19.07/19.01 ( hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2) = c_List_Olist_ONil(T_b) % 19.07/19.01 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 19.07/19.01 | V_xs_2 = c_List_Olist_ONil(T_b) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_take__0,axiom, % 19.07/19.01 ! [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) ). % 19.07/19.01 % 19.07/19.01 fof(fact_list_Osize_I3_J,axiom, % 19.07/19.01 ! [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) ). % 19.07/19.01 % 19.07/19.01 fof(fact_length__0__conv,axiom, % 19.07/19.01 ! [V_xs_2,T_b] : % 19.07/19.01 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 19.07/19.01 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_length__list__update,axiom, % 19.07/19.01 ! [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) ). % 19.07/19.01 % 19.07/19.01 fof(fact_take__Cons,axiom, % 19.07/19.01 ! [V_xs_2,V_x_2,V_n_2,T_b] : hAPP(hAPP(c_List_Otake(T_b),V_n_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_Nat_Onat_Onat__case(tc_List_Olist(T_b),c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_Nat_Onat),hAPP(c_List_Olist_OCons(T_b),V_x_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Otake(T_b)),V_xs_2)),V_n_2) ). % 19.07/19.01 % 19.07/19.01 fof(fact_map__is__Nil__conv,axiom, % 19.07/19.01 ! [V_xs_2,V_f_2,T_b,T_c] : % 19.07/19.01 ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = c_List_Olist_ONil(T_b) % 19.07/19.01 <=> V_xs_2 = c_List_Olist_ONil(T_c) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_map__update,axiom, % 19.07/19.01 ! [V_y_2,V_k_2,V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Olist__update(T_c,V_xs_2),V_k_2),V_y_2)) = hAPP(hAPP(c_List_Olist__update(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)),V_k_2),hAPP(V_f_2,V_y_2)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_map_Osimps_I1_J,axiom, % 19.07/19.01 ! [V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Olist_ONil(T_c)) = c_List_Olist_ONil(T_b) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Nil__is__map__conv,axiom, % 19.07/19.01 ! [V_xs_2,V_f_2,T_c,T_b] : % 19.07/19.01 ( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) % 19.07/19.01 <=> V_xs_2 = c_List_Olist_ONil(T_c) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_zip__update,axiom, % 19.07/19.01 ! [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)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_update__zip,axiom, % 19.07/19.01 ! [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))) ). % 19.07/19.01 % 19.07/19.01 fof(fact_sublist__nil,axiom, % 19.07/19.01 ! [V_A_2,T_b] : c_List_Osublist(T_b,c_List_Olist_ONil(T_b),V_A_2) = c_List_Olist_ONil(T_b) ). % 19.07/19.01 % 19.07/19.01 fof(fact_sublist__empty,axiom, % 19.07/19.01 ! [V_xs_2,T_b] : c_List_Osublist(T_b,V_xs_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = c_List_Olist_ONil(T_b) ). % 19.07/19.01 % 19.07/19.01 fof(fact_insort__key_Osimps_I1_J,axiom, % 19.07/19.01 ! [V_x_2,V_f_2,T_b,T_c] : % 19.07/19.01 ( class_Orderings_Olinorder(T_c) % 19.07/19.01 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),c_List_Olist_ONil(T_b)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_list__update__code_I3_J,axiom, % 19.07/19.01 ! [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)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_list_Osimps_I2_J,axiom, % 19.07/19.01 ! [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) ). % 19.07/19.01 % 19.07/19.01 fof(fact_list_Osimps_I3_J,axiom, % 19.07/19.01 ! [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) ). % 19.07/19.01 % 19.07/19.01 fof(fact_list__update__code_I2_J,axiom, % 19.07/19.01 ! [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) ). % 19.07/19.01 % 19.07/19.01 fof(fact_list__update_Osimps_I2_J,axiom, % 19.07/19.01 ! [V_v_2,V_i_2,V_xs_2,V_x_2,T_b] : hAPP(hAPP(c_List_Olist__update(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_i_2),V_v_2) = c_Nat_Onat_Onat__case(tc_List_Olist(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_v_2),V_xs_2),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_Nat_Onat),hAPP(c_List_Olist_OCons(T_b),V_x_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,T_b,tc_List_Olist(T_b)),c_List_Olist__update(T_b,V_xs_2)),V_v_2)),V_i_2) ). % 19.07/19.01 % 19.07/19.01 fof(fact_sorted__list__of__set__empty,axiom, % 19.07/19.01 ! [T_b] : % 19.07/19.01 ( class_Orderings_Olinorder(T_b) % 19.07/19.01 => c_List_Olinorder__class_Osorted__list__of__set(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_List_Olist_ONil(T_b) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_zip__Nil,axiom, % 19.07/19.01 ! [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)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_zip_Osimps_I1_J,axiom, % 19.07/19.01 ! [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)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_upto__empty,axiom, % 19.07/19.01 ! [V_i,V_j] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j),V_i)) % 19.07/19.01 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_foldr_Osimps_I1_J,axiom, % 19.07/19.01 ! [V_a_2,V_f_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_f_2,c_List_Olist_ONil(T_c),V_a_2) = V_a_2 ). % 19.07/19.01 % 19.07/19.01 fof(fact_map__of__Cons__code_I1_J,axiom, % 19.07/19.01 ! [V_k,T_a,T_b] : 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) ). % 19.07/19.01 % 19.07/19.01 fof(fact_map__of_Osimps_I1_J,axiom, % 19.07/19.01 ! [V_x_1,T_b,T_a] : 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) ). % 19.07/19.01 % 19.07/19.01 fof(fact_list__update__swap,axiom, % 19.07/19.01 ! [V_x_H,V_x,V_xs,T_a,V_i_H,V_i] : % 19.07/19.01 ( V_i != V_i_H % 19.07/19.01 => 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) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_list__update__overwrite,axiom, % 19.07/19.01 ! [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) ). % 19.07/19.01 % 19.07/19.01 fof(fact_list__update__code_I1_J,axiom, % 19.07/19.01 ! [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) ). % 19.07/19.01 % 19.07/19.01 fof(fact_list__update_Osimps_I1_J,axiom, % 19.07/19.01 ! [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) ). % 19.07/19.01 % 19.07/19.01 fof(fact_list__update__nonempty,axiom, % 19.07/19.01 ! [V_x_2,V_k_2,V_xs_2,T_b] : % 19.07/19.01 ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_k_2),V_x_2) = c_List_Olist_ONil(T_b) % 19.07/19.01 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_remove1_Osimps_I1_J,axiom, % 19.07/19.01 ! [V_x,T_a] : c_List_Oremove1(T_a,V_x,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 19.07/19.01 % 19.07/19.01 fof(fact_distinct_Osimps_I1_J,axiom, % 19.07/19.01 ! [T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olist_ONil(T_a))) ). % 19.07/19.01 % 19.07/19.01 fof(fact_insort__not__Nil,axiom, % 19.07/19.01 ! [V_xs_2,V_a_2,V_f_2,T_b,T_c] : % 19.07/19.01 ( class_Orderings_Olinorder(T_c) % 19.07/19.01 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_a_2),V_xs_2) != c_List_Olist_ONil(T_b) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_listrelp_Oequations_I1_J,axiom, % 19.07/19.01 ! [V_r_2,T_b] : c_List_Olistrelp(T_b,V_r_2,c_List_Olist_ONil(T_b),c_List_Olist_ONil(T_b)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_listrelp_ONil,axiom, % 19.07/19.01 ! [V_r_2,T_b] : c_List_Olistrelp(T_b,V_r_2,c_List_Olist_ONil(T_b),c_List_Olist_ONil(T_b)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_set__empty,axiom, % 19.07/19.01 ! [V_xs_2,T_b] : % 19.07/19.01 ( hAPP(c_List_Oset(T_b),V_xs_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 19.07/19.01 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_set__empty2,axiom, % 19.07/19.01 ! [V_xs_2,T_b] : % 19.07/19.01 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_List_Oset(T_b),V_xs_2) % 19.07/19.01 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_List_Oset_Osimps_I1_J,axiom, % 19.07/19.01 ! [T_b] : hAPP(c_List_Oset(T_b),c_List_Olist_ONil(T_b)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_listsum__simps_I1_J,axiom, % 19.07/19.01 ! [T_a] : % 19.07/19.01 ( class_Groups_Omonoid__add(T_a) % 19.07/19.01 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_length__greater__0__conv,axiom, % 19.07/19.01 ! [V_xs_2,T_b] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 19.07/19.01 <=> V_xs_2 != c_List_Olist_ONil(T_b) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_set__update__subsetI,axiom, % 19.07/19.01 ! [V_i_2,V_x_2,V_A_2,V_xs_2,T_b] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),V_A_2)) % 19.07/19.01 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/19.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2))),V_A_2)) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_take__1__Cons,axiom, % 19.07/19.01 ! [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)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_set__update__subset__insert,axiom, % 19.07/19.01 ! [V_x_2,V_i_2,V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2))),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))) ). % 19.07/19.01 % 19.07/19.01 fof(fact_nth__list__update__eq,axiom, % 19.07/19.01 ! [V_x,V_xs,T_a,V_i] : % 19.07/19.01 ( 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))) % 19.07/19.01 => 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 ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_list__update__same__conv,axiom, % 19.07/19.01 ! [V_x_2,V_xs_2,T_b,V_i_2] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 19.07/19.01 => ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2) = V_xs_2 % 19.07/19.01 <=> hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2) = V_x_2 ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_nth__list__update,axiom, % 19.07/19.01 ! [V_x,V_j,V_xs,T_a,V_i] : % 19.07/19.01 ( 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))) % 19.07/19.01 => ( ( V_i = V_j % 19.07/19.01 => 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 ) % 19.07/19.01 & ( V_i != V_j % 19.07/19.01 => 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) ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_listrel_ONil,axiom, % 19.07/19.01 ! [V_r_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_List_Olist_ONil(T_b))),c_List_Olistrel(T_b,V_r_2))) ). % 19.07/19.01 % 19.07/19.01 fof(fact_lexord__Nil__right,axiom, % 19.07/19.01 ! [V_r_2,V_x_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),c_List_Olist_ONil(T_b))),c_List_Olexord(T_b,V_r_2))) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Nil__notin__lex,axiom, % 19.07/19.01 ! [V_r_2,V_ys_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_ys_2)),c_List_Olex(T_b,V_r_2))) ). % 19.07/19.01 % 19.07/19.01 fof(fact_Nil2__notin__lex,axiom, % 19.07/19.01 ! [V_r_2,V_xs_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),c_List_Olist_ONil(T_b))),c_List_Olex(T_b,V_r_2))) ). % 19.07/19.01 % 19.07/19.01 fof(fact_set__update__memI,axiom, % 19.07/19.01 ! [V_x_2,V_xs_2,T_b,V_n_2] : % 19.07/19.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 19.07/19.01 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_n_2),V_x_2)))) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_upto_Osimps,axiom, % 19.07/19.01 ! [V_j,V_i] : % 19.07/19.01 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 19.07/19.01 => 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)) ) % 19.07/19.01 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 19.07/19.01 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_sublist__singleton,axiom, % 19.07/19.01 ! [V_x_2,T_b,V_A_2] : % 19.07/19.01 ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)) % 19.07/19.01 => c_List_Osublist(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)),V_A_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) % 19.07/19.01 & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)) % 19.07/19.01 => c_List_Osublist(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)),V_A_2) = c_List_Olist_ONil(T_b) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_take__Cons_H,axiom, % 19.07/19.01 ! [V_xs,V_x,T_a,V_n] : % 19.07/19.01 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 19.07/19.01 => 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) ) % 19.07/19.01 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 19.07/19.01 => 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)) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_upto__rec__number__of,axiom, % 19.07/19.01 ! [V_n,V_m] : % 19.07/19.01 ( ( 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))) % 19.07/19.01 => 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))) ) % 19.07/19.01 & ( ~ 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))) % 19.07/19.01 => 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) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_select,axiom, % 19.07/19.01 ! [V_s_2,T_b,V_xs_2] : % 19.07/19.01 ( V_xs_2 != c_List_Olist_ONil(T_b) % 19.07/19.01 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Product__Type_Ofst(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect(T_b,V_xs_2),V_s_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_listrel__Nil,axiom, % 19.07/19.01 ! [V_r_2,T_b] : hAPP(c_Relation_OImage(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))) ). % 19.07/19.01 % 19.07/19.01 fof(fact_set__Cons__sing__Nil,axiom, % 19.07/19.01 ! [V_A_2,T_b] : c_List_Oset__Cons(T_b,V_A_2,hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))) = hAPP(c_Set_Oimage(T_b,tc_List_Olist(T_b),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))),V_A_2) ). % 19.07/19.01 % 19.07/19.01 fof(fact_take__Cons__number__of,axiom, % 19.07/19.01 ! [V_xs,V_x,T_a,V_v] : % 19.07/19.01 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 19.07/19.01 => 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) ) % 19.07/19.01 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 19.07/19.01 => 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)) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_distinct__list__update,axiom, % 19.07/19.01 ! [V_i_2,V_a_2,V_xs_2,T_b] : % 19.07/19.01 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 19.07/19.01 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) % 19.07/19.01 => hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_a_2))) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_upto_Opsimps,axiom, % 19.07/19.01 ! [V_j_2,V_i_2] : % 19.07/19.01 ( 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))) % 19.07/19.01 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2)) % 19.07/19.01 => 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)) ) % 19.07/19.01 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2)) % 19.07/19.01 => c_List_Oupto(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Int_Oint) ) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_anamorph_Osimps,axiom, % 19.07/19.01 ! [V_x_2,V_f_2,T_b,T_c,V_k_2] : % 19.07/19.01 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 19.07/19.01 => hAPP(c_Lazy__Sequence_Oanamorph(T_c,T_b,V_f_2,V_k_2),V_x_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),T_c),c_List_Olist_ONil(T_b)),V_x_2) ) % 19.07/19.01 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 19.07/19.01 => hAPP(c_Lazy__Sequence_Oanamorph(T_c,T_b,V_f_2,V_k_2),V_x_2) = hAPP(c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(T_b,T_c),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),T_c),c_List_Olist_ONil(T_b)),V_x_2),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_prod(tc_List_Olist(T_b),T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c)),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(tc_List_Olist(T_b),T_c)),tc_fun(tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c)),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),T_b),c_COMBB(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(tc_List_Olist(T_b),T_c),T_c)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),tc_fun(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(tc_List_Olist(T_b),T_c)),T_b),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),T_c,tc_prod(tc_List_Olist(T_b),T_c))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),T_b),hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c)),tc_List_Olist(T_b)),c_Product__Type_OPair(tc_List_Olist(T_b),T_c))),c_List_Olist_OCons(T_b))))),c_Lazy__Sequence_Oanamorph(T_c,T_b,V_f_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_k_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))))),hAPP(V_f_2,V_x_2)) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_listset_Osimps_I1_J,axiom, % 19.07/19.01 ! [T_b] : c_List_Olistset(T_b,c_List_Olist_ONil(tc_fun(T_b,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))) ). % 19.07/19.01 % 19.07/19.01 fof(fact_zip__Cons,axiom, % 19.07/19.01 ! [V_ys_2,V_y_2,V_xs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(T_b,T_c)),T_b,c_List_Olist_ONil(tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_b,T_c)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_b,T_c)))),T_b),c_COMBB(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c))),T_b),c_List_Olist_OCons(tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_prod(T_b,T_c)),c_Product__Type_OPair(T_b,T_c)),V_y_2)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c))),c_List_Ozip(T_b,T_c)),V_ys_2))),V_xs_2) ). % 19.07/19.01 % 19.07/19.01 fof(fact_list_Osimps_I5_J,axiom, % 19.07/19.01 ! [V_list_2,V_a_2,V_f2_2,V_f1_2,T_c,T_b] : hAPP(c_List_Olist_Olist__case(T_b,T_c,V_f1_2,V_f2_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_a_2),V_list_2)) = hAPP(hAPP(V_f2_2,V_a_2),V_list_2) ). % 19.07/19.01 % 19.07/19.01 fof(fact_list_Osimps_I4_J,axiom, % 19.07/19.01 ! [V_f2_2,V_f1_2,T_c,T_b] : hAPP(c_List_Olist_Olist__case(T_b,T_c,V_f1_2,V_f2_2),c_List_Olist_ONil(T_c)) = V_f1_2 ). % 19.07/19.01 % 19.07/19.01 fof(fact_listset_Osimps_I2_J,axiom, % 19.07/19.01 ! [V_As_2,V_A_2,T_b] : c_List_Olistset(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_As_2)) = c_List_Oset__Cons(T_b,V_A_2,c_List_Olistset(T_b,V_As_2)) ). % 19.07/19.01 % 19.07/19.01 fof(fact_zip__Cons1,axiom, % 19.07/19.01 ! [V_ys_2,V_xs_2,V_x_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_ys_2) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(T_b,T_c)),T_c,c_List_Olist_ONil(tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c)))),T_c),c_COMBB(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(T_c))),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c))),T_c),c_List_Olist_OCons(tc_prod(T_b,T_c))),hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2)))),hAPP(c_List_Ozip(T_b,T_c),V_xs_2))),V_ys_2) ). % 19.07/19.01 % 19.07/19.01 fof(fact_upto_Opinduct,axiom, % 19.07/19.01 ! [V_Pa_2,V_a1_2,V_a0_2] : % 19.07/19.01 ( 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))) % 19.07/19.01 => ( ! [B_i,B_j] : % 19.07/19.01 ( 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))) % 19.07/19.01 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_i),B_j)) % 19.07/19.01 => hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_i),c_Groups_Oone__class_Oone(tc_Int_Oint))),B_j)) ) % 19.07/19.01 => hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j)) ) ) % 19.07/19.01 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ). % 19.07/19.01 % 19.07/19.01 fof(fact_map__upd__upds__conv__if,axiom, % 19.07/19.01 ! [V_y_2,V_f_2,V_xs_2,V_ys_2,T_c,V_x_2,T_b] : % 19.07/19.01 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)),V_xs_2)))) % 19.07/19.02 => c_Map_Omap__upds(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_f_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2)),V_xs_2,V_ys_2) = c_Map_Omap__upds(T_b,T_c,V_f_2,V_xs_2,V_ys_2) ) % 19.07/19.02 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)),V_xs_2)))) % 19.07/19.02 => c_Map_Omap__upds(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_f_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2)),V_xs_2,V_ys_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Omap__upds(T_b,T_c,V_f_2,V_xs_2,V_ys_2)),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2)) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_map__upds__Nil2,axiom, % 19.07/19.02 ! [V_as_2,V_m_2,T_c,T_b] : c_Map_Omap__upds(T_b,T_c,V_m_2,V_as_2,c_List_Olist_ONil(T_c)) = V_m_2 ). % 19.07/19.02 % 19.07/19.02 fof(fact_map__upds__Nil1,axiom, % 19.07/19.02 ! [V_bs_2,V_m_2,T_c,T_b] : c_Map_Omap__upds(T_b,T_c,V_m_2,c_List_Olist_ONil(T_b),V_bs_2) = V_m_2 ). % 19.07/19.02 % 19.07/19.02 fof(fact_map__upds__apply__nontin,axiom, % 19.07/19.02 ! [V_ys_2,V_f_2,T_c,V_xs_2,V_x_2,T_b] : % 19.07/19.02 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 19.07/19.02 => hAPP(c_Map_Omap__upds(T_b,T_c,V_f_2,V_xs_2,V_ys_2),V_x_2) = hAPP(V_f_2,V_x_2) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_map__add__upds,axiom, % 19.07/19.02 ! [V_ys_2,V_xs_2,V_m2_2,V_m1_2,T_c,T_b] : c_Map_Omap__add(T_b,T_c,V_m1_2,c_Map_Omap__upds(T_b,T_c,V_m2_2,V_xs_2,V_ys_2)) = c_Map_Omap__upds(T_b,T_c,c_Map_Omap__add(T_b,T_c,V_m1_2,V_m2_2),V_xs_2,V_ys_2) ). % 19.07/19.02 % 19.07/19.02 fof(fact_map__upds__Cons,axiom, % 19.07/19.02 ! [V_bs_2,V_b_2,V_as_2,V_a_2,V_m_2,T_c,T_b] : c_Map_Omap__upds(T_b,T_c,V_m_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_as_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_b_2),V_bs_2)) = c_Map_Omap__upds(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_c),V_b_2)),V_as_2,V_bs_2) ). % 19.07/19.02 % 19.07/19.02 fof(fact_map__upds__list__update2__drop,axiom, % 19.07/19.02 ! [V_y_2,V_m_2,V_ys_2,T_c,V_i_2,V_xs_2,T_b] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),V_i_2)) % 19.07/19.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2))) % 19.07/19.02 => c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,hAPP(hAPP(c_List_Olist__update(T_c,V_ys_2),V_i_2),V_y_2)) = c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,V_ys_2) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_map__upds__twist,axiom, % 19.07/19.02 ! [V_bs_2,V_b_2,V_m_2,T_c,V_as_2,V_a_2,T_b] : % 19.07/19.02 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_as_2))) % 19.07/19.02 => c_Map_Omap__upds(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_c),V_b_2)),V_as_2,V_bs_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Omap__upds(T_b,T_c,V_m_2,V_as_2,V_bs_2)),V_a_2),hAPP(c_Option_Ooption_OSome(T_c),V_b_2)) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_restrict__map__upds,axiom, % 19.07/19.02 ! [V_m_2,V_D_2,V_ys_2,T_c,V_xs_2,T_b] : % 19.07/19.02 ( 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) % 19.07/19.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),V_D_2)) % 19.07/19.02 => c_Map_Orestrict__map(T_b,T_c,c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,V_ys_2),V_D_2) = c_Map_Omap__upds(T_b,T_c,c_Map_Orestrict__map(T_b,T_c,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_D_2),hAPP(c_List_Oset(T_b),V_xs_2))),V_xs_2,V_ys_2) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_dom__map__upds,axiom, % 19.07/19.02 ! [V_ys_2,V_xs_2,V_m_2,T_c,T_b] : c_Map_Odom(T_b,T_c,c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,V_ys_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)),V_xs_2))),c_Map_Odom(T_b,T_c,V_m_2)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_map__upds__append1,axiom, % 19.07/19.02 ! [V_x_2,V_m_2,V_ys_2,T_c,V_xs_2,T_b] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2))) % 19.07/19.02 => c_Map_Omap__upds(T_b,T_c,V_m_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))),V_ys_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,V_ys_2)),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),hAPP(hAPP(c_List_Onth(T_c),V_ys_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_sublist__Cons,axiom, % 19.07/19.02 ! [V_A_2,V_l_2,V_x_2,T_b] : c_List_Osublist(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_l_2),V_A_2) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(hAPP(c_If(tc_List_Olist(T_b)),hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))),c_List_Olist_ONil(T_b))),c_List_Osublist(T_b,V_l_2,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),V_A_2)))) ). % 19.07/19.02 % 19.07/19.02 fof(fact_append__eq__Cons__conv,axiom, % 19.07/19.02 ! [V_xs_2,V_x_2,V_zs_2,V_ys_2,T_b] : % 19.07/19.02 ( hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_zs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) % 19.07/19.02 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_b) % 19.07/19.02 & V_zs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) ) % 19.07/19.02 | ? [B_ys_H] : % 19.07/19.02 ( V_ys_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H) % 19.07/19.02 & hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2) = V_xs_2 ) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_Cons__eq__append__conv,axiom, % 19.07/19.02 ! [V_zs_2,V_ys_2,V_xs_2,V_x_2,T_b] : % 19.07/19.02 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_zs_2) % 19.07/19.02 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_b) % 19.07/19.02 & hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = V_zs_2 ) % 19.07/19.02 | ? [B_ys_H] : % 19.07/19.02 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H) = V_ys_2 % 19.07/19.02 & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2) ) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_append1__eq__conv,axiom, % 19.07/19.02 ! [V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] : % 19.07/19.02 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))) = hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),c_List_Olist_ONil(T_b))) % 19.07/19.02 <=> ( V_xs_2 = V_ys_2 % 19.07/19.02 & V_x_2 = V_y_2 ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_fun__upds__append__drop,axiom, % 19.07/19.02 ! [V_zs_2,V_m_2,V_ys_2,T_c,V_xs_2,T_b] : % 19.07/19.02 ( 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) % 19.07/19.02 => c_Map_Omap__upds(T_b,T_c,V_m_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_zs_2),V_ys_2) = c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,V_ys_2) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_fun__upds__append2__drop,axiom, % 19.07/19.02 ! [V_zs_2,V_m_2,V_ys_2,T_c,V_xs_2,T_b] : % 19.07/19.02 ( 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) % 19.07/19.02 => c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,hAPP(hAPP(c_List_Oappend(T_c),V_ys_2),V_zs_2)) = c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,V_ys_2) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_nth__append__length,axiom, % 19.07/19.02 ! [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 ). % 19.07/19.02 % 19.07/19.02 fof(fact_append__Cons,axiom, % 19.07/19.02 ! [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)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_Cons__eq__appendI,axiom, % 19.07/19.02 ! [V_zs,V_xs,V_ys,V_xs1,V_x,T_a] : % 19.07/19.02 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs1) = V_ys % 19.07/19.02 => ( V_xs = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_zs) % 19.07/19.02 => hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_list__update__length,axiom, % 19.07/19.02 ! [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)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_list__update__append1,axiom, % 19.07/19.02 ! [V_x,V_ys,V_xs,T_a,V_i] : % 19.07/19.02 ( 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))) % 19.07/19.02 => 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) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_nth__append__length__plus,axiom, % 19.07/19.02 ! [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) ). % 19.07/19.02 % 19.07/19.02 fof(fact_length__append,axiom, % 19.07/19.02 ! [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)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_zip__append,axiom, % 19.07/19.02 ! [V_vs,V_ys,V_us,T_b,V_xs,T_a] : % 19.07/19.02 ( 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) % 19.07/19.02 => ( 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) % 19.07/19.02 => 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)) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_map__append,axiom, % 19.07/19.02 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_ys_2)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_foldr__append,axiom, % 19.07/19.02 ! [V_a_2,V_ys_2,V_xs_2,V_f_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_f_2,hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2),V_a_2) = c_List_Ofoldr(T_c,T_b,V_f_2,V_xs_2,c_List_Ofoldr(T_c,T_b,V_f_2,V_ys_2,V_a_2)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_map__of__append,axiom, % 19.07/19.02 ! [V_ys_2,V_xs_2,T_c,T_b] : c_Map_Omap__of(T_b,T_c,hAPP(hAPP(c_List_Oappend(tc_prod(T_b,T_c)),V_xs_2),V_ys_2)) = c_Map_Omap__add(T_b,T_c,c_Map_Omap__of(T_b,T_c,V_ys_2),c_Map_Omap__of(T_b,T_c,V_xs_2)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_append__eq__appendI,axiom, % 19.07/19.02 ! [V_us,V_ys,V_zs,V_xs1,V_xs,T_a] : % 19.07/19.02 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_xs1) = V_zs % 19.07/19.02 => ( V_ys = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_us) % 19.07/19.02 => hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys) = hAPP(hAPP(c_List_Oappend(T_a),V_zs),V_us) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_append__same__eq,axiom, % 19.07/19.02 ! [V_zs_2,V_xs_2,V_ys_2,T_b] : % 19.07/19.02 ( hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_xs_2) = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),V_xs_2) % 19.07/19.02 <=> V_ys_2 = V_zs_2 ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_same__append__eq,axiom, % 19.07/19.02 ! [V_zs_2,V_ys_2,V_xs_2,T_b] : % 19.07/19.02 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_zs_2) % 19.07/19.02 <=> V_ys_2 = V_zs_2 ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_append__eq__append__conv2,axiom, % 19.07/19.02 ! [V_ts_2,V_zs_2,V_ys_2,V_xs_2,T_b] : % 19.07/19.02 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),V_ts_2) % 19.07/19.02 <=> ? [B_us] : % 19.07/19.02 ( ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),B_us) % 19.07/19.02 & hAPP(hAPP(c_List_Oappend(T_b),B_us),V_ys_2) = V_ts_2 ) % 19.07/19.02 | ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),B_us) = V_zs_2 % 19.07/19.02 & V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),V_ts_2) ) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_append__assoc,axiom, % 19.07/19.02 ! [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)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_set__append,axiom, % 19.07/19.02 ! [V_ys_2,V_xs_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_ys_2)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_listsum__append,axiom, % 19.07/19.02 ! [V_ys,V_xs,T_a] : % 19.07/19.02 ( class_Groups_Omonoid__add(T_a) % 19.07/19.02 => 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)) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_remove1__append,axiom, % 19.07/19.02 ! [V_ys_2,V_xs_2,V_x_2,T_b] : % 19.07/19.02 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 19.07/19.02 => c_List_Oremove1(T_b,V_x_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),c_List_Oremove1(T_b,V_x_2,V_xs_2)),V_ys_2) ) % 19.07/19.02 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 19.07/19.02 => c_List_Oremove1(T_b,V_x_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),c_List_Oremove1(T_b,V_x_2,V_ys_2)) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_take__append,axiom, % 19.07/19.02 ! [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)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_append__Nil,axiom, % 19.07/19.02 ! [V_ys,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) = V_ys ). % 19.07/19.02 % 19.07/19.02 fof(fact_Nil__is__append__conv,axiom, % 19.07/19.02 ! [V_ys_2,V_xs_2,T_b] : % 19.07/19.02 ( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) % 19.07/19.02 <=> ( V_xs_2 = c_List_Olist_ONil(T_b) % 19.07/19.02 & V_ys_2 = c_List_Olist_ONil(T_b) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_append__Nil2,axiom, % 19.07/19.02 ! [V_xs,T_a] : hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Olist_ONil(T_a)) = V_xs ). % 19.07/19.02 % 19.07/19.02 fof(fact_self__append__conv,axiom, % 19.07/19.02 ! [V_ys_2,T_b,V_xs_2] : % 19.07/19.02 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) % 19.07/19.02 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_self__append__conv2,axiom, % 19.07/19.02 ! [V_xs_2,T_b,V_ys_2] : % 19.07/19.02 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) % 19.07/19.02 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_append__is__Nil__conv,axiom, % 19.07/19.02 ! [V_ys_2,V_xs_2,T_b] : % 19.07/19.02 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = c_List_Olist_ONil(T_b) % 19.07/19.02 <=> ( V_xs_2 = c_List_Olist_ONil(T_b) % 19.07/19.02 & V_ys_2 = c_List_Olist_ONil(T_b) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_append__self__conv,axiom, % 19.07/19.02 ! [V_ys_2,V_xs_2,T_b] : % 19.07/19.02 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_xs_2 % 19.07/19.02 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_append__self__conv2,axiom, % 19.07/19.02 ! [V_ys_2,V_xs_2,T_b] : % 19.07/19.02 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_ys_2 % 19.07/19.02 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_eq__Nil__appendI,axiom, % 19.07/19.02 ! [T_a,V_ys,V_xs] : % 19.07/19.02 ( V_xs = V_ys % 19.07/19.02 => V_xs = hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_lexord__append__leftI,axiom, % 19.07/19.02 ! [V_x_2,V_r_2,V_v_2,V_u_2,T_b] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_u_2),V_v_2)),c_List_Olexord(T_b,V_r_2))) % 19.07/19.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_u_2)),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_v_2))),c_List_Olexord(T_b,V_r_2))) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_distinct__append,axiom, % 19.07/19.02 ! [V_ys_2,V_xs_2,T_b] : % 19.07/19.02 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))) % 19.07/19.02 <=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 19.07/19.02 & hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2)) % 19.07/19.02 & hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_ys_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_nth__append,axiom, % 19.07/19.02 ! [V_ys,V_xs,T_a,V_n] : % 19.07/19.02 ( ( 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))) % 19.07/19.02 => 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) ) % 19.07/19.02 & ( ~ 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))) % 19.07/19.02 => 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))) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_list__update__append,axiom, % 19.07/19.02 ! [V_x,V_ys,V_xs,T_a,V_n] : % 19.07/19.02 ( ( 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))) % 19.07/19.02 => 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) ) % 19.07/19.02 & ( ~ 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))) % 19.07/19.02 => 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)) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_sublist__append,axiom, % 19.07/19.02 ! [V_A_2,V_l_H_2,V_l_2,T_b] : c_List_Osublist(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_l_2),V_l_H_2),V_A_2) = hAPP(hAPP(c_List_Oappend(T_b),c_List_Osublist(T_b,V_l_2,V_A_2)),c_List_Osublist(T_b,V_l_H_2,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_l_2)))),V_A_2)))) ). % 19.07/19.02 % 19.07/19.02 fof(fact_lexord__append__left__rightI,axiom, % 19.07/19.02 ! [V_y_2,V_x_2,V_u_2,V_r_2,V_b_2,V_a_2,T_b] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) % 19.07/19.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_u_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_x_2))),hAPP(hAPP(c_List_Oappend(T_b),V_u_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_b_2),V_y_2)))),c_List_Olexord(T_b,V_r_2))) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_take__Suc__conv__app__nth,axiom, % 19.07/19.02 ! [V_xs,T_a,V_i] : % 19.07/19.02 ( 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))) % 19.07/19.02 => 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))) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_snoc__listrel1__snoc__iff,axiom, % 19.07/19.02 ! [V_r_2,V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)))),hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),c_List_Olist_ONil(T_b))))),c_List_Olistrel1(T_b,V_r_2))) % 19.07/19.02 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) % 19.07/19.02 & V_x_2 = V_y_2 ) % 19.07/19.02 | ( V_xs_2 = V_ys_2 % 19.07/19.02 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_lexord__append__leftD,axiom, % 19.07/19.02 ! [V_r_2,V_v_2,V_u_2,V_x_2,T_b] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_u_2)),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_v_2))),c_List_Olexord(T_b,V_r_2))) % 19.07/19.02 => ( ! [B_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_a),B_a)),V_r_2)) % 19.07/19.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_u_2),V_v_2)),c_List_Olexord(T_b,V_r_2))) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_Cons__acc__listrel1I,axiom, % 19.07/19.02 ! [V_xs_2,V_r_2,V_x_2,T_b] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) % 19.07/19.02 => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) % 19.07/19.02 => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_listrel1__rtrancl__subset__rtrancl__listrel1,axiom, % 19.07/19.02 ! [V_r_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel1(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ). % 19.07/19.02 % 19.07/19.02 fof(fact_listrel1__converse,axiom, % 19.07/19.02 ! [V_r_2,T_b] : c_List_Olistrel1(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) = hAPP(c_Relation_Oconverse(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olistrel1(T_b,V_r_2)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_listrel__rtrancl__eq__rtrancl__listrel1,axiom, % 19.07/19.02 ! [V_r_2,T_b] : c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_listrel1__mono,axiom, % 19.07/19.02 ! [V_s_2,V_r_2,T_b] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) % 19.07/19.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel1(T_b,V_r_2)),c_List_Olistrel1(T_b,V_s_2))) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_listrel__subset__rtrancl__listrel1,axiom, % 19.07/19.02 ! [V_r_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel(T_b,V_r_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ). % 19.07/19.02 % 19.07/19.02 fof(fact_listrel1I2,axiom, % 19.07/19.02 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) % 19.07/19.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_ys_2))),c_List_Olistrel1(T_b,V_r_2))) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_rtrancl__listrel1__ConsI1,axiom, % 19.07/19.02 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) % 19.07/19.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_ys_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_listrel1__eq__len,axiom, % 19.07/19.02 ! [V_r_2,V_ys_2,V_xs_2,T_b] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) % 19.07/19.02 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_rtrancl__listrel1__eq__len,axiom, % 19.07/19.02 ! [V_r_2,V_y_2,V_x_2,T_b] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) % 19.07/19.02 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_not__Nil__listrel1,axiom, % 19.07/19.02 ! [V_r_2,V_xs_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xs_2)),c_List_Olistrel1(T_b,V_r_2))) ). % 19.07/19.02 % 19.07/19.02 fof(fact_not__listrel1__Nil,axiom, % 19.07/19.02 ! [V_r_2,V_xs_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),c_List_Olist_ONil(T_b))),c_List_Olistrel1(T_b,V_r_2))) ). % 19.07/19.02 % 19.07/19.02 fof(fact_append__listrel1I,axiom, % 19.07/19.02 ! [V_vs_2,V_us_2,V_r_2,V_ys_2,V_xs_2,T_b] : % 19.07/19.02 ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) % 19.07/19.02 & V_us_2 = V_vs_2 ) % 19.07/19.02 | ( V_xs_2 = V_ys_2 % 19.07/19.02 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_us_2),V_vs_2)),c_List_Olistrel1(T_b,V_r_2))) ) ) % 19.07/19.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_us_2)),hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_vs_2))),c_List_Olistrel1(T_b,V_r_2))) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_in__listrel1__converse,axiom, % 19.07/19.02 ! [V_r_2,V_y_2,V_x_2,T_b] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olistrel1(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)))) % 19.07/19.02 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olistrel1(T_b,V_r_2)))) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_rtrancl__listrel1__if__listrel,axiom, % 19.07/19.02 ! [V_r_2,V_ys_2,V_xs_2,T_b] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2))) % 19.07/19.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_listrel__reflcl__if__listrel1,axiom, % 19.07/19.02 ! [V_r_2,V_ys_2,V_xs_2,T_b] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) % 19.07/19.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)))) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_listrel1I1,axiom, % 19.07/19.02 ! [V_xs_2,V_r_2,V_y_2,V_x_2,T_b] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) % 19.07/19.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_xs_2))),c_List_Olistrel1(T_b,V_r_2))) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_Cons__listrel1__Cons,axiom, % 19.07/19.02 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olistrel1(T_b,V_r_2))) % 19.07/19.02 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) % 19.07/19.02 & V_xs_2 = V_ys_2 ) % 19.07/19.02 | ( V_x_2 = V_y_2 % 19.07/19.02 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) ) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_listrel1__subset__listrel,axiom, % 19.07/19.02 ! [V_r_H_2,V_r_2,T_b] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_r_H_2)) % 19.07/19.02 => ( c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_r_H_2) % 19.07/19.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel1(T_b,V_r_2)),c_List_Olistrel(T_b,V_r_H_2))) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_listrel1I,axiom, % 19.07/19.02 ! [V_ys_2,V_vs_2,V_us_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) % 19.07/19.02 => ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_us_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_vs_2)) % 19.07/19.02 => ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),V_us_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_vs_2)) % 19.07/19.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) ) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_rtrancl__listrel1__ConsI2,axiom, % 19.07/19.02 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 19.07/19.02 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) % 19.07/19.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_listrel1__iff__update,axiom, % 19.07/19.02 ! [V_r_2,V_ys_2,V_xs_2,T_b] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) % 19.07/19.02 <=> ? [B_y,B_n] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n)),B_y)),V_r_2)) % 19.07/19.02 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 19.07/19.02 & V_ys_2 = hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),B_n),B_y) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_listrel1E,axiom, % 19.07/19.02 ! [V_r_2,V_ys_2,V_xs_2,T_b] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) % 19.07/19.02 => ~ ! [B_x,B_y] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2)) % 19.07/19.02 => ! [B_us,B_vs] : % 19.07/19.02 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_vs)) % 19.07/19.02 => V_ys_2 != hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_vs)) ) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_rotate1__def,axiom, % 19.07/19.02 ! [V_xs_2,T_b] : hAPP(c_List_Orotate1(T_b),V_xs_2) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Oappend(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b)))),V_xs_2) ). % 19.07/19.02 % 19.07/19.02 fof(fact_upd__conv__take__nth__drop,axiom, % 19.07/19.02 ! [V_a,V_xs,T_a,V_i] : % 19.07/19.02 ( 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))) % 19.07/19.02 => 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))) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_append__eq__conv__conj,axiom, % 19.07/19.02 ! [V_zs_2,V_ys_2,V_xs_2,T_b] : % 19.07/19.02 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_zs_2 % 19.07/19.02 <=> ( V_xs_2 = hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),V_zs_2) % 19.07/19.02 & V_ys_2 = hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),V_zs_2) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_rotate1__is__Nil__conv,axiom, % 19.07/19.02 ! [V_xs_2,T_b] : % 19.07/19.02 ( hAPP(c_List_Orotate1(T_b),V_xs_2) = c_List_Olist_ONil(T_b) % 19.07/19.02 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_drop__Nil,axiom, % 19.07/19.02 ! [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) ). % 19.07/19.02 % 19.07/19.02 fof(fact_drop__eq__Nil,axiom, % 19.07/19.02 ! [V_xs_2,V_n_2,T_b] : % 19.07/19.02 ( hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2) = c_List_Olist_ONil(T_b) % 19.07/19.02 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),V_n_2)) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_drop__all,axiom, % 19.07/19.02 ! [V_n,V_xs,T_a] : % 19.07/19.02 ( 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)) % 19.07/19.02 => hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = c_List_Olist_ONil(T_a) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_take__drop,axiom, % 19.07/19.02 ! [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)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_drop__take,axiom, % 19.07/19.02 ! [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)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_in__set__dropD,axiom, % 19.07/19.02 ! [V_xs_2,V_n_2,V_x_2,T_b] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2)))) % 19.07/19.02 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_set__rotate1,axiom, % 19.07/19.02 ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Orotate1(T_b),V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2) ). % 19.07/19.02 % 19.07/19.02 fof(fact_set__drop__subset,axiom, % 19.07/19.02 ! [V_xs_2,V_n_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ). % 19.07/19.02 % 19.07/19.02 fof(fact_distinct__drop,axiom, % 19.07/19.02 ! [V_i,V_xs,T_a] : % 19.07/19.02 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 19.07/19.02 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_distinct1__rotate,axiom, % 19.07/19.02 ! [V_xs_2,T_b] : % 19.07/19.02 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate1(T_b),V_xs_2))) % 19.07/19.02 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_drop__drop,axiom, % 19.07/19.02 ! [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) ). % 19.07/19.02 % 19.07/19.02 fof(fact_drop__0,axiom, % 19.07/19.02 ! [V_xs,T_a] : hAPP(hAPP(c_List_Odrop(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs) = V_xs ). % 19.07/19.02 % 19.07/19.02 fof(fact_drop__zip,axiom, % 19.07/19.02 ! [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)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_drop__map,axiom, % 19.07/19.02 ! [V_xs_2,V_f_2,T_c,V_n_2,T_b] : hAPP(hAPP(c_List_Odrop(T_b),V_n_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Odrop(T_c),V_n_2),V_xs_2)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_length__drop,axiom, % 19.07/19.02 ! [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) ). % 19.07/19.02 % 19.07/19.02 fof(fact_length__rotate1,axiom, % 19.07/19.02 ! [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) ). % 19.07/19.02 % 19.07/19.02 fof(fact_set__drop__subset__set__drop,axiom, % 19.07/19.02 ! [V_xs_2,T_b,V_m_2,V_n_2] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) % 19.07/19.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_m_2),V_xs_2))),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2)))) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_drop__1__Cons,axiom, % 19.07/19.02 ! [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 ). % 19.07/19.02 % 19.07/19.02 fof(fact_drop__Suc__Cons,axiom, % 19.07/19.02 ! [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) ). % 19.07/19.02 % 19.07/19.02 fof(fact_nth__via__drop,axiom, % 19.07/19.02 ! [V_ys,V_y,V_xs,V_n,T_a] : % 19.07/19.02 ( hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys) % 19.07/19.02 => hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) = V_y ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_drop__append,axiom, % 19.07/19.02 ! [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)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_append__take__drop__id,axiom, % 19.07/19.02 ! [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 ). % 19.07/19.02 % 19.07/19.02 fof(fact_drop__Cons,axiom, % 19.07/19.02 ! [V_xs_2,V_x_2,V_n_2,T_b] : hAPP(hAPP(c_List_Odrop(T_b),V_n_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_Nat_Onat_Onat__case(tc_List_Olist(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Odrop(T_b)),V_xs_2),V_n_2) ). % 19.07/19.02 % 19.07/19.02 fof(fact_drop__Cons_H,axiom, % 19.07/19.02 ! [V_xs,V_x,T_a,V_n] : % 19.07/19.02 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 19.07/19.02 => 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) ) % 19.07/19.02 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 19.07/19.02 => 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) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_nth__drop,axiom, % 19.07/19.02 ! [V_xs,T_a,V_i,V_n] : % 19.07/19.02 ( 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))) % 19.07/19.02 => 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)) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_append__eq__append__conv__if,axiom, % 19.07/19.02 ! [V_ys_092_060_094isub_0622_2,V_ys_092_060_094isub_0621_2,V_xs_092_060_094isub_0622_2,V_xs_092_060_094isub_0621_2,T_b] : % 19.07/19.02 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_092_060_094isub_0621_2),V_xs_092_060_094isub_0622_2) = hAPP(hAPP(c_List_Oappend(T_b),V_ys_092_060_094isub_0621_2),V_ys_092_060_094isub_0622_2) % 19.07/19.02 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2))) % 19.07/19.02 => ( V_xs_092_060_094isub_0621_2 = hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),V_ys_092_060_094isub_0621_2) % 19.07/19.02 & V_xs_092_060_094isub_0622_2 = hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),V_ys_092_060_094isub_0621_2)),V_ys_092_060_094isub_0622_2) ) ) % 19.07/19.02 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2))) % 19.07/19.02 => ( hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2)),V_xs_092_060_094isub_0621_2) = V_ys_092_060_094isub_0621_2 % 19.07/19.02 & hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2)),V_xs_092_060_094isub_0621_2)),V_xs_092_060_094isub_0622_2) = V_ys_092_060_094isub_0622_2 ) ) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_nth__drop_H,axiom, % 19.07/19.02 ! [V_xs,T_a,V_i] : % 19.07/19.02 ( 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))) % 19.07/19.02 => 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) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_rotate__simps,axiom, % 19.07/19.02 ! [V_xs,V_x,T_b,T_a] : % 19.07/19.02 ( hAPP(c_List_Orotate1(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) % 19.07/19.02 & 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))) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_drop__Cons__number__of,axiom, % 19.07/19.02 ! [V_xs,V_x,T_a,V_v] : % 19.07/19.02 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 19.07/19.02 => 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) ) % 19.07/19.02 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 19.07/19.02 => 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) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_take__add,axiom, % 19.07/19.02 ! [V_xs,T_a,V_j,V_i] : % 19.07/19.02 ( 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))) % 19.07/19.02 => 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))) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_rotate1__length01,axiom, % 19.07/19.02 ! [V_xs,T_a] : % 19.07/19.02 ( 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)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) % 19.07/19.02 => hAPP(c_List_Orotate1(T_a),V_xs) = V_xs ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_zip__append1,axiom, % 19.07/19.02 ! [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))) ). % 19.07/19.02 % 19.07/19.02 fof(fact_zip__append2,axiom, % 19.07/19.02 ! [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)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_id__take__nth__drop,axiom, % 19.07/19.02 ! [V_xs,T_a,V_i] : % 19.07/19.02 ( 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))) % 19.07/19.02 => 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))) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_take__hd__drop,axiom, % 19.07/19.02 ! [V_xs,T_a,V_n] : % 19.07/19.02 ( 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))) % 19.07/19.02 => 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) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_hd__drop__conv__nth,axiom, % 19.07/19.02 ! [V_n,T_a,V_xs] : % 19.07/19.02 ( V_xs != c_List_Olist_ONil(T_a) % 19.07/19.02 => ( 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))) % 19.07/19.02 => 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) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_hd__append,axiom, % 19.07/19.02 ! [V_ys,T_a,V_xs] : % 19.07/19.02 ( ( V_xs = c_List_Olist_ONil(T_a) % 19.07/19.02 => 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) ) % 19.07/19.02 & ( V_xs != c_List_Olist_ONil(T_a) % 19.07/19.02 => 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) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_hd__append2,axiom, % 19.07/19.02 ! [V_ys,T_a,V_xs] : % 19.07/19.02 ( V_xs != c_List_Olist_ONil(T_a) % 19.07/19.02 => 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) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_hd_Osimps,axiom, % 19.07/19.02 ! [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 ). % 19.07/19.02 % 19.07/19.02 fof(fact_hd__map,axiom, % 19.07/19.02 ! [V_f_2,T_c,T_b,V_xs_2] : % 19.07/19.02 ( V_xs_2 != c_List_Olist_ONil(T_b) % 19.07/19.02 => hAPP(c_List_Ohd(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(V_f_2,hAPP(c_List_Ohd(T_b),V_xs_2)) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_hd__in__set,axiom, % 19.07/19.02 ! [T_b,V_xs_2] : % 19.07/19.02 ( V_xs_2 != c_List_Olist_ONil(T_b) % 19.07/19.02 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_List_Ohd(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_xs_2))) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_hd__conv__nth,axiom, % 19.07/19.02 ! [T_a,V_xs] : % 19.07/19.02 ( V_xs != c_List_Olist_ONil(T_a) % 19.07/19.02 => 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)) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_rotate1__hd__tl,axiom, % 19.07/19.02 ! [T_a,V_xs] : % 19.07/19.02 ( V_xs != c_List_Olist_ONil(T_a) % 19.07/19.02 => 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))) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_hd__rotate__conv__nth,axiom, % 19.07/19.02 ! [V_n,T_a,V_xs] : % 19.07/19.02 ( V_xs != c_List_Olist_ONil(T_a) % 19.07/19.02 => 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))) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_drop__Suc,axiom, % 19.07/19.02 ! [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)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_tl__drop,axiom, % 19.07/19.02 ! [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)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_drop__tl,axiom, % 19.07/19.02 ! [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)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_rotate__is__Nil__conv,axiom, % 19.07/19.02 ! [V_xs_2,V_n_2,T_b] : % 19.07/19.02 ( hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2) = c_List_Olist_ONil(T_b) % 19.07/19.02 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_tl_Osimps_I1_J,axiom, % 19.07/19.02 ! [T_a] : hAPP(c_List_Otl(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 19.07/19.02 % 19.07/19.02 fof(fact_take__tl,axiom, % 19.07/19.02 ! [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)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_set__rotate,axiom, % 19.07/19.02 ! [V_xs_2,V_n_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2) ). % 19.07/19.02 % 19.07/19.02 fof(fact_distinct__tl,axiom, % 19.07/19.02 ! [V_xs,T_a] : % 19.07/19.02 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 19.07/19.02 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Otl(T_a),V_xs))) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_distinct__rotate,axiom, % 19.07/19.02 ! [V_xs_2,V_n_2,T_b] : % 19.07/19.02 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2))) % 19.07/19.02 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_rotate__rotate,axiom, % 19.07/19.02 ! [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) ). % 19.07/19.02 % 19.07/19.02 fof(fact_map__tl,axiom, % 19.07/19.02 ! [V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Otl(T_c),V_xs_2)) = hAPP(c_List_Otl(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_rotate__map,axiom, % 19.07/19.02 ! [V_xs_2,V_f_2,T_c,V_n_2,T_b] : hAPP(c_List_Orotate(T_b,V_n_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Orotate(T_c,V_n_2),V_xs_2)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_length__rotate,axiom, % 19.07/19.02 ! [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) ). % 19.07/19.02 % 19.07/19.02 fof(fact_rotate__conv__mod,axiom, % 19.07/19.02 ! [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) ). % 19.07/19.02 % 19.07/19.02 fof(fact_tl_Osimps_I2_J,axiom, % 19.07/19.02 ! [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 ). % 19.07/19.02 % 19.07/19.02 fof(fact_tl__append2,axiom, % 19.07/19.02 ! [V_ys,T_a,V_xs] : % 19.07/19.02 ( V_xs != c_List_Olist_ONil(T_a) % 19.07/19.02 => 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) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_rotate__def,axiom, % 19.07/19.02 ! [V_n_2,T_b] : c_List_Orotate(T_b,V_n_2) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_n_2),c_List_Orotate1(T_b)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_rotate1__rotate__swap,axiom, % 19.07/19.02 ! [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)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_rotate__Suc,axiom, % 19.07/19.02 ! [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)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_tl__append,axiom, % 19.07/19.02 ! [V_ys_2,V_xs_2,T_b] : hAPP(c_List_Otl(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,hAPP(c_List_Otl(T_b),V_ys_2),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Oappend(T_b)),V_ys_2))),V_xs_2) ). % 19.07/19.02 % 19.07/19.02 fof(fact_rotate0,axiom, % 19.07/19.02 ! [T_b] : c_List_Orotate(T_b,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(T_b)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_rotate__add,axiom, % 19.07/19.02 ! [V_n_2,V_m_2,T_b] : c_List_Orotate(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)) = hAPP(c_Fun_Ocomp(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Orotate(T_b,V_m_2)),c_List_Orotate(T_b,V_n_2)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_rotate__id,axiom, % 19.07/19.02 ! [V_xs,T_a,V_n] : % 19.07/19.02 ( 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) % 19.07/19.02 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_rotate__length01,axiom, % 19.07/19.02 ! [V_n,V_xs,T_a] : % 19.07/19.02 ( 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)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) % 19.07/19.02 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_length__tl,axiom, % 19.07/19.02 ! [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)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_tl__take,axiom, % 19.07/19.02 ! [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)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_take__Suc,axiom, % 19.07/19.02 ! [V_n,T_a,V_xs] : % 19.07/19.02 ( V_xs != c_List_Olist_ONil(T_a) % 19.07/19.02 => 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))) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_rotate__drop__take,axiom, % 19.07/19.02 ! [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)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_fold1__set,axiom, % 19.07/19.02 ! [V_xs_2,T_b] : % 19.07/19.02 ( class_Lattices_Oab__semigroup__idem__mult(T_b) % 19.07/19.02 => ( V_xs_2 != c_List_Olist_ONil(T_b) % 19.07/19.02 => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),hAPP(c_List_Ohd(T_b),V_xs_2)),hAPP(c_List_Otl(T_b),V_xs_2)) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_list_Osize_I2_J,axiom, % 19.07/19.02 ! [V_list_2,V_a_2,V_fa_2,T_b] : c_List_Olist_Olist__size(T_b,V_fa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_list_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),c_List_Olist_Olist__size(T_b,V_fa_2,V_list_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 19.07/19.02 % 19.07/19.02 fof(fact_foldl__append,axiom, % 19.07/19.02 ! [V_ys_2,V_xs_2,V_a_2,V_f_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2)) = hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),V_xs_2)),V_ys_2) ). % 19.07/19.02 % 19.07/19.02 fof(fact_foldl__Cons,axiom, % 19.07/19.02 ! [V_xs_2,V_x_2,V_a_2,V_f_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,hAPP(hAPP(V_f_2,V_a_2),V_x_2)),V_xs_2) ). % 19.07/19.02 % 19.07/19.02 fof(fact_foldl__map,axiom, % 19.07/19.02 ! [V_xs_2,V_f_2,T_d,V_a_2,V_g_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_g_2,V_a_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_d,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,T_c),tc_fun(T_d,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),tc_fun(tc_fun(T_d,T_c),tc_fun(T_d,T_b)),T_b),c_COMBB(T_c,T_b,T_d)),V_g_2)),V_f_2),V_a_2),V_xs_2) ). % 19.07/19.02 % 19.07/19.02 fof(fact_list__size__map,axiom, % 19.07/19.02 ! [V_xs_2,V_g_2,T_c,V_f_2,T_b] : c_List_Olist_Olist__size(T_b,V_f_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2)) = c_List_Olist_Olist__size(T_c,hAPP(c_Fun_Ocomp(T_b,tc_Nat_Onat,T_c,V_f_2),V_g_2),V_xs_2) ). % 19.07/19.02 % 19.07/19.02 fof(fact_foldr__conv__foldl,axiom, % 19.07/19.02 ! [V_a_2,V_xs_2,T_b] : % 19.07/19.02 ( class_Groups_Oab__semigroup__add(T_b) % 19.07/19.02 => c_List_Ofoldr(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_xs_2,V_a_2) = hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_xs_2) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_foldl__absorb0,axiom, % 19.07/19.02 ! [V_zs_2,V_x_2,T_b] : % 19.07/19.02 ( class_Groups_Omonoid__add(T_b) % 19.07/19.02 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_zs_2)) = hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_zs_2) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_foldl__assoc,axiom, % 19.07/19.02 ! [V_zs_2,V_y_2,V_x_2,T_b] : % 19.07/19.02 ( class_Groups_Osemigroup__add(T_b) % 19.07/19.02 => hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_y_2)),V_zs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_y_2),V_zs_2)) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_start__le__sum,axiom, % 19.07/19.02 ! [V_ns_2,V_n_2,V_m_2] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 19.07/19.02 => 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))) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_foldl__Nil,axiom, % 19.07/19.02 ! [V_a_2,V_f_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),c_List_Olist_ONil(T_c)) = V_a_2 ). % 19.07/19.02 % 19.07/19.02 fof(fact_listsum__foldl,axiom, % 19.07/19.02 ! [T_b] : % 19.07/19.02 ( class_Groups_Omonoid__add(T_b) % 19.07/19.02 => c_List_Omonoid__add__class_Olistsum(T_b) = c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),c_Groups_Ozero__class_Ozero(T_b)) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_foldl__foldr1__lemma,axiom, % 19.07/19.02 ! [V_xs_2,V_a_2,T_b] : % 19.07/19.02 ( class_Groups_Omonoid__add(T_b) % 19.07/19.02 => hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_xs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),c_List_Ofoldr(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_xs_2,c_Groups_Ozero__class_Ozero(T_b))) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_foldl__foldr1,axiom, % 19.07/19.02 ! [V_xs_2,T_b] : % 19.07/19.02 ( class_Groups_Omonoid__add(T_b) % 19.07/19.02 => hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_xs_2) = c_List_Ofoldr(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_xs_2,c_Groups_Ozero__class_Ozero(T_b)) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_sum__eq__0__conv,axiom, % 19.07/19.02 ! [V_ns_2,V_m_2] : % 19.07/19.02 ( 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) % 19.07/19.02 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 19.07/19.02 & ! [B_x] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) % 19.07/19.02 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_list_Osize_I1_J,axiom, % 19.07/19.02 ! [V_fa_2,T_b] : c_List_Olist_Olist__size(T_b,V_fa_2,c_List_Olist_ONil(T_b)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 19.07/19.02 % 19.07/19.02 fof(fact_fun__left__comm__idem_Ofold__set,axiom, % 19.07/19.02 ! [V_xs_2,V_y_2,V_f_2,T_c,T_b] : % 19.07/19.02 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) % 19.07/19.02 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_c,T_b,hAPP(c_COMBC(T_b,T_c,T_c),V_f_2),V_y_2),V_xs_2) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_Sup__set__fold,axiom, % 19.07/19.02 ! [V_xs_2,T_b] : % 19.07/19.02 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 19.07/19.02 => c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Orderings_Obot__class_Obot(T_b)),V_xs_2) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_Inf__set__fold,axiom, % 19.07/19.02 ! [V_xs_2,T_b] : % 19.07/19.02 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 19.07/19.02 => c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Orderings_Otop__class_Otop(T_b)),V_xs_2) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_Sup__fin__set__fold,axiom, % 19.07/19.02 ! [V_xs_2,V_x_2,T_b] : % 19.07/19.02 ( class_Lattices_Olattice(T_b) % 19.07/19.02 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_xs_2) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_Inf__fin__set__fold,axiom, % 19.07/19.02 ! [V_xs_2,V_x_2,T_b] : % 19.07/19.02 ( class_Lattices_Olattice(T_b) % 19.07/19.02 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_xs_2) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_Min__fin__set__fold,axiom, % 19.07/19.02 ! [V_xs_2,V_x_2,T_b] : % 19.07/19.02 ( class_Orderings_Olinorder(T_b) % 19.07/19.02 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Orderings_Oord__class_Omin(T_b),V_x_2),V_xs_2) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_Max__fin__set__fold,axiom, % 19.07/19.02 ! [V_xs_2,V_x_2,T_b] : % 19.07/19.02 ( class_Orderings_Olinorder(T_b) % 19.07/19.02 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_x_2),V_xs_2) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_min__max_OInf__fin__set__fold,axiom, % 19.07/19.02 ! [V_xs_2,V_x_2,T_b] : % 19.07/19.02 ( class_Orderings_Olinorder(T_b) % 19.07/19.02 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Orderings_Oord__class_Omin(T_b),V_x_2),V_xs_2) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_min__max_OSup__fin__set__fold,axiom, % 19.07/19.02 ! [V_xs_2,V_x_2,T_b] : % 19.07/19.02 ( class_Orderings_Olinorder(T_b) % 19.07/19.02 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_x_2),V_xs_2) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_SUPR__set__fold,axiom, % 19.07/19.02 ! [V_f_2,V_xs_2,T_c,T_b] : % 19.07/19.02 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 19.07/19.02 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),hAPP(c_List_Oset(T_c),V_xs_2)),V_f_2) = hAPP(c_List_Ofoldl(T_b,T_c,hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_f_2)),c_Orderings_Obot__class_Obot(T_b)),V_xs_2) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_INFI__set__fold,axiom, % 19.07/19.02 ! [V_f_2,V_xs_2,T_c,T_b] : % 19.07/19.02 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 19.07/19.02 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),hAPP(c_List_Oset(T_c),V_xs_2)),V_f_2) = hAPP(c_List_Ofoldl(T_b,T_c,hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_f_2)),c_Orderings_Otop__class_Otop(T_b)),V_xs_2) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_list__size__estimation,axiom, % 19.07/19.02 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 19.07/19.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2))) % 19.07/19.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),c_List_Olist_Olist__size(T_b,V_f_2,V_xs_2))) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_list__size__estimation_H,axiom, % 19.07/19.02 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 19.07/19.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2))) % 19.07/19.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),c_List_Olist_Olist__size(T_b,V_f_2,V_xs_2))) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_map__upds__fold__map__upd,axiom, % 19.07/19.02 ! [V_vs_2,V_ks_2,V_m_2,T_c,T_b] : c_Map_Omap__upds(T_b,T_c,V_m_2,V_ks_2,V_vs_2) = hAPP(c_List_Ofoldl(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_prod(T_b,T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_fun(T_b,tc_Option_Ooption(T_c)))),tc_fun(tc_prod(T_b,T_c),tc_fun(T_b,tc_Option_Ooption(T_c))),tc_fun(T_b,tc_Option_Ooption(T_c))),c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_b,tc_Option_Ooption(T_c)))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_b,tc_fun(T_c,tc_fun(T_b,tc_Option_Ooption(T_c))))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_fun(T_b,tc_Option_Ooption(T_c))))),tc_fun(tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_b,tc_fun(T_c,tc_fun(T_b,tc_Option_Ooption(T_c))))),tc_fun(T_b,tc_Option_Ooption(T_c))),c_COMBC(T_b,tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_fun(T_b,tc_Option_Ooption(T_c))))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_Option_Ooption(T_c),tc_fun(T_b,tc_Option_Ooption(T_c)))),tc_fun(T_b,tc_fun(tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_fun(T_b,tc_Option_Ooption(T_c))))),tc_fun(T_b,tc_Option_Ooption(T_c))),hAPP(c_COMBB(tc_fun(tc_Option_Ooption(T_c),tc_fun(T_b,tc_Option_Ooption(T_c))),tc_fun(tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_fun(T_b,tc_Option_Ooption(T_c)))),T_b),c_COMBB(tc_Option_Ooption(T_c),tc_fun(T_b,tc_Option_Ooption(T_c)),T_c))),c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c))))),c_Option_Ooption_OSome(T_c))),V_m_2),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_ks_2),V_vs_2)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_elem__le__sum,axiom, % 19.07/19.02 ! [V_ns_2,V_n_2] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_n_2),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) % 19.07/19.02 => 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))) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_list__size__conv__listsum,axiom, % 19.07/19.02 ! [V_xs_2,V_f_2,T_b] : c_List_Olist_Olist__size(T_b,V_f_2,V_xs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(T_b,tc_Nat_Onat),V_f_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_listrel__subset,axiom, % 19.07/19.02 ! [V_A_2,V_r_2,T_b] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) % 19.07/19.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olists(T_b,V_A_2)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_List_Olist(T_b)),c_List_Olists(T_b,V_A_2))))) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_lists__accI,axiom, % 19.07/19.02 ! [V_r_2,V_xs_2,T_b] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) % 19.07/19.02 => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,c_Wellfounded_Oacc(T_b,V_r_2)))) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_lists_ONil,axiom, % 19.07/19.02 ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_List_Olists(T_b,V_A_2))) ). % 19.07/19.02 % 19.07/19.02 fof(fact_listrel__refl__on,axiom, % 19.07/19.02 ! [V_r_2,V_A_2,T_b] : % 19.07/19.02 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 19.07/19.02 => c_Relation_Orefl__on(tc_List_Olist(T_b),c_List_Olists(T_b,V_A_2),c_List_Olistrel(T_b,V_r_2)) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_equiv__listrel,axiom, % 19.07/19.02 ! [V_r_2,V_A_2,T_b] : % 19.07/19.02 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 19.07/19.02 => c_Equiv__Relations_Oequiv(tc_List_Olist(T_b),c_List_Olists(T_b,V_A_2),c_List_Olistrel(T_b,V_r_2)) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_lists__mono,axiom, % 19.07/19.02 ! [V_B_2,V_A_2,T_b] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 19.07/19.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),c_List_Olists(T_b,V_A_2)),c_List_Olists(T_b,V_B_2))) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_lists__UNIV,axiom, % 19.07/19.02 ! [T_b] : c_List_Olists(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_append__in__lists__conv,axiom, % 19.07/19.02 ! [V_A_2,V_ys_2,V_xs_2,T_b] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)),c_List_Olists(T_b,V_A_2))) % 19.07/19.02 <=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2))) % 19.07/19.02 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_ys_2),c_List_Olists(T_b,V_A_2))) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_Cons__in__lists__iff,axiom, % 19.07/19.02 ! [V_A_2,V_xs_2,V_x_2,T_b] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),c_List_Olists(T_b,V_A_2))) % 19.07/19.02 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 19.07/19.02 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2))) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_in__lists__conv__set,axiom, % 19.07/19.02 ! [V_A_2,V_xs_2,T_b] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2))) % 19.07/19.02 <=> ! [B_x] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 19.07/19.02 => hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_lists__eq__set,axiom, % 19.07/19.02 ! [V_A_2,T_b] : c_List_Olists(T_b,V_A_2) = hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),c_List_Oset(T_b))),V_A_2)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_lists__empty,axiom, % 19.07/19.02 ! [T_b] : c_List_Olists(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))) ). % 19.07/19.02 % 19.07/19.02 fof(fact_lists__accD,axiom, % 19.07/19.02 ! [V_r_2,V_xs_2,T_b] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,c_Wellfounded_Oacc(T_b,V_r_2)))) % 19.07/19.02 => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_lexord__append__rightI,axiom, % 19.07/19.02 ! [V_r_2,V_x_2,T_b,V_y_2] : % 19.07/19.02 ( ? [B_b,B_z] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_b),B_z) % 19.07/19.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_y_2))),c_List_Olexord(T_b,V_r_2))) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_lexord__Nil__left,axiom, % 19.07/19.02 ! [V_r_2,V_y_2,T_b] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_y_2)),c_List_Olexord(T_b,V_r_2))) % 19.07/19.02 <=> ? [B_a,B_x] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_x) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_last__list__update,axiom, % 19.07/19.02 ! [V_x,V_k,T_a,V_xs] : % 19.07/19.02 ( V_xs != c_List_Olist_ONil(T_a) % 19.07/19.02 => ( ( 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)) % 19.07/19.02 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = V_x ) % 19.07/19.02 & ( 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)) % 19.07/19.02 => 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) ) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_listsum__mono,axiom, % 19.07/19.02 ! [V_g_2,V_f_2,V_xs_2,T_b,T_c] : % 19.07/19.02 ( ( class_Groups_Omonoid__add(T_c) % 19.07/19.02 & class_Groups_Oordered__ab__semigroup__add(T_c) ) % 19.07/19.02 => ( ! [B_x] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 19.07/19.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 19.07/19.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_g_2),V_xs_2)))) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_last__ConsL,axiom, % 19.07/19.02 ! [V_x,T_a,V_xs] : % 19.07/19.02 ( V_xs = c_List_Olist_ONil(T_a) % 19.07/19.02 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_last__ConsR,axiom, % 19.07/19.02 ! [V_x,T_a,V_xs] : % 19.07/19.02 ( V_xs != c_List_Olist_ONil(T_a) % 19.07/19.02 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_last_Osimps,axiom, % 19.07/19.02 ! [V_x,T_a,V_xs] : % 19.07/19.02 ( ( V_xs = c_List_Olist_ONil(T_a) % 19.07/19.02 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) % 19.07/19.02 & ( V_xs != c_List_Olist_ONil(T_a) % 19.07/19.02 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_last__appendL,axiom, % 19.07/19.02 ! [V_xs,T_a,V_ys] : % 19.07/19.02 ( V_ys = c_List_Olist_ONil(T_a) % 19.07/19.02 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_last__appendR,axiom, % 19.07/19.02 ! [V_xs,T_a,V_ys] : % 19.07/19.02 ( V_ys != c_List_Olist_ONil(T_a) % 19.07/19.02 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_last__append,axiom, % 19.07/19.02 ! [V_xs,T_a,V_ys] : % 19.07/19.02 ( ( V_ys = c_List_Olist_ONil(T_a) % 19.07/19.02 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) % 19.07/19.02 & ( V_ys != c_List_Olist_ONil(T_a) % 19.07/19.02 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_last__map,axiom, % 19.07/19.02 ! [V_f_2,T_c,T_b,V_xs_2] : % 19.07/19.02 ( V_xs_2 != c_List_Olist_ONil(T_b) % 19.07/19.02 => c_List_Olast(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(V_f_2,c_List_Olast(T_b,V_xs_2)) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_last__in__set,axiom, % 19.07/19.02 ! [T_b,V_as_2] : % 19.07/19.02 ( V_as_2 != c_List_Olist_ONil(T_b) % 19.07/19.02 => hBOOL(hAPP(hAPP(c_member(T_b),c_List_Olast(T_b,V_as_2)),hAPP(c_List_Oset(T_b),V_as_2))) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_last__snoc,axiom, % 19.07/19.02 ! [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 ). % 19.07/19.02 % 19.07/19.02 fof(fact_last__drop,axiom, % 19.07/19.02 ! [V_xs,T_a,V_n] : % 19.07/19.02 ( 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))) % 19.07/19.02 => c_List_Olast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = c_List_Olast(T_a,V_xs) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_last__conv__nth,axiom, % 19.07/19.02 ! [T_a,V_xs] : % 19.07/19.02 ( V_xs != c_List_Olist_ONil(T_a) % 19.07/19.02 => 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))) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_lexord__linear,axiom, % 19.07/19.02 ! [V_y_2,V_x_2,V_r_2,T_b] : % 19.07/19.02 ( ! [B_a,B_b] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_a),B_b)),V_r_2)) % 19.07/19.02 | B_a = B_b % 19.07/19.02 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_b),B_a)),V_r_2)) ) % 19.07/19.02 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2))) % 19.07/19.02 | V_x_2 = V_y_2 % 19.07/19.02 | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_y_2),V_x_2)),c_List_Olexord(T_b,V_r_2))) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_lexord__irreflexive,axiom, % 19.07/19.02 ! [V_y_2,V_r_2,T_b] : % 19.07/19.02 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) % 19.07/19.02 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_y_2),V_y_2)),c_List_Olexord(T_b,V_r_2))) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_lists_Osimps,axiom, % 19.07/19.02 ! [V_A_2,V_a_2,T_b] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_a_2),c_List_Olists(T_b,V_A_2))) % 19.07/19.02 <=> ( V_a_2 = c_List_Olist_ONil(T_b) % 19.07/19.02 | ? [B_a,B_l] : % 19.07/19.02 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_l) % 19.07/19.02 & hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2)) % 19.07/19.02 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_l),c_List_Olists(T_b,V_A_2))) ) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_list__size__pointwise,axiom, % 19.07/19.02 ! [V_g_2,V_f_2,V_xs_2,T_b] : % 19.07/19.02 ( ! [B_x] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 19.07/19.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 19.07/19.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(T_b,V_f_2,V_xs_2)),c_List_Olist_Olist__size(T_b,V_g_2,V_xs_2))) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_butlast__take,axiom, % 19.07/19.02 ! [V_xs,T_a,V_n] : % 19.07/19.02 ( 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))) % 19.07/19.02 => 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) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_nth__take__lemma,axiom, % 19.07/19.02 ! [V_ys,V_xs,T_a,V_k] : % 19.07/19.02 ( 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))) % 19.07/19.02 => ( 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))) % 19.07/19.02 => ( ! [B_i] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_k)) % 19.07/19.02 => hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys),B_i) ) % 19.07/19.02 => hAPP(hAPP(c_List_Otake(T_a),V_k),V_xs) = hAPP(hAPP(c_List_Otake(T_a),V_k),V_ys) ) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_map__butlast,axiom, % 19.07/19.02 ! [V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Obutlast(T_c,V_xs_2)) = c_List_Obutlast(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_butlast__append,axiom, % 19.07/19.02 ! [V_xs,T_a,V_ys] : % 19.07/19.02 ( ( V_ys = c_List_Olist_ONil(T_a) % 19.07/19.02 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Obutlast(T_a,V_xs) ) % 19.07/19.02 & ( V_ys != c_List_Olist_ONil(T_a) % 19.07/19.02 => 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)) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_butlast_Osimps_I2_J,axiom, % 19.07/19.02 ! [V_x,T_a,V_xs] : % 19.07/19.02 ( ( V_xs = c_List_Olist_ONil(T_a) % 19.07/19.02 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) ) % 19.07/19.02 & ( V_xs != c_List_Olist_ONil(T_a) % 19.07/19.02 => 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)) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_in__set__butlastD,axiom, % 19.07/19.02 ! [V_xs_2,V_x_2,T_b] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2)))) % 19.07/19.02 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_distinct__butlast,axiom, % 19.07/19.02 ! [T_a,V_xs] : % 19.07/19.02 ( V_xs != c_List_Olist_ONil(T_a) % 19.07/19.02 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 19.07/19.02 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Obutlast(T_a,V_xs))) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_butlast_Osimps_I1_J,axiom, % 19.07/19.02 ! [T_a] : c_List_Obutlast(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 19.07/19.02 % 19.07/19.02 fof(fact_drop__butlast,axiom, % 19.07/19.02 ! [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)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_butlast__drop,axiom, % 19.07/19.02 ! [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)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_in__set__butlast__appendI,axiom, % 19.07/19.02 ! [V_ys_2,V_xs_2,V_x_2,T_b] : % 19.07/19.02 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2)))) % 19.07/19.02 | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_ys_2)))) ) % 19.07/19.02 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))))) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_butlast__snoc,axiom, % 19.07/19.02 ! [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 ). % 19.07/19.02 % 19.07/19.02 fof(fact_take__butlast,axiom, % 19.07/19.02 ! [V_xs,T_a,V_n] : % 19.07/19.02 ( 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))) % 19.07/19.02 => 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) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_length__butlast,axiom, % 19.07/19.02 ! [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)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_butlast__conv__take,axiom, % 19.07/19.02 ! [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) ). % 19.07/19.02 % 19.07/19.02 fof(fact_butlast__list__update,axiom, % 19.07/19.02 ! [V_x,V_xs,T_a,V_k] : % 19.07/19.02 ( ( 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)) % 19.07/19.02 => 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) ) % 19.07/19.02 & ( 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)) % 19.07/19.02 => 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) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_snoc__eq__iff__butlast,axiom, % 19.07/19.02 ! [V_ys_2,V_x_2,V_xs_2,T_b] : % 19.07/19.02 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))) = V_ys_2 % 19.07/19.02 <=> ( V_ys_2 != c_List_Olist_ONil(T_b) % 19.07/19.02 & c_List_Obutlast(T_b,V_ys_2) = V_xs_2 % 19.07/19.02 & c_List_Olast(T_b,V_ys_2) = V_x_2 ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_append__butlast__last__id,axiom, % 19.07/19.02 ! [T_a,V_xs] : % 19.07/19.02 ( V_xs != c_List_Olist_ONil(T_a) % 19.07/19.02 => 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 ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_transpose__aux__max,axiom, % 19.07/19.02 ! [V_xss_2,T_c,V_xs_2,T_b] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))),c_List_Ofoldr(tc_List_Olist(T_c),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_c)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_c))),V_xss_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),c_List_Ofoldr(tc_List_Olist(T_c),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_c)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_c)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_c)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_List_Ofilter(tc_List_Olist(T_c),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_c)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_List_Olist(T_c),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_c)))),V_xss_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ). % 19.07/19.02 % 19.07/19.02 fof(fact_partition__set,axiom, % 19.07/19.02 ! [V_no_2,V_yes_2,V_xs_2,V_Pa_2,T_b] : % 19.07/19.02 ( c_List_Opartition(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_yes_2),V_no_2) % 19.07/19.02 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_yes_2)),hAPP(c_List_Oset(T_b),V_no_2)) = hAPP(c_List_Oset(T_b),V_xs_2) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_length__filter__map,axiom, % 19.07/19.02 ! [V_xs_2,V_f_2,T_c,V_Pa_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),hAPP(c_List_Ofilter(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_Pa_2),V_f_2)),V_xs_2)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_length__filter__le,axiom, % 19.07/19.02 ! [V_xs_2,V_Pa_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ). % 19.07/19.02 % 19.07/19.02 fof(fact_filter__is__subset,axiom, % 19.07/19.02 ! [V_xs_2,V_Pa_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ). % 19.07/19.02 % 19.07/19.02 fof(fact_filter_Osimps_I1_J,axiom, % 19.07/19.02 ! [V_Pa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Pa_2),c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b) ). % 19.07/19.02 % 19.07/19.02 fof(fact_filter__empty__conv,axiom, % 19.07/19.02 ! [V_xs_2,V_Pa_2,T_b] : % 19.07/19.02 ( hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) = c_List_Olist_ONil(T_b) % 19.07/19.02 <=> ! [B_x] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 19.07/19.02 => ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_filter__id__conv,axiom, % 19.07/19.02 ! [V_xs_2,V_Pa_2,T_b] : % 19.07/19.02 ( hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) = V_xs_2 % 19.07/19.02 <=> ! [B_x] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 19.07/19.02 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_filter__insort__triv,axiom, % 19.07/19.02 ! [V_xs_2,V_f_2,T_b,V_x_2,V_Pa_2,T_c] : % 19.07/19.02 ( class_Orderings_Olinorder(T_c) % 19.07/19.02 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 19.07/19.02 => hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_distinct__filter,axiom, % 19.07/19.02 ! [V_Pa_2,V_xs_2,T_b] : % 19.07/19.02 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 19.07/19.02 => hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_remove1__filter__not,axiom, % 19.07/19.02 ! [V_xs_2,T_b,V_x_2,V_Pa_2] : % 19.07/19.02 ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 19.07/19.02 => c_List_Oremove1(T_b,V_x_2,hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_filter__remove1,axiom, % 19.07/19.02 ! [V_xs_2,V_x_2,V_Qa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Qa_2),c_List_Oremove1(T_b,V_x_2,V_xs_2)) = c_List_Oremove1(T_b,V_x_2,hAPP(c_List_Ofilter(T_b,V_Qa_2),V_xs_2)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_filter__filter,axiom, % 19.07/19.02 ! [V_xs_2,V_Qa_2,V_Pa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(c_List_Ofilter(T_b,V_Qa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Qa_2)),V_Pa_2)),V_xs_2) ). % 19.07/19.02 % 19.07/19.02 fof(fact_partition__filter1,axiom, % 19.07/19.02 ! [V_xs_2,V_Pa_2,T_b] : hAPP(c_Product__Type_Ofst(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Opartition(T_b,V_Pa_2,V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) ). % 19.07/19.02 % 19.07/19.02 fof(fact_sum__length__filter__compl,axiom, % 19.07/19.02 ! [V_xs_2,V_Pa_2,T_b] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_Pa_2)),V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) ). % 19.07/19.02 % 19.07/19.02 fof(fact_filter_Osimps_I2_J,axiom, % 19.07/19.02 ! [V_xs_2,T_b,V_x_2,V_Pa_2] : % 19.07/19.02 ( ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 19.07/19.02 => hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) ) % 19.07/19.02 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 19.07/19.02 => hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_filter__append,axiom, % 19.07/19.02 ! [V_ys_2,V_xs_2,V_Pa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_ys_2)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_set__filter,axiom, % 19.07/19.02 ! [V_xs_2,V_Pa_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),hAPP(c_List_Oset(T_b),V_xs_2)))),V_Pa_2)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_partition__filter__conv,axiom, % 19.07/19.02 ! [V_xs_2,V_f_2,T_b] : c_List_Opartition(T_b,V_f_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_f_2),V_xs_2)),hAPP(c_List_Ofilter(T_b,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,T_b,c_fNot),V_f_2)),V_xs_2)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_filter__map,axiom, % 19.07/19.02 ! [V_xs_2,V_f_2,T_c,V_Pa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_Pa_2),V_f_2)),V_xs_2)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_partition__filter2,axiom, % 19.07/19.02 ! [V_xs_2,V_Pa_2,T_b] : hAPP(c_Product__Type_Osnd(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Opartition(T_b,V_Pa_2,V_xs_2)) = hAPP(c_List_Ofilter(T_b,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,T_b,c_fNot),V_Pa_2)),V_xs_2) ). % 19.07/19.02 % 19.07/19.02 fof(fact_length__filter__less,axiom, % 19.07/19.02 ! [V_Pa_2,V_xs_2,V_x_2,T_b] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 19.07/19.02 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 19.07/19.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_set__minus__filter__out,axiom, % 19.07/19.02 ! [V_y_2,V_xs_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_List_Oset(T_b),hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_y_2))),V_xs_2)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_partition__P,axiom, % 19.07/19.02 ! [V_no_2,V_yes_2,V_xs_2,V_Pa_2,T_b] : % 19.07/19.02 ( c_List_Opartition(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_yes_2),V_no_2) % 19.07/19.02 => ( ! [B_x] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_yes_2))) % 19.07/19.02 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 19.07/19.02 & ! [B_x] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_no_2))) % 19.07/19.02 => ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_partition_Osimps_I1_J,axiom, % 19.07/19.02 ! [V_Pa_2,T_b] : c_List_Opartition(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_List_Olist_ONil(T_b)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_filter__in__sublist,axiom, % 19.07/19.02 ! [V_s_2,V_xs_2,T_b] : % 19.07/19.02 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 19.07/19.02 => hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_s_2)))),V_xs_2) = c_List_Osublist(T_b,V_xs_2,V_s_2) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_partition_Osimps_I2_J,axiom, % 19.07/19.02 ! [V_xs_2,V_x_2,V_Pa_2,T_b] : c_List_Opartition(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_List_Olist(T_b)),c_COMBS(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_List_Olist(T_b)),hAPP(c_If(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(V_Pa_2,V_x_2)))),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_List_Olist(T_b)),c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(c_List_Olist_OCons(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_List_Olist(T_b)),c_COMBB(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_List_Olist(T_b))),c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(c_List_Olist_OCons(T_b),V_x_2)))),c_List_Opartition(T_b,V_Pa_2,V_xs_2)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_length__filter__conv__card,axiom, % 19.07/19.02 ! [V_xs_2,V_p_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_p_2),V_xs_2)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,tc_Nat_Onat),V_p_2),hAPP(c_List_Onth(T_b),V_xs_2))))) ). % 19.07/19.02 % 19.07/19.02 fof(fact_map__filter__def,axiom, % 19.07/19.02 ! [V_xs_2,V_f_2,T_b,T_c] : c_List_Omap__filter(T_c,T_b,V_f_2,V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_c,c_Option_Othe(T_b)),V_f_2)),hAPP(c_List_Ofilter(T_c,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),hAPP(hAPP(c_COMBC(T_c,tc_Option_Ooption(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_b),tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool),T_c),c_fequal),V_f_2)),c_Option_Ooption_ONone(T_b)))),V_xs_2)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_transpose__max__length,axiom, % 19.07/19.02 ! [V_xs_2,T_b] : c_List_Ofoldr(tc_List_Olist(T_b),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_b)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_b)))),V_xs_2)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_map__of__filter__in,axiom, % 19.07/19.02 ! [V_Pa_2,V_z_2,V_k_2,V_xs_2,T_b,T_c] : % 19.07/19.02 ( hAPP(c_Map_Omap__of(T_c,T_b,V_xs_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_z_2) % 19.07/19.02 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_k_2),V_z_2)) % 19.07/19.02 => hAPP(c_Map_Omap__of(T_c,T_b,hAPP(c_List_Ofilter(tc_prod(T_c,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_HOL_Obool),V_Pa_2)),V_xs_2)),V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_z_2) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_transpose__map__map,axiom, % 19.07/19.02 ! [V_xs_2,V_f_2,T_c,T_b] : c_List_Otranspose(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_b)),hAPP(c_List_Omap(T_c,T_b),V_f_2)),V_xs_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_b)),hAPP(c_List_Omap(T_c,T_b),V_f_2)),c_List_Otranspose(T_c,V_xs_2)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_map__filter__simps_I1_J,axiom, % 19.07/19.02 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] : c_List_Omap__filter(T_c,T_b,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(c_Option_Ooption_Ooption__case(tc_List_Olist(T_b),T_b,c_List_Omap__filter(T_c,T_b,V_f_2,V_xs_2),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Omap__filter(T_c,T_b,V_f_2,V_xs_2))),hAPP(V_f_2,V_x_2)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_transpose_Osimps_I2_J,axiom, % 19.07/19.02 ! [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) ). % 19.07/19.02 % 19.07/19.02 fof(fact_transpose__empty,axiom, % 19.07/19.02 ! [V_xs_2,T_b] : % 19.07/19.02 ( c_List_Otranspose(T_b,V_xs_2) = c_List_Olist_ONil(tc_List_Olist(T_b)) % 19.07/19.02 <=> ! [B_x] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2))) % 19.07/19.02 => B_x = c_List_Olist_ONil(T_b) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_transpose_Osimps_I1_J,axiom, % 19.07/19.02 ! [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)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_map__filter__simps_I2_J,axiom, % 19.07/19.02 ! [V_f_2,T_b,T_c] : c_List_Omap__filter(T_c,T_b,V_f_2,c_List_Olist_ONil(T_c)) = c_List_Olist_ONil(T_b) ). % 19.07/19.02 % 19.07/19.02 fof(fact_sublist__shift__lemma__Suc,axiom, % 19.07/19.02 ! [V_is_2,V_xs_2,V_Pa_2,T_b] : hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(T_b,tc_Nat_Onat)),V_Pa_2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(T_b,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(T_b,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),V_is_2))) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(T_b,tc_Nat_Onat)),V_Pa_2),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),V_is_2)))) ). % 19.07/19.02 % 19.07/19.02 fof(fact_select__weigth__drop__zero,axiom, % 19.07/19.02 ! [V_xs_2,T_b] : c_Random_Oselect__weight(T_b,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),V_xs_2)) = c_Random_Oselect__weight(T_b,V_xs_2) ). % 19.07/19.02 % 19.07/19.02 fof(fact_pick__drop__zero,axiom, % 19.07/19.02 ! [V_xs_2,T_b] : c_Random_Opick(T_b,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),V_xs_2)) = c_Random_Opick(T_b,V_xs_2) ). % 19.07/19.02 % 19.07/19.02 fof(fact_nth__transpose,axiom, % 19.07/19.02 ! [V_xs_2,T_b,V_i_2] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)))) % 19.07/19.02 => hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),c_List_Otranspose(T_b,V_xs_2)),V_i_2) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,T_b),c_List_Onth(T_b)),V_i_2)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_xs_2)) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_length__transpose,axiom, % 19.07/19.02 ! [V_xs_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)) = c_List_Ofoldr(tc_List_Olist(T_b),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_b)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_map__filter__map__filter,axiom, % 19.07/19.02 ! [V_xs_2,V_Pa_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2)) = c_List_Omap__filter(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,tc_Option_Ooption(T_b),tc_Option_Ooption(T_b)),hAPP(hAPP(c_COMBS(T_c,tc_Option_Ooption(T_b),tc_fun(tc_Option_Ooption(T_b),tc_Option_Ooption(T_b))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(T_b),tc_fun(tc_Option_Ooption(T_b),tc_Option_Ooption(T_b))),T_c),c_If(tc_Option_Ooption(T_b))),V_Pa_2)),hAPP(hAPP(c_COMBB(T_b,tc_Option_Ooption(T_b),T_c),c_Option_Ooption_OSome(T_b)),V_f_2))),c_Option_Ooption_ONone(T_b)),V_xs_2) ). % 19.07/19.02 % 19.07/19.02 fof(fact_insort__key__remove1,axiom, % 19.07/19.02 ! [V_f_2,V_xs_2,V_a_2,T_b,T_c] : % 19.07/19.02 ( class_Orderings_Olinorder(T_c) % 19.07/19.02 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 19.07/19.02 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) % 19.07/19.02 => ( hAPP(c_List_Ohd(T_b),hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(T_c,tc_HOL_Obool,T_b),hAPP(c_fequal,hAPP(V_f_2,V_a_2))),V_f_2)),V_xs_2)) = V_a_2 % 19.07/19.02 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_a_2),c_List_Oremove1(T_b,V_a_2,V_xs_2)) = V_xs_2 ) ) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_sublist__def,axiom, % 19.07/19.02 ! [V_A_2,V_xs_2,T_b] : c_List_Osublist(T_b,V_xs_2,V_A_2) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_b,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(T_b,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))))) ). % 19.07/19.02 % 19.07/19.02 fof(fact_sorted_ONil,axiom, % 19.07/19.02 ! [T_a] : % 19.07/19.02 ( class_Orderings_Olinorder(T_a) % 19.07/19.02 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_sorted__single,axiom, % 19.07/19.02 ! [V_x,T_a] : % 19.07/19.02 ( class_Orderings_Olinorder(T_a) % 19.07/19.02 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_sorted__same,axiom, % 19.07/19.02 ! [V_xs_2,V_g_2,T_b] : % 19.07/19.02 ( class_Orderings_Olinorder(T_b) % 19.07/19.02 => c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),hAPP(V_g_2,V_xs_2))),V_xs_2)) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_sorted__map__same,axiom, % 19.07/19.02 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] : % 19.07/19.02 ( class_Orderings_Olinorder(T_b) % 19.07/19.02 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,hAPP(hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_c),c_fequal),V_f_2)),hAPP(V_g_2,V_xs_2))),V_xs_2))) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_sorted__filter,axiom, % 19.07/19.02 ! [V_Pa_2,V_xs_2,V_f_2,T_c,T_b] : % 19.07/19.02 ( class_Orderings_Olinorder(T_b) % 19.07/19.02 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) % 19.07/19.02 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2))) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_length__upt,axiom, % 19.07/19.02 ! [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) ). % 19.07/19.02 % 19.07/19.02 fof(fact_sorted__butlast,axiom, % 19.07/19.02 ! [V_xs,T_a] : % 19.07/19.02 ( class_Orderings_Olinorder(T_a) % 19.07/19.02 => ( V_xs != c_List_Olist_ONil(T_a) % 19.07/19.02 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 19.07/19.02 => c_List_Olinorder__class_Osorted(T_a,c_List_Obutlast(T_a,V_xs)) ) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_upt__eq__Cons__conv,axiom, % 19.07/19.02 ! [V_xs_2,V_x_2,V_j_2,V_i_2] : % 19.07/19.02 ( c_List_Oupt(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_x_2),V_xs_2) % 19.07/19.02 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_j_2)) % 19.07/19.02 & V_i_2 = V_x_2 % 19.07/19.02 & 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 ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_sorted__append,axiom, % 19.07/19.02 ! [V_ys_2,V_xs_2,T_b] : % 19.07/19.02 ( class_Orderings_Olinorder(T_b) % 19.07/19.02 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) % 19.07/19.02 <=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2) % 19.07/19.02 & c_List_Olinorder__class_Osorted(T_b,V_ys_2) % 19.07/19.02 & ! [B_x] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 19.07/19.02 => ! [B_xa] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(c_List_Oset(T_b),V_ys_2))) % 19.07/19.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa)) ) ) ) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_upt__Suc,axiom, % 19.07/19.02 ! [V_j,V_i] : % 19.07/19.02 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 19.07/19.02 => 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))) ) % 19.07/19.02 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 19.07/19.02 => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_upt__Suc__append,axiom, % 19.07/19.02 ! [V_j,V_i] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 19.07/19.02 => 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))) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_upt__add__eq__append,axiom, % 19.07/19.02 ! [V_k,V_j,V_i] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 19.07/19.02 => 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))) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_sorted__many,axiom, % 19.07/19.02 ! [V_zs,V_y,V_x,T_a] : % 19.07/19.02 ( class_Orderings_Olinorder(T_a) % 19.07/19.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 19.07/19.02 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs)) % 19.07/19.02 => 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))) ) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_sorted__many__eq,axiom, % 19.07/19.02 ! [V_zs_2,V_y_2,V_x_2,T_b] : % 19.07/19.02 ( class_Orderings_Olinorder(T_b) % 19.07/19.02 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_zs_2))) % 19.07/19.02 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 19.07/19.02 & c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_zs_2)) ) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_take__upt,axiom, % 19.07/19.02 ! [V_n,V_m,V_i] : % 19.07/19.02 ( 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)) % 19.07/19.02 => 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)) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_upt__conv__Nil,axiom, % 19.07/19.02 ! [V_i,V_j] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i)) % 19.07/19.02 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_upt__eq__Nil__conv,axiom, % 19.07/19.02 ! [V_j_2,V_i_2] : % 19.07/19.02 ( c_List_Oupt(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Nat_Onat) % 19.07/19.02 <=> ( V_j_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 19.07/19.02 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_sorted__Cons,axiom, % 19.07/19.02 ! [V_xs_2,V_x_2,T_b] : % 19.07/19.02 ( class_Orderings_Olinorder(T_b) % 19.07/19.02 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) % 19.07/19.02 <=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2) % 19.07/19.02 & ! [B_x] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 19.07/19.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_drop__upt,axiom, % 19.07/19.02 ! [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) ). % 19.07/19.02 % 19.07/19.02 fof(fact_sorted__drop,axiom, % 19.07/19.02 ! [V_n,V_xs,T_a] : % 19.07/19.02 ( class_Orderings_Olinorder(T_a) % 19.07/19.02 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 19.07/19.02 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_hd__upt,axiom, % 19.07/19.02 ! [V_j,V_i] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 19.07/19.02 => hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(V_i,V_j)) = V_i ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_upt__0,axiom, % 19.07/19.02 ! [V_i] : c_List_Oupt(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat) ). % 19.07/19.02 % 19.07/19.02 fof(fact_sorted_Oequations_I1_J,axiom, % 19.07/19.02 ! [T_a] : % 19.07/19.02 ( class_Orderings_Olinorder(T_a) % 19.07/19.02 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_sorted__take,axiom, % 19.07/19.02 ! [V_n,V_xs,T_a] : % 19.07/19.02 ( class_Orderings_Olinorder(T_a) % 19.07/19.02 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 19.07/19.02 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_atLeastLessThan__upt,axiom, % 19.07/19.02 ! [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)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_set__upt,axiom, % 19.07/19.02 ! [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) ). % 19.07/19.02 % 19.07/19.02 fof(fact_sorted__distinct__set__unique,axiom, % 19.07/19.02 ! [V_ys_2,V_xs_2,T_b] : % 19.07/19.02 ( class_Orderings_Olinorder(T_b) % 19.07/19.02 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2) % 19.07/19.02 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 19.07/19.02 => ( c_List_Olinorder__class_Osorted(T_b,V_ys_2) % 19.07/19.02 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2)) % 19.07/19.02 => ( hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2) % 19.07/19.02 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_sorted__insort,axiom, % 19.07/19.02 ! [V_xs_2,V_x_2,T_b] : % 19.07/19.02 ( class_Orderings_Olinorder(T_b) % 19.07/19.02 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2)) % 19.07/19.02 <=> c_List_Olinorder__class_Osorted(T_b,V_xs_2) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_distinct__upt,axiom, % 19.07/19.02 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(V_i,V_j))) ). % 19.07/19.02 % 19.07/19.02 fof(fact_sorted__remove1,axiom, % 19.07/19.02 ! [V_a,V_xs,T_a] : % 19.07/19.02 ( class_Orderings_Olinorder(T_a) % 19.07/19.02 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 19.07/19.02 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremove1(T_a,V_a,V_xs)) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_sorted__upt,axiom, % 19.07/19.02 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(V_i,V_j)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_sorted__upto,axiom, % 19.07/19.02 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(V_i,V_j)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_sorted__list__of__set__range,axiom, % 19.07/19.02 ! [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) ). % 19.07/19.02 % 19.07/19.02 fof(fact_sorted__insort__insert,axiom, % 19.07/19.02 ! [V_x_2,V_xs_2,T_b] : % 19.07/19.02 ( class_Orderings_Olinorder(T_b) % 19.07/19.02 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2) % 19.07/19.02 => c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2)) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_upt__conv__Cons,axiom, % 19.07/19.02 ! [V_j,V_i] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 19.07/19.02 => 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)) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_upt__rec,axiom, % 19.07/19.02 ! [V_j,V_i] : % 19.07/19.02 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 19.07/19.02 => 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)) ) % 19.07/19.02 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 19.07/19.02 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_sorted__tl,axiom, % 19.07/19.02 ! [V_xs,T_a] : % 19.07/19.02 ( class_Orderings_Olinorder(T_a) % 19.07/19.02 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 19.07/19.02 => c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Otl(T_a),V_xs)) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_upt__rec__number__of,axiom, % 19.07/19.02 ! [V_n,V_m] : % 19.07/19.02 ( ( 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))) % 19.07/19.02 => 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))) ) % 19.07/19.02 & ( ~ 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))) % 19.07/19.02 => 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) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_sorted__insort__key,axiom, % 19.07/19.02 ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] : % 19.07/19.02 ( class_Orderings_Olinorder(T_b) % 19.07/19.02 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2))) % 19.07/19.02 <=> c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_sorted__map__remove1,axiom, % 19.07/19.02 ! [V_x_2,V_xs_2,V_f_2,T_c,T_b] : % 19.07/19.02 ( class_Orderings_Olinorder(T_b) % 19.07/19.02 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) % 19.07/19.02 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oremove1(T_c,V_x_2,V_xs_2))) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_sorted__insort__insert__key,axiom, % 19.07/19.02 ! [V_x_2,V_xs_2,V_f_2,T_c,T_b] : % 19.07/19.02 ( class_Orderings_Olinorder(T_b) % 19.07/19.02 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) % 19.07/19.02 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2))) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_map__Suc__upt,axiom, % 19.07/19.02 ! [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)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_last__upt,axiom, % 19.07/19.02 ! [V_j,V_i] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 19.07/19.02 => 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)) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_filter__insort,axiom, % 19.07/19.02 ! [V_x_2,V_Pa_2,V_xs_2,V_f_2,T_c,T_b] : % 19.07/19.02 ( class_Orderings_Olinorder(T_b) % 19.07/19.02 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) % 19.07/19.02 => ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 19.07/19.02 => hAPP(c_List_Ofilter(T_c,V_Pa_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2)) ) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_map__nth,axiom, % 19.07/19.02 ! [V_xs_2,T_b] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),hAPP(c_List_Onth(T_b),V_xs_2)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) = V_xs_2 ). % 19.07/19.02 % 19.07/19.02 fof(fact_atLeastAtMost__upt,axiom, % 19.07/19.02 ! [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))) ). % 19.07/19.02 % 19.07/19.02 fof(fact_atLeast__upt,axiom, % 19.07/19.02 ! [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)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_setsum__set__upt__conv__listsum__nat,axiom, % 19.07/19.02 ! [V_n_2,V_m_2,V_f_2,T_b] : % 19.07/19.02 ( class_Groups_Ocomm__monoid__add(T_b) % 19.07/19.02 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_m_2,V_n_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),V_f_2),c_List_Oupt(V_m_2,V_n_2))) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_interv__listsum__conv__setsum__set__nat,axiom, % 19.07/19.02 ! [V_n_2,V_m_2,V_f_2,T_b] : % 19.07/19.02 ( class_Groups_Ocomm__monoid__add(T_b) % 19.07/19.02 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),V_f_2),c_List_Oupt(V_m_2,V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_m_2,V_n_2))) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_nth__upt,axiom, % 19.07/19.02 ! [V_j,V_k,V_i] : % 19.07/19.02 ( 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)) % 19.07/19.02 => 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) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_greaterThanAtMost__upt,axiom, % 19.07/19.02 ! [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))) ). % 19.07/19.02 % 19.07/19.02 fof(fact_sorted_Oequations_I2_J,axiom, % 19.07/19.02 ! [V_a1_2,V_a2_2,T_b] : % 19.07/19.02 ( class_Orderings_Olinorder(T_b) % 19.07/19.02 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a2_2),V_a1_2)) % 19.07/19.02 <=> ( ! [B_x] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_a1_2))) % 19.07/19.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a2_2),B_x)) ) % 19.07/19.02 & c_List_Olinorder__class_Osorted(T_b,V_a1_2) ) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_greaterThanLessThan__upt,axiom, % 19.07/19.02 ! [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)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_nth__map__upt,axiom, % 19.07/19.02 ! [V_f_2,T_b,V_m_2,V_n_2,V_i_2] : % 19.07/19.02 ( 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))) % 19.07/19.02 => hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),V_f_2),c_List_Oupt(V_m_2,V_n_2))),V_i_2) = hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_i_2)) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_sorted__list__of__set,axiom, % 19.07/19.02 ! [V_A_2,T_b] : % 19.07/19.02 ( class_Orderings_Olinorder(T_b) % 19.07/19.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 19.07/19.02 => ( hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)) = V_A_2 % 19.07/19.02 & c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)) % 19.07/19.02 & hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2))) ) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_atMost__upto,axiom, % 19.07/19.02 ! [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))) ). % 19.07/19.02 % 19.07/19.02 fof(fact_insort__remove1,axiom, % 19.07/19.02 ! [V_xs_2,V_a_2,T_b] : % 19.07/19.02 ( class_Orderings_Olinorder(T_b) % 19.07/19.02 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 19.07/19.02 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2) % 19.07/19.02 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_a_2),c_List_Oremove1(T_b,V_a_2,V_xs_2)) = V_xs_2 ) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_sorted__equals__nth__mono,axiom, % 19.07/19.02 ! [V_xs_2,T_b] : % 19.07/19.02 ( class_Orderings_Olinorder(T_b) % 19.07/19.02 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2) % 19.07/19.02 <=> ! [B_j] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 19.07/19.02 => ! [B_i] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j)) % 19.07/19.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i)),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_j))) ) ) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_sorted__nth__mono,axiom, % 19.07/19.02 ! [V_j,V_i,V_xs,T_a] : % 19.07/19.02 ( class_Orderings_Olinorder(T_a) % 19.07/19.02 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 19.07/19.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 19.07/19.02 => ( 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))) % 19.07/19.02 => 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))) ) ) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_map__sorted__distinct__set__unique,axiom, % 19.07/19.02 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] : % 19.07/19.02 ( class_Orderings_Olinorder(T_c) % 19.07/19.02 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_ys_2))) % 19.07/19.02 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) % 19.07/19.02 => ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))) % 19.07/19.02 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2)) % 19.07/19.02 => ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2))) % 19.07/19.02 => ( hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2) % 19.07/19.02 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_sublist__shift__lemma,axiom, % 19.07/19.02 ! [V_i_2,V_xs_2,V_A_2,T_b] : hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_b,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(T_b,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),c_List_Oupt(V_i_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))))) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_b,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(T_b,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(T_b,tc_Nat_Onat),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_prod(T_b,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),V_i_2))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))))) ). % 19.07/19.02 % 19.07/19.02 fof(fact_transpose__rectangle,axiom, % 19.07/19.02 ! [V_n_2,T_b,V_xs_2] : % 19.07/19.02 ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b)) % 19.07/19.02 => V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 19.07/19.02 => ( ! [B_i] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2))) % 19.07/19.02 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),B_i)) = V_n_2 ) % 19.07/19.02 => c_List_Otranspose(T_b,V_xs_2) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(T_b)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(T_b)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,T_b)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_Nat_Onat,T_b),tc_Nat_Onat),c_List_Onth(T_b)),hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_transpose_Opsimps_I2_J,axiom, % 19.07/19.02 ! [V_xss_2,T_b] : % 19.07/19.02 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_b)),c_List_Otranspose__rel(T_b)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xss_2))) % 19.07/19.02 => c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xss_2)) = c_List_Otranspose(T_b,V_xss_2) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_transpose_Opsimps_I1_J,axiom, % 19.07/19.02 ! [T_b] : % 19.07/19.02 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_b)),c_List_Otranspose__rel(T_b)),c_List_Olist_ONil(tc_List_Olist(T_b)))) % 19.07/19.02 => c_List_Otranspose(T_b,c_List_Olist_ONil(tc_List_Olist(T_b))) = c_List_Olist_ONil(tc_List_Olist(T_b)) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_transpose__column,axiom, % 19.07/19.02 ! [V_i_2,V_xs_2,T_b] : % 19.07/19.02 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2))) % 19.07/19.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2))) % 19.07/19.02 => hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,T_b),c_List_Onth(T_b)),V_i_2)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),c_List_Otranspose(T_b,V_xs_2))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),V_i_2) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_transpose__aux__filter__head,axiom, % 19.07/19.02 ! [V_xss_2,T_b] : c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),c_COMBK(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))))),V_xss_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),T_b),c_List_Ohd(T_b)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_b)))),V_xss_2)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_inj__on__rev,axiom, % 19.07/19.02 ! [V_A_2,T_b] : c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Orev(T_b),V_A_2) ). % 19.07/19.02 % 19.07/19.02 fof(fact_filter__concat,axiom, % 19.07/19.02 ! [V_xs_2,V_p_2,T_b] : hAPP(c_List_Ofilter(T_b,V_p_2),c_List_Oconcat(T_b,V_xs_2)) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Ofilter(T_b,V_p_2)),V_xs_2)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_length__concat,axiom, % 19.07/19.02 ! [V_xss_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oconcat(T_b,V_xss_2)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xss_2)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_rev_Osimps_I2_J,axiom, % 19.07/19.02 ! [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))) ). % 19.07/19.02 % 19.07/19.02 fof(fact_rev__eq__Cons__iff,axiom, % 19.07/19.02 ! [V_ys_2,V_y_2,V_xs_2,T_b] : % 19.07/19.02 ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2) % 19.07/19.02 <=> V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),hAPP(c_List_Orev(T_b),V_ys_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),c_List_Olist_ONil(T_b))) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_rev__is__Nil__conv,axiom, % 19.07/19.02 ! [V_xs_2,T_b] : % 19.07/19.02 ( hAPP(c_List_Orev(T_b),V_xs_2) = c_List_Olist_ONil(T_b) % 19.07/19.02 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_Nil__is__rev__conv,axiom, % 19.07/19.02 ! [V_xs_2,T_b] : % 19.07/19.02 ( c_List_Olist_ONil(T_b) = hAPP(c_List_Orev(T_b),V_xs_2) % 19.07/19.02 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_concat_Osimps_I1_J,axiom, % 19.07/19.02 ! [T_a] : c_List_Oconcat(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(T_a) ). % 19.07/19.02 % 19.07/19.02 fof(fact_rev_Osimps_I1_J,axiom, % 19.07/19.02 ! [T_a] : hAPP(c_List_Orev(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 19.07/19.02 % 19.07/19.02 fof(fact_concat__eq__Nil__conv,axiom, % 19.07/19.02 ! [V_xss_2,T_b] : % 19.07/19.02 ( c_List_Oconcat(T_b,V_xss_2) = c_List_Olist_ONil(T_b) % 19.07/19.02 <=> ! [B_x] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2))) % 19.07/19.02 => B_x = c_List_Olist_ONil(T_b) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_Nil__eq__concat__conv,axiom, % 19.07/19.02 ! [V_xss_2,T_b] : % 19.07/19.02 ( c_List_Olist_ONil(T_b) = c_List_Oconcat(T_b,V_xss_2) % 19.07/19.02 <=> ! [B_x] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2))) % 19.07/19.02 => B_x = c_List_Olist_ONil(T_b) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_singleton__rev__conv,axiom, % 19.07/19.02 ! [V_xs_2,V_x_2,T_b] : % 19.07/19.02 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) = hAPP(c_List_Orev(T_b),V_xs_2) % 19.07/19.02 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_rev__singleton__conv,axiom, % 19.07/19.02 ! [V_x_2,V_xs_2,T_b] : % 19.07/19.02 ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) % 19.07/19.02 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_concat_Osimps_I2_J,axiom, % 19.07/19.02 ! [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)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_map__concat,axiom, % 19.07/19.02 ! [V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oconcat(T_c,V_xs_2)) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_b)),hAPP(c_List_Omap(T_c,T_b),V_f_2)),V_xs_2)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_rev__map,axiom, % 19.07/19.02 ! [V_xs_2,V_f_2,T_c,T_b] : hAPP(c_List_Orev(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Orev(T_c),V_xs_2)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_rev__concat,axiom, % 19.07/19.02 ! [V_xs_2,T_b] : hAPP(c_List_Orev(T_b),c_List_Oconcat(T_b,V_xs_2)) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Orev(T_b)),hAPP(c_List_Orev(tc_List_Olist(T_b)),V_xs_2))) ). % 19.07/19.02 % 19.07/19.02 fof(fact_rev__foldl__cons,axiom, % 19.07/19.02 ! [V_xs_2,T_b] : hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_b),T_b,hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b)),V_xs_2) ). % 19.07/19.02 % 19.07/19.02 fof(fact_concat__conv__foldl,axiom, % 19.07/19.02 ! [V_xss_2,T_b] : c_List_Oconcat(T_b,V_xss_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Oappend(T_b),c_List_Olist_ONil(T_b)),V_xss_2) ). % 19.07/19.02 % 19.07/19.02 fof(fact_foldl__conv__concat,axiom, % 19.07/19.02 ! [V_xss_2,V_xs_2,T_b] : hAPP(c_List_Ofoldl(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Oappend(T_b),V_xs_2),V_xss_2) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),c_List_Oconcat(T_b,V_xss_2)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_concat__append,axiom, % 19.07/19.02 ! [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)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_rev__append,axiom, % 19.07/19.02 ! [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)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_distinct__rev,axiom, % 19.07/19.02 ! [V_xs_2,T_b] : % 19.07/19.02 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orev(T_b),V_xs_2))) % 19.07/19.02 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_set__concat,axiom, % 19.07/19.02 ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Oconcat(T_b,V_xs_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)),c_List_Oset(T_b)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_length__rev,axiom, % 19.07/19.02 ! [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) ). % 19.07/19.02 % 19.07/19.02 fof(fact_listsum__rev,axiom, % 19.07/19.02 ! [V_xs,T_a] : % 19.07/19.02 ( class_Groups_Ocomm__monoid__add(T_a) % 19.07/19.02 => 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) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_rev__rev__ident,axiom, % 19.07/19.02 ! [V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(c_List_Orev(T_a),V_xs)) = V_xs ). % 19.07/19.02 % 19.07/19.02 fof(fact_rev__swap,axiom, % 19.07/19.02 ! [V_ys_2,V_xs_2,T_b] : % 19.07/19.02 ( hAPP(c_List_Orev(T_b),V_xs_2) = V_ys_2 % 19.07/19.02 <=> V_xs_2 = hAPP(c_List_Orev(T_b),V_ys_2) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_rev__is__rev__conv,axiom, % 19.07/19.02 ! [V_ys_2,V_xs_2,T_b] : % 19.07/19.02 ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(c_List_Orev(T_b),V_ys_2) % 19.07/19.02 <=> V_xs_2 = V_ys_2 ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_foldl__foldr,axiom, % 19.07/19.02 ! [V_xs_2,V_a_2,V_f_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),V_xs_2) = c_List_Ofoldr(T_c,T_b,hAPP(c_COMBC(T_b,T_c,T_b),V_f_2),hAPP(c_List_Orev(T_c),V_xs_2),V_a_2) ). % 19.07/19.02 % 19.07/19.02 fof(fact_foldr__foldl,axiom, % 19.07/19.02 ! [V_a_2,V_xs_2,V_f_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_f_2,V_xs_2,V_a_2) = hAPP(c_List_Ofoldl(T_b,T_c,hAPP(c_COMBC(T_c,T_b,T_b),V_f_2),V_a_2),hAPP(c_List_Orev(T_c),V_xs_2)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_set__rev,axiom, % 19.07/19.02 ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Orev(T_b),V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2) ). % 19.07/19.02 % 19.07/19.02 fof(fact_zip__rev,axiom, % 19.07/19.02 ! [V_ys,T_b,V_xs,T_a] : % 19.07/19.02 ( 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_ys) % 19.07/19.02 => 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)) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_rev__filter,axiom, % 19.07/19.02 ! [V_xs_2,V_Pa_2,T_b] : hAPP(c_List_Orev(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(c_List_Orev(T_b),V_xs_2)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_hd__rev,axiom, % 19.07/19.02 ! [T_a,V_xs] : % 19.07/19.02 ( V_xs != c_List_Olist_ONil(T_a) % 19.07/19.02 => hAPP(c_List_Ohd(T_a),hAPP(c_List_Orev(T_a),V_xs)) = c_List_Olast(T_a,V_xs) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_last__rev,axiom, % 19.07/19.02 ! [T_a,V_xs] : % 19.07/19.02 ( V_xs != c_List_Olist_ONil(T_a) % 19.07/19.02 => c_List_Olast(T_a,hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Ohd(T_a),V_xs) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_sorted__transpose,axiom, % 19.07/19.02 ! [V_xs_2,T_b] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)))) ). % 19.07/19.02 % 19.07/19.02 fof(fact_rev__drop,axiom, % 19.07/19.02 ! [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)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_rev__take,axiom, % 19.07/19.02 ! [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)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_rotate__rev,axiom, % 19.07/19.02 ! [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)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_transpose_Osimps_I3_J,axiom, % 19.07/19.02 ! [V_xss_2,V_xs_2,V_x_2,T_b] : c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_xss_2)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),c_COMBK(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))))),V_xss_2)))),c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),V_xs_2),c_List_Oconcat(tc_List_Olist(T_b),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_b)),T_b,c_List_Olist_ONil(tc_List_Olist(T_b)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_OCons(tc_List_Olist(T_b))),c_List_Olist_ONil(tc_List_Olist(T_b)))))),V_xss_2))))) ). % 19.07/19.02 % 19.07/19.02 fof(fact_rev__nth,axiom, % 19.07/19.02 ! [V_xs,T_a,V_n] : % 19.07/19.02 ( 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))) % 19.07/19.02 => 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))) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_concat__injective,axiom, % 19.07/19.02 ! [V_ys_2,V_xs_2,T_b] : % 19.07/19.02 ( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2) % 19.07/19.02 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_ys_2) % 19.07/19.02 => ( ! [B_x] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),B_x),hAPP(c_List_Oset(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)))) % 19.07/19.02 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),B_x)) ) % 19.07/19.02 => V_xs_2 = V_ys_2 ) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_concat__eq__concat__iff,axiom, % 19.07/19.02 ! [V_ys_2,V_xs_2,T_b] : % 19.07/19.02 ( ! [B_x] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),B_x),hAPP(c_List_Oset(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)))) % 19.07/19.02 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),B_x)) ) % 19.07/19.02 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_ys_2) % 19.07/19.02 => ( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2) % 19.07/19.02 <=> V_xs_2 = V_ys_2 ) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_rev__update,axiom, % 19.07/19.02 ! [V_y,V_xs,T_a,V_k] : % 19.07/19.02 ( 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))) % 19.07/19.02 => 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) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_concat__map__singleton,axiom, % 19.07/19.02 ! [V_xs_2,V_f_2,T_c,T_b] : c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(T_c,tc_List_Olist(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_c),c_List_Olist_OCons(T_b)),V_f_2)),c_List_Olist_ONil(T_b))),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) ). % 19.07/19.02 % 19.07/19.02 fof(fact_sorted__rev__nth__mono,axiom, % 19.07/19.02 ! [V_j,V_i,V_xs,T_a] : % 19.07/19.02 ( class_Orderings_Olinorder(T_a) % 19.07/19.02 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs)) % 19.07/19.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 19.07/19.02 => ( 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))) % 19.07/19.02 => 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))) ) ) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_foldr__max__sorted,axiom, % 19.07/19.02 ! [V_y_2,V_xs_2,T_b] : % 19.07/19.02 ( class_Orderings_Olinorder(T_b) % 19.07/19.02 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Orev(T_b),V_xs_2)) % 19.07/19.02 => ( ( V_xs_2 = c_List_Olist_ONil(T_b) % 19.07/19.02 => c_List_Ofoldr(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_xs_2,V_y_2) = V_y_2 ) % 19.07/19.02 & ( V_xs_2 != c_List_Olist_ONil(T_b) % 19.07/19.02 => c_List_Ofoldr(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_xs_2,V_y_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_y_2) ) ) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_transpose_Opsimps_I3_J,axiom, % 19.07/19.02 ! [V_xss_2,V_xs_2,V_x_2,T_b] : % 19.07/19.02 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_b)),c_List_Otranspose__rel(T_b)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_xss_2))) % 19.07/19.02 => c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_xss_2)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),c_COMBK(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))))),V_xss_2)))),c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),V_xs_2),c_List_Oconcat(tc_List_Olist(T_b),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_b)),T_b,c_List_Olist_ONil(tc_List_Olist(T_b)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_OCons(tc_List_Olist(T_b))),c_List_Olist_ONil(tc_List_Olist(T_b)))))),V_xss_2))))) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_length__transpose__sorted,axiom, % 19.07/19.02 ! [V_xs_2,T_b] : % 19.07/19.02 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2))) % 19.07/19.02 => ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b)) % 19.07/19.02 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 19.07/19.02 & ( V_xs_2 != c_List_Olist_ONil(tc_List_Olist(T_b)) % 19.07/19.02 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_transpose__column__length,axiom, % 19.07/19.02 ! [V_i_2,V_xs_2,T_b] : % 19.07/19.02 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2))) % 19.07/19.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2))) % 19.07/19.02 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),c_List_Otranspose(T_b,V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),V_i_2)) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_transpose__aux__filter__tail,axiom, % 19.07/19.02 ! [V_xss_2,T_b] : c_List_Oconcat(tc_List_Olist(T_b),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_b)),T_b,c_List_Olist_ONil(tc_List_Olist(T_b)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_OCons(tc_List_Olist(T_b))),c_List_Olist_ONil(tc_List_Olist(T_b)))))),V_xss_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Otl(T_b)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_b)))),V_xss_2)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_nth__nth__transpose__sorted,axiom, % 19.07/19.02 ! [V_j_2,V_i_2,V_xs_2,T_b] : % 19.07/19.02 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2))) % 19.07/19.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)))) % 19.07/19.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_xs_2)))) % 19.07/19.02 => hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),c_List_Otranspose(T_b,V_xs_2)),V_i_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),V_j_2)),V_i_2) ) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_transpose__transpose,axiom, % 19.07/19.02 ! [V_xs_2,T_b] : % 19.07/19.02 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2))) % 19.07/19.02 => c_List_Otranspose(T_b,c_List_Otranspose(T_b,V_xs_2)) = c_List_OtakeWhile(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_b))),V_xs_2) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_transfer__nat__int__list__functions_I2_J,axiom, % 19.07/19.02 c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_takeWhile__map,axiom, % 19.07/19.02 ! [V_xs_2,V_f_2,T_c,V_Pa_2,T_b] : c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_OtakeWhile(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_Pa_2),V_f_2),V_xs_2)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_return__list__def,axiom, % 19.07/19.02 ! [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) ). % 19.07/19.02 % 19.07/19.02 fof(fact_zip__takeWhile__snd,axiom, % 19.07/19.02 ! [V_ys_2,V_Pa_2,V_xs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),c_List_OtakeWhile(T_c,V_Pa_2,V_ys_2)) = c_List_OtakeWhile(tc_prod(T_b,T_c),hAPP(c_Fun_Ocomp(T_c,tc_HOL_Obool,tc_prod(T_b,T_c),V_Pa_2),c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_zip__takeWhile__fst,axiom, % 19.07/19.02 ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)),V_ys_2) = c_List_OtakeWhile(tc_prod(T_b,T_c),hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,tc_prod(T_b,T_c),V_Pa_2),c_Product__Type_Ofst(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) ). % 19.07/19.02 % 19.07/19.02 fof(fact_set__takeWhileD,axiom, % 19.07/19.02 ! [V_xs_2,V_Pa_2,V_x_2,T_b] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)))) % 19.07/19.02 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 19.07/19.02 & hBOOL(hAPP(V_Pa_2,V_x_2)) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_takeWhile__eq__all__conv,axiom, % 19.07/19.02 ! [V_xs_2,V_Pa_2,T_b] : % 19.07/19.02 ( c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) = V_xs_2 % 19.07/19.02 <=> ! [B_x] : % 19.07/19.02 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 19.07/19.02 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 19.07/19.02 % 19.07/19.02 fof(fact_length__takeWhile__le,axiom, % 19.07/19.02 ! [V_xs_2,V_Pa_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ). % 19.07/19.02 % 19.07/19.02 fof(fact_takeWhile__eq__take,axiom, % 19.07/19.02 ! [V_xs_2,V_Pa_2,T_b] : c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))),V_xs_2) ). % 19.07/19.02 % 19.07/19.02 fof(fact_distinct__takeWhile,axiom, % 19.07/19.02 ! [V_Pa_2,V_xs_2,T_b] : % 19.07/19.02 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 19.07/19.02 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))) ) ). % 19.07/19.02 % 19.07/19.02 %----Arity declarations (201) % 19.07/19.02 fof(arity_HOL__Obool__Lattices_Obounded__lattice,axiom, % 19.07/19.02 class_Lattices_Obounded__lattice(tc_HOL_Obool) ). % 19.07/19.02 % 19.07/19.02 fof(arity_fun__Lattices_Obounded__lattice,axiom, % 19.07/19.02 ! [T_2,T_1] : % 19.07/19.02 ( class_Lattices_Obounded__lattice(T_1) % 19.07/19.02 => class_Lattices_Obounded__lattice(tc_fun(T_2,T_1)) ) ). % 19.07/19.02 % 19.07/19.02 fof(arity_fun__Complete__Lattice_Ocomplete__lattice,axiom, % 19.23/19.02 ! [T_2,T_1] : % 19.23/19.02 ( class_Complete__Lattice_Ocomplete__lattice(T_1) % 19.23/19.02 => class_Complete__Lattice_Ocomplete__lattice(tc_fun(T_2,T_1)) ) ). % 19.23/19.02 % 19.23/19.02 fof(arity_fun__Lattices_Obounded__lattice__top,axiom, % 19.23/19.02 ! [T_2,T_1] : % 19.23/19.02 ( class_Lattices_Obounded__lattice(T_1) % 19.23/19.02 => class_Lattices_Obounded__lattice__top(tc_fun(T_2,T_1)) ) ). % 19.23/19.02 % 19.23/19.02 fof(arity_fun__Lattices_Obounded__lattice__bot,axiom, % 19.23/19.02 ! [T_2,T_1] : % 19.23/19.02 ( class_Lattices_Obounded__lattice(T_1) % 19.23/19.02 => class_Lattices_Obounded__lattice__bot(tc_fun(T_2,T_1)) ) ). % 19.23/19.02 % 19.23/19.02 fof(arity_fun__Lattices_Osemilattice__sup,axiom, % 19.23/19.02 ! [T_2,T_1] : % 19.23/19.02 ( class_Lattices_Olattice(T_1) % 19.23/19.02 => class_Lattices_Osemilattice__sup(tc_fun(T_2,T_1)) ) ). % 19.23/19.02 % 19.23/19.02 fof(arity_fun__Lattices_Osemilattice__inf,axiom, % 19.23/19.02 ! [T_2,T_1] : % 19.23/19.02 ( class_Lattices_Olattice(T_1) % 19.23/19.02 => class_Lattices_Osemilattice__inf(tc_fun(T_2,T_1)) ) ). % 19.23/19.02 % 19.23/19.02 fof(arity_fun__Lattices_Odistrib__lattice,axiom, % 19.23/19.02 ! [T_2,T_1] : % 19.23/19.02 ( class_Lattices_Odistrib__lattice(T_1) % 19.23/19.02 => class_Lattices_Odistrib__lattice(tc_fun(T_2,T_1)) ) ). % 19.23/19.02 % 19.23/19.02 fof(arity_fun__Lattices_Oboolean__algebra,axiom, % 19.23/19.02 ! [T_2,T_1] : % 19.23/19.02 ( class_Lattices_Oboolean__algebra(T_1) % 19.23/19.02 => class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)) ) ). % 19.23/19.02 % 19.23/19.02 fof(arity_fun__Orderings_Opreorder,axiom, % 19.23/19.02 ! [T_2,T_1] : % 19.23/19.02 ( class_Orderings_Opreorder(T_1) % 19.23/19.02 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ). % 19.23/19.02 % 19.23/19.02 fof(arity_fun__Finite__Set_Ofinite,axiom, % 19.23/19.02 ! [T_1,T_2] : % 19.23/19.02 ( ( class_Finite__Set_Ofinite(T_2) % 19.23/19.02 & class_Finite__Set_Ofinite(T_1) ) % 19.23/19.02 => class_Finite__Set_Ofinite(tc_fun(T_2,T_1)) ) ). % 19.23/19.02 % 19.23/19.02 fof(arity_fun__Lattices_Olattice,axiom, % 19.23/19.02 ! [T_2,T_1] : % 19.23/19.02 ( class_Lattices_Olattice(T_1) % 19.23/19.02 => class_Lattices_Olattice(tc_fun(T_2,T_1)) ) ). % 19.23/19.02 % 19.23/19.02 fof(arity_fun__Orderings_Oorder,axiom, % 19.23/19.02 ! [T_2,T_1] : % 19.23/19.02 ( class_Orderings_Oorder(T_1) % 19.23/19.02 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ). % 19.23/19.02 % 19.23/19.02 fof(arity_fun__Orderings_Otop,axiom, % 19.23/19.02 ! [T_2,T_1] : % 19.23/19.02 ( class_Orderings_Otop(T_1) % 19.23/19.02 => class_Orderings_Otop(tc_fun(T_2,T_1)) ) ). % 19.23/19.02 % 19.23/19.02 fof(arity_fun__Orderings_Oord,axiom, % 19.23/19.02 ! [T_2,T_1] : % 19.23/19.02 ( class_Orderings_Oord(T_1) % 19.23/19.02 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ). % 19.23/19.02 % 19.23/19.02 fof(arity_fun__Orderings_Obot,axiom, % 19.23/19.02 ! [T_2,T_1] : % 19.23/19.02 ( class_Orderings_Obot(T_1) % 19.23/19.02 => class_Orderings_Obot(tc_fun(T_2,T_1)) ) ). % 19.23/19.02 % 19.23/19.02 fof(arity_fun__Groups_Ouminus,axiom, % 19.23/19.02 ! [T_2,T_1] : % 19.23/19.02 ( class_Groups_Ouminus(T_1) % 19.23/19.02 => class_Groups_Ouminus(tc_fun(T_2,T_1)) ) ). % 19.23/19.02 % 19.23/19.02 fof(arity_fun__Groups_Ominus,axiom, % 19.23/19.02 ! [T_2,T_1] : % 19.23/19.02 ( class_Groups_Ominus(T_1) % 19.23/19.02 => class_Groups_Ominus(tc_fun(T_2,T_1)) ) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom, % 19.23/19.02 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 19.23/19.02 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 19.23/19.02 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom, % 19.23/19.02 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom, % 19.23/19.02 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Groups_Olinordered__ab__semigroup__add,axiom, % 19.23/19.02 class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom, % 19.23/19.02 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom, % 19.23/19.02 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom, % 19.23/19.02 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom, % 19.23/19.02 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom, % 19.23/19.02 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom, % 19.23/19.02 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom, % 19.23/19.02 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom, % 19.23/19.02 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom, % 19.23/19.02 class_Rings_Olinordered__ring__strict(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom, % 19.23/19.02 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom, % 19.23/19.02 class_Rings_Oordered__comm__semiring(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom, % 19.23/19.02 class_Rings_Olinordered__semiring__1(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom, % 19.23/19.02 class_Groups_Oordered__ab__group__add(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom, % 19.23/19.02 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom, % 19.23/19.02 class_Rings_Olinordered__semiring(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom, % 19.23/19.02 class_Rings_Olinordered__semidom(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Lattices_Osemilattice__sup,axiom, % 19.23/19.02 class_Lattices_Osemilattice__sup(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Lattices_Osemilattice__inf,axiom, % 19.23/19.02 class_Lattices_Osemilattice__inf(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Lattices_Odistrib__lattice,axiom, % 19.23/19.02 class_Lattices_Odistrib__lattice(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom, % 19.23/19.02 class_Groups_Oab__semigroup__mult(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom, % 19.23/19.02 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom, % 19.23/19.02 class_Groups_Oab__semigroup__add(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Rings_Oordered__semiring,axiom, % 19.23/19.02 class_Rings_Oordered__semiring(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom, % 19.23/19.02 class_Rings_Oordered__ring__abs(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom, % 19.23/19.02 class_Rings_Ono__zero__divisors(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom, % 19.23/19.02 class_Groups_Ocomm__monoid__add(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Rings_Olinordered__ring,axiom, % 19.23/19.02 class_Rings_Olinordered__ring(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Rings_Olinordered__idom,axiom, % 19.23/19.02 class_Rings_Olinordered__idom(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom, % 19.23/19.02 class_Rings_Ocomm__semiring__1(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Groups_Osemigroup__add,axiom, % 19.23/19.02 class_Groups_Osemigroup__add(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Divides_Osemiring__div,axiom, % 19.23/19.02 class_Divides_Osemiring__div(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom, % 19.23/19.02 class_Rings_Ocomm__semiring(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Nat_Osemiring__char__0,axiom, % 19.23/19.02 class_Nat_Osemiring__char__0(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Groups_Oab__group__add,axiom, % 19.23/19.02 class_Groups_Oab__group__add(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom, % 19.23/19.02 class_Rings_Ozero__neq__one(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Rings_Oordered__ring,axiom, % 19.23/19.02 class_Rings_Oordered__ring(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Orderings_Opreorder,axiom, % 19.23/19.02 class_Orderings_Opreorder(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Orderings_Olinorder,axiom, % 19.23/19.02 class_Orderings_Olinorder(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Groups_Omonoid__mult,axiom, % 19.23/19.02 class_Groups_Omonoid__mult(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom, % 19.23/19.02 class_Rings_Ocomm__ring__1(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Groups_Omonoid__add,axiom, % 19.23/19.02 class_Groups_Omonoid__add(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Smallcheck_Osmall,axiom, % 19.23/19.02 class_Smallcheck_Osmall(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Rings_Osemiring__1,axiom, % 19.23/19.02 class_Rings_Osemiring__1(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Rings_Osemiring__0,axiom, % 19.23/19.02 class_Rings_Osemiring__0(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Lattices_Olattice,axiom, % 19.23/19.02 class_Lattices_Olattice(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Groups_Ogroup__add,axiom, % 19.23/19.02 class_Groups_Ogroup__add(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Divides_Oring__div,axiom, % 19.23/19.02 class_Divides_Oring__div(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Rings_Omult__zero,axiom, % 19.23/19.02 class_Rings_Omult__zero(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Rings_Ocomm__ring,axiom, % 19.23/19.02 class_Rings_Ocomm__ring(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Orderings_Oorder,axiom, % 19.23/19.02 class_Orderings_Oorder(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Int_Oring__char__0,axiom, % 19.23/19.02 class_Int_Oring__char__0(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Int_Onumber__ring,axiom, % 19.23/19.02 class_Int_Onumber__ring(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Rings_Osemiring,axiom, % 19.23/19.02 class_Rings_Osemiring(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Orderings_Oord,axiom, % 19.23/19.02 class_Orderings_Oord(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Groups_Ouminus,axiom, % 19.23/19.02 class_Groups_Ouminus(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Groups_Osgn__if,axiom, % 19.23/19.02 class_Groups_Osgn__if(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Groups_Oabs__if,axiom, % 19.23/19.02 class_Groups_Oabs__if(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Rings_Oring__1,axiom, % 19.23/19.02 class_Rings_Oring__1(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Groups_Ominus,axiom, % 19.23/19.02 class_Groups_Ominus(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Power_Opower,axiom, % 19.23/19.02 class_Power_Opower(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Groups_Ozero,axiom, % 19.23/19.02 class_Groups_Ozero(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Rings_Oring,axiom, % 19.23/19.02 class_Rings_Oring(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Rings_Oidom,axiom, % 19.23/19.02 class_Rings_Oidom(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Int_Onumber,axiom, % 19.23/19.02 class_Int_Onumber(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Groups_Oone,axiom, % 19.23/19.02 class_Groups_Oone(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Int__Oint__Rings_Odvd,axiom, % 19.23/19.02 class_Rings_Odvd(tc_Int_Oint) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom, % 19.23/19.02 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 19.23/19.02 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 19.23/19.02 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom, % 19.23/19.02 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add,axiom, % 19.23/19.02 class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom, % 19.23/19.02 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom, % 19.23/19.02 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom, % 19.23/19.02 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom, % 19.23/19.02 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom, % 19.23/19.02 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom, % 19.23/19.02 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom, % 19.23/19.02 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom, % 19.23/19.02 class_Rings_Olinordered__semiring(tc_Nat_Onat) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom, % 19.23/19.02 class_Rings_Olinordered__semidom(tc_Nat_Onat) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Nat__Onat__Lattices_Osemilattice__sup,axiom, % 19.23/19.02 class_Lattices_Osemilattice__sup(tc_Nat_Onat) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Nat__Onat__Lattices_Osemilattice__inf,axiom, % 19.23/19.02 class_Lattices_Osemilattice__inf(tc_Nat_Onat) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Nat__Onat__Lattices_Odistrib__lattice,axiom, % 19.23/19.02 class_Lattices_Odistrib__lattice(tc_Nat_Onat) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom, % 19.23/19.02 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom, % 19.23/19.02 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom, % 19.23/19.02 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom, % 19.23/19.02 class_Rings_Oordered__semiring(tc_Nat_Onat) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom, % 19.23/19.02 class_Rings_Ono__zero__divisors(tc_Nat_Onat) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom, % 19.23/19.02 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom, % 19.23/19.02 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Nat__Onat__Groups_Osemigroup__add,axiom, % 19.23/19.02 class_Groups_Osemigroup__add(tc_Nat_Onat) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Nat__Onat__Divides_Osemiring__div,axiom, % 19.23/19.02 class_Divides_Osemiring__div(tc_Nat_Onat) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom, % 19.23/19.02 class_Rings_Ocomm__semiring(tc_Nat_Onat) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Nat__Onat__Orderings_Owellorder,axiom, % 19.23/19.02 class_Orderings_Owellorder(tc_Nat_Onat) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Nat__Onat__Nat_Osemiring__char__0,axiom, % 19.23/19.02 class_Nat_Osemiring__char__0(tc_Nat_Onat) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom, % 19.23/19.02 class_Rings_Ozero__neq__one(tc_Nat_Onat) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Nat__Onat__Orderings_Opreorder,axiom, % 19.23/19.02 class_Orderings_Opreorder(tc_Nat_Onat) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Nat__Onat__Orderings_Olinorder,axiom, % 19.23/19.02 class_Orderings_Olinorder(tc_Nat_Onat) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom, % 19.23/19.02 class_Groups_Omonoid__mult(tc_Nat_Onat) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom, % 19.23/19.02 class_Groups_Omonoid__add(tc_Nat_Onat) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Nat__Onat__Rings_Osemiring__1,axiom, % 19.23/19.02 class_Rings_Osemiring__1(tc_Nat_Onat) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Nat__Onat__Rings_Osemiring__0,axiom, % 19.23/19.02 class_Rings_Osemiring__0(tc_Nat_Onat) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Nat__Onat__Lattices_Olattice,axiom, % 19.23/19.02 class_Lattices_Olattice(tc_Nat_Onat) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Nat__Onat__Rings_Omult__zero,axiom, % 19.23/19.02 class_Rings_Omult__zero(tc_Nat_Onat) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Nat__Onat__Orderings_Oorder,axiom, % 19.23/19.02 class_Orderings_Oorder(tc_Nat_Onat) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Nat__Onat__Rings_Osemiring,axiom, % 19.23/19.02 class_Rings_Osemiring(tc_Nat_Onat) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Nat__Onat__Orderings_Oord,axiom, % 19.23/19.02 class_Orderings_Oord(tc_Nat_Onat) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Nat__Onat__Orderings_Obot,axiom, % 19.23/19.02 class_Orderings_Obot(tc_Nat_Onat) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Nat__Onat__Groups_Ominus,axiom, % 19.23/19.02 class_Groups_Ominus(tc_Nat_Onat) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Nat__Onat__Power_Opower,axiom, % 19.23/19.02 class_Power_Opower(tc_Nat_Onat) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Nat__Onat__Groups_Ozero,axiom, % 19.23/19.02 class_Groups_Ozero(tc_Nat_Onat) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Nat__Onat__Int_Onumber,axiom, % 19.23/19.02 class_Int_Onumber(tc_Nat_Onat) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Nat__Onat__Groups_Oone,axiom, % 19.23/19.02 class_Groups_Oone(tc_Nat_Onat) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Nat__Onat__Rings_Odvd,axiom, % 19.23/19.02 class_Rings_Odvd(tc_Nat_Onat) ). % 19.23/19.02 % 19.23/19.02 fof(arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice,axiom, % 19.23/19.02 class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool) ). % 19.23/19.02 % 19.23/19.02 fof(arity_HOL__Obool__Lattices_Obounded__lattice__top,axiom, % 19.23/19.02 class_Lattices_Obounded__lattice__top(tc_HOL_Obool) ). % 19.23/19.02 % 19.23/19.02 fof(arity_HOL__Obool__Lattices_Obounded__lattice__bot,axiom, % 19.23/19.02 class_Lattices_Obounded__lattice__bot(tc_HOL_Obool) ). % 19.23/19.02 % 19.23/19.02 fof(arity_HOL__Obool__Lattices_Osemilattice__sup,axiom, % 19.23/19.02 class_Lattices_Osemilattice__sup(tc_HOL_Obool) ). % 19.23/19.02 % 19.23/19.02 fof(arity_HOL__Obool__Lattices_Osemilattice__inf,axiom, % 19.23/19.02 class_Lattices_Osemilattice__inf(tc_HOL_Obool) ). % 19.23/19.02 % 19.23/19.02 fof(arity_HOL__Obool__Lattices_Odistrib__lattice,axiom, % 19.23/19.02 class_Lattices_Odistrib__lattice(tc_HOL_Obool) ). % 19.23/19.02 % 19.23/19.02 fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom, % 19.23/19.02 class_Lattices_Oboolean__algebra(tc_HOL_Obool) ). % 19.23/19.02 % 19.23/19.02 fof(arity_HOL__Obool__Orderings_Opreorder,axiom, % 19.23/19.02 class_Orderings_Opreorder(tc_HOL_Obool) ). % 19.23/19.02 % 19.23/19.02 fof(arity_HOL__Obool__Finite__Set_Ofinite,axiom, % 19.23/19.02 class_Finite__Set_Ofinite(tc_HOL_Obool) ). % 19.23/19.02 % 19.23/19.02 fof(arity_HOL__Obool__Lattices_Olattice,axiom, % 19.23/19.02 class_Lattices_Olattice(tc_HOL_Obool) ). % 19.23/19.02 % 19.23/19.02 fof(arity_HOL__Obool__Orderings_Oorder,axiom, % 19.23/19.02 class_Orderings_Oorder(tc_HOL_Obool) ). % 19.23/19.02 % 19.23/19.02 fof(arity_HOL__Obool__Orderings_Otop,axiom, % 19.23/19.02 class_Orderings_Otop(tc_HOL_Obool) ). % 19.23/19.02 % 19.23/19.02 fof(arity_HOL__Obool__Orderings_Oord,axiom, % 19.23/19.02 class_Orderings_Oord(tc_HOL_Obool) ). % 19.23/19.02 % 19.23/19.02 fof(arity_HOL__Obool__Orderings_Obot,axiom, % 19.23/19.02 class_Orderings_Obot(tc_HOL_Obool) ). % 19.23/19.02 % 19.23/19.02 fof(arity_HOL__Obool__Groups_Ouminus,axiom, % 19.23/19.02 class_Groups_Ouminus(tc_HOL_Obool) ). % 19.23/19.02 % 19.23/19.02 fof(arity_HOL__Obool__Groups_Ominus,axiom, % 19.23/19.02 class_Groups_Ominus(tc_HOL_Obool) ). % 19.23/19.02 % 19.23/19.02 fof(arity_sum__Finite__Set_Ofinite,axiom, % 19.23/19.02 ! [T_1,T_2] : % 19.23/19.02 ( ( class_Finite__Set_Ofinite(T_2) % 19.23/19.02 & class_Finite__Set_Ofinite(T_1) ) % 19.23/19.02 => class_Finite__Set_Ofinite(tc_sum(T_2,T_1)) ) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom, % 19.23/19.02 ! [T_1] : % 19.23/19.02 ( class_Finite__Set_Ofinite(T_1) % 19.23/19.02 => class_Finite__Set_Ofinite(tc_Option_Ooption(T_1)) ) ). % 19.23/19.02 % 19.23/19.02 fof(arity_prod__Finite__Set_Ofinite,axiom, % 19.23/19.02 ! [T_1,T_2] : % 19.23/19.02 ( ( class_Finite__Set_Ofinite(T_2) % 19.23/19.02 & class_Finite__Set_Ofinite(T_1) ) % 19.23/19.02 => class_Finite__Set_Ofinite(tc_prod(T_2,T_1)) ) ). % 19.23/19.02 % 19.23/19.02 fof(arity_prod__Smallcheck_Osmall,axiom, % 19.23/19.02 ! [T_1,T_2] : % 19.23/19.02 ( ( class_Smallcheck_Osmall(T_2) % 19.23/19.02 & class_Smallcheck_Osmall(T_1) ) % 19.23/19.02 => class_Smallcheck_Osmall(tc_prod(T_2,T_1)) ) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom, % 19.23/19.02 class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Product____Type__Ounit__Smallcheck_Osmall,axiom, % 19.23/19.02 class_Smallcheck_Osmall(tc_Product__Type_Ounit) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 19.23/19.02 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 19.23/19.02 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict,axiom, % 19.23/19.02 class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add,axiom, % 19.23/19.02 class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict,axiom, % 19.23/19.02 class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add,axiom, % 19.23/19.02 class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add,axiom, % 19.23/19.02 class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add,axiom, % 19.23/19.02 class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring,axiom, % 19.23/19.02 class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring,axiom, % 19.23/19.02 class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add,axiom, % 19.23/19.02 class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring,axiom, % 19.23/19.02 class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom,axiom, % 19.23/19.02 class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult,axiom, % 19.23/19.02 class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult,axiom, % 19.23/19.02 class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add,axiom, % 19.23/19.02 class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring,axiom, % 19.23/19.02 class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors,axiom, % 19.23/19.02 class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add,axiom, % 19.23/19.02 class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1,axiom, % 19.23/19.02 class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add,axiom, % 19.23/19.02 class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div,axiom, % 19.23/19.02 class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring,axiom, % 19.23/19.02 class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0,axiom, % 19.23/19.02 class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one,axiom, % 19.23/19.02 class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder,axiom, % 19.23/19.02 class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder,axiom, % 19.23/19.02 class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult,axiom, % 19.23/19.02 class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add,axiom, % 19.23/19.02 class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1,axiom, % 19.23/19.02 class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0,axiom, % 19.23/19.02 class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero,axiom, % 19.23/19.02 class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oorder,axiom, % 19.23/19.02 class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring,axiom, % 19.23/19.02 class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oord,axiom, % 19.23/19.02 class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ominus,axiom, % 19.23/19.02 class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Code____Numeral__Ocode____numeral__Power_Opower,axiom, % 19.23/19.02 class_Power_Opower(tc_Code__Numeral_Ocode__numeral) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ozero,axiom, % 19.23/19.02 class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Code____Numeral__Ocode____numeral__Int_Onumber,axiom, % 19.23/19.02 class_Int_Onumber(tc_Code__Numeral_Ocode__numeral) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oone,axiom, % 19.23/19.02 class_Groups_Oone(tc_Code__Numeral_Ocode__numeral) ). % 19.23/19.02 % 19.23/19.02 fof(arity_Code____Numeral__Ocode____numeral__Rings_Odvd,axiom, % 19.23/19.02 class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral) ). % 19.23/19.02 % 19.23/19.02 %----Helper facts (20) % 19.23/19.02 fof(help_c__COMBI__1,axiom, % 19.23/19.02 ! [V_P,T_a] : hAPP(c_COMBI(T_a),V_P) = V_P ). % 19.23/19.02 % 19.23/19.02 fof(help_c__COMBK__1,axiom, % 19.23/19.02 ! [V_Q,V_P,T_b,T_a] : hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q) = V_P ). % 19.23/19.02 % 19.23/19.02 fof(help_c__COMBB__1,axiom, % 19.23/19.02 ! [V_R_2,V_Qa_2,V_Pa_2,T_d,T_b,T_c] : hAPP(hAPP(hAPP(c_COMBB(T_c,T_b,T_d),V_Pa_2),V_Qa_2),V_R_2) = hAPP(V_Pa_2,hAPP(V_Qa_2,V_R_2)) ). % 19.23/19.02 % 19.23/19.02 fof(help_c__COMBC__1,axiom, % 19.23/19.02 ! [V_R_2,V_Qa_2,V_Pa_2,T_b,T_d,T_c] : hAPP(hAPP(hAPP(c_COMBC(T_c,T_d,T_b),V_Pa_2),V_Qa_2),V_R_2) = hAPP(hAPP(V_Pa_2,V_R_2),V_Qa_2) ). % 19.23/19.02 % 19.23/19.02 fof(help_c__COMBS__1,axiom, % 19.23/19.02 ! [V_R_2,V_Qa_2,V_Pa_2,T_b,T_d,T_c] : hAPP(hAPP(hAPP(c_COMBS(T_c,T_d,T_b),V_Pa_2),V_Qa_2),V_R_2) = hAPP(hAPP(V_Pa_2,V_R_2),hAPP(V_Qa_2,V_R_2)) ). % 19.23/19.02 % 19.23/19.02 fof(help_c__fequal__1,axiom, % 19.23/19.02 ! [V_y_2,V_x_2] : % 19.23/19.02 ( ~ hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) % 19.23/19.02 | V_x_2 = V_y_2 ) ). % 19.23/19.02 % 19.23/19.02 fof(help_c__fequal__2,axiom, % 19.23/19.02 ! [V_y_2,V_x_2] : % 19.23/19.02 ( V_x_2 != V_y_2 % 19.23/19.02 | hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) ) ). % 19.23/19.02 % 19.23/19.02 fof(help_c__fFalse__1,axiom, % 19.23/19.02 ~ hBOOL(c_fFalse) ). % 19.23/19.02 % 19.23/19.02 fof(help_c__fTrue__1,axiom, % 19.23/19.02 hBOOL(c_fTrue) ). % 19.23/19.02 % 19.23/19.02 fof(help_c__fNot__1,axiom, % 19.23/19.02 ! [V_Pa_2] : % 19.23/19.02 ( ~ hBOOL(hAPP(c_fNot,V_Pa_2)) % 19.23/19.02 | ~ hBOOL(V_Pa_2) ) ). % 19.23/19.02 % 19.23/19.02 fof(help_c__fNot__2,axiom, % 19.23/19.02 ! [V_Pa_2] : % 19.23/19.02 ( ~ ~ hBOOL(V_Pa_2) % 19.23/19.02 | hBOOL(hAPP(c_fNot,V_Pa_2)) ) ). % 19.23/19.02 % 19.23/19.02 fof(help_c__fconj__1,axiom, % 19.23/19.02 ! [V_Qa_2,V_Pa_2] : % 19.23/19.02 ( ~ hBOOL(V_Pa_2) % 19.23/19.02 | ~ hBOOL(V_Qa_2) % 19.23/19.02 | hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Qa_2)) ) ). % 19.23/19.02 % 19.23/19.02 fof(help_c__fconj__2,axiom, % 19.23/19.02 ! [V_Qa_2,V_Pa_2] : % 19.23/19.02 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Qa_2)) % 19.23/19.02 | hBOOL(V_Pa_2) ) ). % 19.23/19.02 % 19.23/19.02 fof(help_c__fconj__3,axiom, % 19.23/19.02 ! [V_Qa_2,V_Pa_2] : % 19.23/19.02 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Qa_2)) % 19.23/19.02 | hBOOL(V_Qa_2) ) ). % 19.23/19.02 % 19.23/19.02 fof(help_c__fdisj__1,axiom, % 19.23/19.02 ! [V_Qa_2,V_Pa_2] : % 19.23/19.02 ( ~ hBOOL(V_Pa_2) % 19.23/19.02 | hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Qa_2)) ) ). % 19.23/19.02 % 19.23/19.02 fof(help_c__fdisj__2,axiom, % 19.23/19.02 ! [V_Pa_2,V_Qa_2] : % 19.23/19.02 ( ~ hBOOL(V_Qa_2) % 19.23/19.02 | hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Qa_2)) ) ). % 19.23/19.02 % 19.23/19.02 fof(help_c__fdisj__3,axiom, % 19.23/19.02 ! [V_Qa_2,V_Pa_2] : % 19.23/19.02 ( ~ hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Qa_2)) % 19.23/19.02 | hBOOL(V_Pa_2) % 19.23/19.02 | hBOOL(V_Qa_2) ) ). % 19.23/19.02 % 19.23/19.02 fof(help_c__fimplies__1,axiom, % 19.23/19.02 ! [V_Qa_2,V_Pa_2] : % 19.23/19.02 ( hBOOL(V_Pa_2) % 19.23/19.02 | hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Qa_2)) ) ). % 19.23/19.02 % 19.23/19.02 fof(help_c__fimplies__2,axiom, % 19.23/19.02 ! [V_Pa_2,V_Qa_2] : % 19.23/19.02 ( ~ hBOOL(V_Qa_2) % 19.23/19.02 | hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Qa_2)) ) ). % 19.23/19.02 % 19.23/19.02 fof(help_c__fimplies__3,axiom, % 19.23/19.02 ! [V_Qa_2,V_Pa_2] : % 19.23/19.02 ( ~ hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Qa_2)) % 19.23/19.02 | ~ hBOOL(V_Pa_2) % 19.23/19.02 | hBOOL(V_Qa_2) ) ). % 19.23/19.02 % 19.23/19.02 %----Conjectures (1) % 19.23/19.02 fof(conj_0,conjecture, % 19.23/19.02 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),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)) ). % 19.23/19.02 % 19.23/19.02 %------------------------------------------------------------------------------ % 19.23/19.02 %------------------------------------------- % 19.23/19.02 % Proof found % 19.23/19.02 % SZS status Theorem for theBenchmark % 19.23/19.02 % SZS output start Proof % 19.23/19.02 %ClaNum:10048(EqnAxiom:2815) % 19.23/19.02 %VarNum:67911(SingletonVarNum:20242) % 19.23/19.02 %MaxLitNum:8 % 19.23/19.02 %MaxfuncDepth:13 % 19.23/19.02 %SharedTerms:1069 % 19.23/19.02 %goalClause: 4486 % 19.23/19.02 %singleGoalClaCount:1 % 19.23/19.02 [2819]P1(a857) % 19.23/19.02 [2820]P1(a1) % 19.23/19.02 [2821]P1(a108) % 19.23/19.02 [2822]P85(a183) % 19.23/19.02 [2823]P2(a857) % 19.23/19.02 [2824]P2(a1) % 19.23/19.02 [2825]P2(a108) % 19.23/19.02 [2826]P63(a857) % 19.23/19.02 [2827]P63(a1) % 19.23/19.02 [2828]P63(a108) % 19.23/19.02 [2829]P64(a857) % 19.23/19.02 [2830]P64(a1) % 19.23/19.02 [2831]P64(a108) % 19.23/19.02 [2832]P67(a857) % 19.23/19.02 [2833]P67(a1) % 19.23/19.02 [2834]P67(a108) % 19.23/19.02 [2835]P68(a857) % 19.23/19.02 [2836]P68(a1) % 19.23/19.02 [2837]P68(a108) % 19.23/19.02 [2838]P69(a1) % 19.23/19.02 [2839]P86(a857) % 19.23/19.02 [2840]P86(a1) % 19.23/19.02 [2841]P86(a108) % 19.23/19.02 [2842]P111(a857) % 19.23/19.02 [2843]P111(a1) % 19.23/19.02 [2844]P112(a857) % 19.23/19.02 [2845]P112(a1) % 19.23/19.02 [2846]P112(a108) % 19.23/19.02 [2847]P74(a857) % 19.23/19.02 [2848]P74(a1) % 19.23/19.02 [2849]P74(a108) % 19.23/19.02 [2850]P80(a857) % 19.23/19.02 [2851]P80(a1) % 19.23/19.02 [2852]P80(a108) % 19.23/19.02 [2853]P81(a857) % 19.23/19.02 [2854]P81(a1) % 19.23/19.02 [2855]P81(a108) % 19.23/19.02 [2856]P113(a1) % 19.23/19.02 [2857]P120(a857) % 19.23/19.02 [2858]P120(a1) % 19.23/19.02 [2859]P120(a108) % 19.23/19.02 [2860]P87(a857) % 19.23/19.02 [2861]P87(a1) % 19.23/19.02 [2862]P87(a108) % 19.23/19.02 [2863]P100(a857) % 19.23/19.02 [2864]P100(a850) % 19.23/19.02 [2865]P100(a1) % 19.23/19.02 [2866]P100(a108) % 19.23/19.02 [2867]P101(a857) % 19.23/19.02 [2868]P101(a1) % 19.23/19.02 [2869]P101(a108) % 19.23/19.02 [2870]P104(a857) % 19.23/19.02 [2871]P104(a850) % 19.23/19.02 [2872]P104(a1) % 19.23/19.02 [2873]P104(a108) % 19.23/19.02 [2874]P103(a857) % 19.23/19.02 [2875]P103(a850) % 19.23/19.02 [2876]P103(a1) % 19.23/19.02 [2877]P103(a108) % 19.23/19.02 [2878]P123(a1) % 19.23/19.02 [2879]P135(a1) % 19.23/19.02 [2880]P114(a1) % 19.23/19.02 [2881]P136(a1) % 19.23/19.02 [2882]P105(a1) % 19.23/19.02 [2883]P88(a1) % 19.23/19.02 [2884]P70(a1) % 19.23/19.02 [2885]P75(a857) % 19.23/19.02 [2886]P75(a1) % 19.23/19.02 [2887]P75(a108) % 19.23/19.02 [2888]P71(a857) % 19.23/19.02 [2889]P71(a1) % 19.23/19.02 [2890]P71(a108) % 19.23/19.02 [2891]P76(a857) % 19.23/19.02 [2892]P76(a1) % 19.23/19.02 [2893]P76(a108) % 19.23/19.02 [2894]P65(a857) % 19.23/19.02 [2895]P65(a1) % 19.23/19.02 [2896]P65(a108) % 19.23/19.02 [2897]P77(a1) % 19.23/19.02 [2898]P3(a1) % 19.23/19.02 [2899]P124(a857) % 19.23/19.02 [2900]P124(a1) % 19.23/19.02 [2901]P124(a108) % 19.23/19.02 [2902]P137(a1) % 19.23/19.02 [2903]P129(a857) % 19.23/19.02 [2904]P129(a1) % 19.23/19.02 [2905]P129(a108) % 19.23/19.02 [2906]P140(a857) % 19.23/19.02 [2907]P140(a1) % 19.23/19.02 [2908]P140(a108) % 19.23/19.02 [2909]P138(a857) % 19.23/19.02 [2910]P138(a1) % 19.23/19.02 [2911]P138(a108) % 19.23/19.02 [2912]P110(a857) % 19.23/19.02 [2913]P110(a1) % 19.23/19.02 [2914]P110(a108) % 19.23/19.02 [2915]P121(a1) % 19.23/19.02 [2916]P122(a1) % 19.23/19.02 [2917]P125(a857) % 19.23/19.02 [2918]P125(a1) % 19.23/19.02 [2919]P125(a108) % 19.23/19.02 [2920]P118(a857) % 19.23/19.02 [2921]P118(a1) % 19.23/19.02 [2922]P118(a108) % 19.23/19.02 [2923]P82(a1) % 19.23/19.02 [2924]P126(a1) % 19.23/19.02 [2925]P78(a857) % 19.23/19.02 [2926]P78(a1) % 19.23/19.02 [2927]P78(a108) % 19.23/19.02 [2928]P130(a857) % 19.23/19.02 [2929]P130(a1) % 19.23/19.02 [2930]P130(a108) % 19.23/19.02 [2931]P131(a1) % 19.23/19.02 [2932]P133(a857) % 19.23/19.02 [2933]P133(a1) % 19.23/19.02 [2934]P133(a108) % 19.23/19.02 [2935]P132(a857) % 19.23/19.02 [2936]P132(a1) % 19.23/19.02 [2937]P132(a108) % 19.23/19.02 [2938]P127(a857) % 19.23/19.02 [2939]P127(a1) % 19.23/19.02 [2940]P127(a108) % 19.23/19.02 [2941]P128(a1) % 19.23/19.02 [2942]P91(a850) % 19.23/19.02 [2943]P4(a857) % 19.23/19.02 [2944]P4(a1) % 19.23/19.02 [2945]P4(a108) % 19.23/19.02 [2946]P5(a1) % 19.23/19.02 [2947]P84(a850) % 19.23/19.02 [2948]P84(a1) % 19.23/19.02 [2949]P72(a857) % 19.23/19.02 [2950]P72(a850) % 19.23/19.02 [2951]P72(a1) % 19.23/19.02 [2952]P72(a108) % 19.23/19.02 [2953]P89(a1) % 19.23/19.02 [2954]P90(a857) % 19.23/19.02 [2955]P90(a1) % 19.23/19.02 [2956]P90(a108) % 19.23/19.02 [2957]P79(a1) % 19.23/19.02 [2958]P134(a1) % 19.23/19.02 [2959]P66(a1) % 19.23/19.02 [2960]P106(a857) % 19.23/19.02 [2961]P106(a1) % 19.23/19.02 [2962]P106(a108) % 19.23/19.02 [2963]P139(a857) % 19.23/19.02 [2964]P139(a1) % 19.23/19.02 [2965]P139(a108) % 19.23/19.02 [2966]P102(a857) % 19.23/19.02 [2967]P102(a850) % 19.23/19.02 [2968]P115(a857) % 19.23/19.02 [2969]P115(a1) % 19.23/19.02 [2970]P115(a108) % 19.23/19.02 [2971]P109(a1) % 19.23/19.02 [2972]P93(a850) % 19.23/19.02 [2973]P95(a857) % 19.23/19.03 [2974]P95(a850) % 19.23/19.03 [2975]P95(a1) % 19.23/19.03 [2976]P98(a857) % 19.23/19.03 [2977]P98(a850) % 19.23/19.03 [2978]P98(a1) % 19.23/19.03 [2979]P58(a850) % 19.23/19.03 [2980]P58(a860) % 19.23/19.03 [2981]P99(a857) % 19.23/19.03 [2982]P99(a850) % 19.23/19.03 [2983]P99(a1) % 19.23/19.03 [2984]P96(a857) % 19.23/19.03 [2985]P96(a850) % 19.23/19.03 [2986]P96(a1) % 19.23/19.03 [2987]P6(a850) % 19.23/19.03 [2988]P107(a850) % 19.23/19.03 [2989]P97(a850) % 19.23/19.03 [2990]P73(a857) % 19.23/19.03 [2991]P73(a1) % 19.23/19.03 [2992]P73(a108) % 19.23/19.03 [2993]P108(a857) % 19.23/19.03 [2994]P141(a1) % 19.23/19.03 [2995]P141(a860) % 19.23/19.03 [2996]P83(a857) % 19.23/19.03 [2997]P83(a1) % 19.23/19.03 [2998]P83(a108) % 19.23/19.03 [2999]P94(a850) % 19.23/19.03 [3011]P35(a857,a246) % 19.23/19.03 [3012]P35(a857,a332) % 19.23/19.03 [4370]~E(a106,a92) % 19.23/19.03 [4371]~P85(a184) % 19.23/19.03 [2816]E(f2(a1),a92) % 19.23/19.03 [2817]E(f3(a108),a4) % 19.23/19.03 [2818]E(f109(a108),a5) % 19.23/19.03 [3000]E(f36(a25),f2(a857)) % 19.23/19.03 [3001]E(f93(a183),f2(a857)) % 19.23/19.03 [3002]E(f93(a184),f2(a857)) % 19.23/19.03 [3003]E(f185(a857),f2(a857)) % 19.23/19.03 [3004]E(f240(a857),f110(a857)) % 19.23/19.03 [3005]E(f245(a857),f111(a857)) % 19.23/19.03 [3006]E(f112(a1),f41(a1)) % 19.23/19.03 [3007]P7(f2(a1)) % 19.23/19.03 [3008]P7(f87(a1)) % 19.23/19.03 [3052]P85(f341(a26,a25)) % 19.23/19.03 [3063]P35(f863(a857,a857),a47) % 19.23/19.03 [3092]E(f171(a853,a851,a31),a32) % 19.23/19.03 [3402]E(f335(a857,a857,a246,a246),a47) % 19.23/19.03 [4372]~E(f87(a1),f2(a1)) % 19.23/19.03 [3009]E(f120(f2(a857)),f2(a857)) % 19.23/19.03 [3010]E(f6(f2(a108)),f2(a857)) % 19.23/19.03 [3016]E(f341(f88(a1),a92),a92) % 19.23/19.03 [3020]E(f341(a5,f2(a857)),f2(a108)) % 19.23/19.03 [3021]E(f341(a121,f2(a857)),f87(a857)) % 19.23/19.03 [3022]E(f341(a114,f87(a1)),f87(a857)) % 19.23/19.03 [3023]E(f341(a5,f87(a857)),f87(a108)) % 19.23/19.03 [3025]E(f341(f113(a1),a92),f2(a1)) % 19.23/19.03 [3026]E(f341(f113(a108),a92),f2(a108)) % 19.23/19.03 [3027]E(f341(a114,f2(a1)),f2(a857)) % 19.23/19.03 [3028]E(f341(f186(a851),a25),f2(a857)) % 19.23/19.03 [3029]E(f341(f186(a850),a183),f2(a857)) % 19.23/19.03 [3030]E(f341(f186(a850),a184),f2(a857)) % 19.23/19.03 [3031]E(f341(f113(a857),a92),f2(a857)) % 19.23/19.03 [3037]E(f341(f88(a1),f87(a1)),a106) % 19.23/19.03 [3045]E(f341(f186(a108),f2(a108)),f2(a857)) % 19.23/19.03 [3046]E(f341(f109(a1),f2(a857)),f2(a1)) % 19.23/19.03 [3047]E(f341(f109(a1),f87(a857)),f87(a1)) % 19.23/19.03 [3048]E(f341(f88(a1),f2(a1)),f2(a1)) % 19.23/19.03 [3059]E(f341(a114,f87(a1)),f341(a121,f2(a857))) % 19.23/19.03 [3061]E(f333(f863(a857,a857),a47),a48) % 19.23/19.03 [3062]E(f334(f863(a857,a857),a47),a49) % 19.23/19.03 [3083]E(f341(f266(a857),f2(a857)),f185(f864(a857,a850))) % 19.23/19.03 [3084]E(f341(f267(a857),f2(a857)),f248(f864(a857,a850))) % 19.23/19.03 [3094]P37(f185(f864(a1,a850))) % 19.23/19.03 [3129]E(f341(f341(f3(a108),f2(a108)),f87(a108)),f2(a108)) % 19.23/19.03 [3199]P85(f341(f341(f242(a1),a106),f2(a1))) % 19.23/19.03 [3224]P85(f341(f341(f242(a1),f2(a1)),f87(a1))) % 19.23/19.03 [3226]P85(f341(f341(f241(a1),f2(a1)),f87(a1))) % 19.23/19.03 [3393]P85(f341(f71(a853),f174(a853,a851,a32))) % 19.23/19.03 [3435]E(f341(f341(f290(a857,a857,a857),a332),f309(a857,a332)),a246) % 19.23/19.03 [3476]P39(a1,a857,a114,f341(f241(a1),f2(a1))) % 19.23/19.03 [3479]E(f341(f341(f54(a857,f864(a857,a850)),f248(f864(a857,a850))),f302(a857)),f248(f864(a857,a850))) % 19.23/19.03 [3480]E(f341(f341(f54(a857,f864(a857,a850)),f248(f864(a857,a850))),f266(a857)),f248(f864(a857,a850))) % 19.23/19.03 [3481]E(f341(f341(f54(a857,f864(a857,a850)),f248(f864(a857,a850))),f267(a857)),f248(f864(a857,a850))) % 19.23/19.03 [3482]E(f341(f341(f55(a857,f864(a857,a850)),f248(f864(a857,a850))),f305(a857)),f185(f864(a857,a850))) % 19.23/19.03 [3498]P26(a857,a1,f109(a1),f248(f864(a857,a850))) % 19.23/19.03 [3512]P39(a857,a1,f109(a1),f341(f18(a850,a857),a183)) % 19.23/19.03 [3642]E(f341(f82(a857,a108,a1,a5),a114),f113(a108)) % 19.23/19.03 [3861]P54(a108,a857,a22,a5,f248(f864(a857,a850))) % 19.23/19.03 [3869]P54(a1,f864(f863(a857,a857),a850),a117,a98,a107) % 19.23/19.03 [4135]E(f261(a1,a1,a1,a1,f41(a1),f88(a1)),a66) % 19.23/19.03 [4405]~E(f341(f113(a1),a106),f341(f113(a1),a92)) % 19.23/19.03 [4406]~P85(f341(a191,f2(a1))) % 19.23/19.03 [4407]~P85(f341(a191,f87(a1))) % 19.23/19.03 [4463]~P85(f341(f341(f242(a1),a92),f2(a1))) % 19.23/19.03 [3077]E(f341(f341(f3(a1),a106),a106),a92) % 19.23/19.03 [3091]E(f341(f109(a1),f341(a121,f2(a857))),f87(a1)) % 19.23/19.03 [3152]E(f341(f50(a860),f248(f864(a860,a850))),f87(a857)) % 19.23/19.03 [3174]P85(f341(a191,f341(f113(a1),a106))) % 19.23/19.03 [3175]P85(f341(f341(f242(a1),a106),a92)) % 19.23/19.03 [3177]P85(f341(f341(f241(a1),a106),a92)) % 19.23/19.03 [3235]E(f341(f341(f311(a857),f2(a857)),f185(f864(a857,a850))),f341(f302(a857),f2(a857))) % 19.23/19.03 [3291]P85(f341(f341(f241(a1),f2(a1)),f341(f113(a1),a92))) % 19.23/19.03 [3302]E(f341(f312(a857,a857,a121),f248(f864(a857,a850))),f341(f305(a857),f2(a857))) % 19.23/19.03 [3340]P9(f863(a857,a857),f248(f864(f863(a857,a857),a850)),a118) % 19.23/19.03 [3649]E(f341(f82(a857,a1,a108,f109(a1)),a22),a23) % 19.23/19.03 [3709]P35(a857,f341(f265(f863(a857,a857)),f341(f260(a857,a857,a850),f242(a857)))) % 19.23/19.03 [4454]~P85(f341(a191,f341(f113(a1),a92))) % 19.23/19.03 [4455]~P85(f341(f341(f242(a1),a106),a106)) % 19.23/19.03 [4456]~P85(f341(f341(f242(a1),a92),a106)) % 19.23/19.03 [4457]~P85(f341(f341(f242(a1),a92),a92)) % 19.23/19.03 [4458]~P85(f341(f341(f241(a1),a92),a106)) % 19.23/19.03 [4473]~P85(f341(f71(a857),f248(f864(a857,a850)))) % 19.23/19.03 [4474]~P85(f341(f71(a1),f248(f864(a1,a850)))) % 19.23/19.03 [4486]~P30(a848,f2(a857),f341(f341(f341(f100(a848),a866),f341(a29,a867)),a868)) % 19.23/19.03 [4300]E(f341(f260(a1,a1,a850),f341(f341(f10(f864(a1,a850),f864(a1,a850),a1),f341(f20(a1,a850,a850),f341(f341(f10(a850,f864(a850,a850),a1),a339),f341(f242(a1),f2(a1))))),f341(f341(f9(a1,a1,f864(a1,a850)),f341(f341(f10(f864(a1,f864(a1,a850)),f864(a1,f864(a1,a850)),a1),f9(a1,a1,a850)),f341(f341(f10(f864(a1,a1),f864(a1,f864(a1,a850)),a1),f341(f10(a1,f864(a1,a850),a1),a338)),a220))),f87(a1)))),a216) % 19.23/19.03 [3375]E(f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106),f341(f88(a1),a106)) % 19.23/19.03 [3417]E(f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106),f341(f341(f3(a1),a92),a106)) % 19.23/19.03 [3574]E(f341(f341(f69(f863(a857,a857)),f248(f864(f863(a857,a857),a850))),a118),a107) % 19.23/19.03 [3604]E(f341(f113(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f87(a1)) % 19.23/19.03 [3605]E(f341(f113(a108),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f87(a108)) % 19.23/19.03 [3606]E(f341(f113(a857),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f87(a857)) % 19.23/19.03 [3609]E(f341(f113(a857),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(a121,f2(a857))) % 19.23/19.03 [3997]E(f341(f341(f110(f864(f863(f863(a857,a857),f863(a857,a857)),a850)),a47),f309(f863(a857,a857),f185(f864(f863(f863(a857,a857),f863(a857,a857)),a850)))),a79) % 19.23/19.03 [4068]E(f341(a98,f341(f286(f863(a857,a857),f863(a857,a857),a118),f341(f341(f311(f863(a857,a857)),f341(f341(f250(a857,a857),f2(a857)),f2(a857))),f185(f864(f863(a857,a857),a850))))),f2(a1)) % 19.23/19.03 [4069]E(f341(a98,f341(f286(f863(a857,a857),f863(a857,a857),a118),f341(f341(f311(f863(a857,a857)),f341(f341(f250(a857,a857),f87(a857)),f2(a857))),f185(f864(f863(a857,a857),a850))))),f87(a1)) % 19.23/19.03 [4083]E(f341(f265(f863(a857,a857)),f341(f260(a857,a857,a850),f341(f341(f10(a857,f864(a857,a850),a857),f341(f9(a857,a857,a850),a338)),a121))),a332) % 19.23/19.03 [4052]E(f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106))),f341(a121,f341(a121,f2(a857)))) % 19.23/19.03 [4055]E(f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106))),f341(f341(f89(a857),f87(a857)),f87(a857))) % 19.23/19.03 [4056]E(f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106))),f341(f50(a850),f248(f864(a850,a850)))) % 19.23/19.03 [4121]P7(f341(f113(a1),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))) % 19.23/19.03 [4194]P27(f864(f863(a857,a857),a850),f341(f341(f250(f864(f863(f864(f863(a857,a857),a850),f864(f863(a857,a857),a850)),a850),f864(f863(f864(f863(a857,a857),a850),f864(f863(a857,a857),a850)),a850)),a48),a80)) % 19.23/19.03 [4195]P27(f864(f863(a857,a857),a850),f341(f341(f250(f864(f863(f864(f863(a857,a857),a850),f864(f863(a857,a857),a850)),a850),f864(f863(f864(f863(a857,a857),a850),f864(f863(a857,a857),a850)),a850)),a49),a78)) % 19.23/19.03 [4232]E(f341(f341(f110(f864(f863(f864(f863(a857,a857),a850),f864(f863(a857,a857),a850)),a850)),f334(f863(a857,a857),a79)),f341(f341(f311(f863(f864(f863(a857,a857),a850),f864(f863(a857,a857),a850))),f341(f341(f250(f864(f863(a857,a857),a850),f864(f863(a857,a857),a850)),f185(f864(f863(a857,a857),a850))),f185(f864(f863(a857,a857),a850)))),f185(f864(f863(f864(f863(a857,a857),a850),f864(f863(a857,a857),a850)),a850)))),a78) % 19.23/19.03 [4233]E(f341(f341(f110(f864(f863(f864(f863(a857,a857),a850),f864(f863(a857,a857),a850)),a850)),f333(f863(a857,a857),a79)),f341(f341(f311(f863(f864(f863(a857,a857),a850),f864(f863(a857,a857),a850))),f341(f341(f250(f864(f863(a857,a857),a850),f864(f863(a857,a857),a850)),f185(f864(f863(a857,a857),a850))),f185(f864(f863(a857,a857),a850)))),f185(f864(f863(f864(f863(a857,a857),a850),f864(f863(a857,a857),a850)),a850)))),a80) % 19.23/19.03 [4123]E(f341(a114,f341(f113(a1),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),f341(a121,f341(a121,f2(a857)))) % 19.23/19.03 [4171]E(f341(f109(a1),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),f341(f113(a1),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))) % 19.23/19.03 [4204]P85(f341(f341(f241(a1),f2(a1)),f341(f113(a1),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106))))) % 19.23/19.03 [4205]E(f341(f113(a857),f341(f341(f3(a1),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106))),a106)),f341(a121,f341(a121,f341(a121,f2(a857))))) % 19.23/19.03 [4245]P7(f341(f113(a1),f341(f341(f3(a1),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106))),a106))) % 19.23/19.03 [4272]E(f341(f109(a1),f341(f113(a857),f341(f341(f3(a1),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106))),a106))),f341(f113(a1),f341(f341(f3(a1),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106))),a106))) % 19.23/19.03 [4286]P85(f341(f341(f241(a1),f2(a1)),f341(f113(a1),f341(f341(f3(a1),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106))),a106)))) % 19.23/19.03 [3013]P8(x30131,a338) % 19.23/19.03 [3403]P26(a857,a857,a121,x34031) % 19.23/19.03 [3032]P35(a1,f115(x30321)) % 19.23/19.03 [3033]P35(a1,f116(x30331)) % 19.23/19.03 [3036]P36(x30361,f188(x30361)) % 19.23/19.03 [3080]P35(f864(x30801,a850),f308(x30801)) % 19.23/19.03 [3120]E(f60(a1,x31201,x31201),f2(a1)) % 19.23/19.03 [3171]P16(x31711,f864(x31711,a850),f311(x31711)) % 19.23/19.03 [4376]~E(f341(a29,x43761),a25) % 19.23/19.03 [4378]~E(f341(a121,x43781),x43781) % 19.23/19.03 [4390]~E(f341(a121,x43901),f2(a857)) % 19.23/19.03 [3014]E(f44(f42(x30141)),f2(a857)) % 19.23/19.03 [3015]E(f44(f43(x30151)),f2(a857)) % 19.23/19.03 [3017]E(f341(f186(a857),x30171),x30171) % 19.23/19.03 [3018]E(f341(f113(a1),x30181),x30181) % 19.23/19.03 [3034]E(f341(a98,f342(x30341)),x30341) % 19.23/19.03 [3035]E(f247(x30351,f2(a108)),f2(a108)) % 19.23/19.03 [3049]E(f123(x30491,f122(x30491)),f122(x30491)) % 19.23/19.03 [3053]E(f341(f186(a852),f42(x30531)),f2(a857)) % 19.23/19.03 [3054]E(f341(f186(a852),f43(x30541)),f2(a857)) % 19.23/19.03 [3055]E(f36(f341(a29,x30551)),f2(a857)) % 19.23/19.03 [3056]E(f341(f147(x30561),f122(x30561)),f122(x30561)) % 19.23/19.03 [3057]E(f341(f162(x30571),f122(x30571)),f122(x30571)) % 19.23/19.03 [3058]E(f341(f148(x30581),f122(x30581)),f122(x30581)) % 19.23/19.03 [3064]E(f341(f113(a1),x30641),f341(f112(a1),x30641)) % 19.23/19.03 [3066]E(f341(a5,f341(a22,x30661)),x30661) % 19.23/19.03 [3067]E(f341(a22,f341(a5,x30671)),x30671) % 19.23/19.03 [3068]E(f341(a98,f341(a117,x30681)),x30681) % 19.23/19.03 [3069]P7(f341(f109(a1),x30691)) % 19.23/19.03 [3073]E(f341(f186(f861(x30731)),f188(x30731)),f2(a857)) % 19.23/19.03 [3074]E(f341(f186(f858(x30741)),f122(x30741)),f2(a857)) % 19.23/19.03 [3079]E(f341(f186(a851),f341(a29,x30791)),f2(a857)) % 19.23/19.03 [3089]E(f234(x30891,f188(x30891)),f185(f864(x30891,a850))) % 19.23/19.03 [3097]E(f341(f341(f89(a857),x30971),f2(a857)),x30971) % 19.23/19.03 [3098]E(f341(f341(f89(a1),x30981),f2(a1)),x30981) % 19.23/19.03 [3099]E(f341(f341(f90(a857),x30991),f87(a857)),x30991) % 19.23/19.03 [3100]E(f341(f341(f90(a1),x31001),f87(a1)),x31001) % 19.23/19.03 [3101]E(f341(f341(f3(a857),x31011),f2(a857)),x31011) % 19.23/19.03 [3102]E(f341(f341(f240(a857),x31021),f2(a857)),x31021) % 19.23/19.03 [3103]E(f341(f341(f90(a857),x31031),f2(a857)),f2(a857)) % 19.23/19.03 [3104]E(f341(f341(f51(a1),x31041),f2(a1)),f2(a1)) % 19.23/19.03 [3105]E(f341(f341(f245(a857),x31051),f2(a857)),f2(a857)) % 19.23/19.03 [3111]E(f341(f163(x31111),f122(x31111)),f185(f864(x31111,a850))) % 19.23/19.03 [3115]P85(f341(f134(x31151),f122(x31151))) % 19.23/19.03 [3121]E(f341(f149(x31211,x31211),f7(x31211)),f41(f858(x31211))) % 19.23/19.03 [3122]E(f341(f149(x31221,x31221),f41(x31221)),f41(f858(x31221))) % 19.23/19.03 [3123]E(f341(f204(x31231,x31231),f7(x31231)),f41(f861(x31231))) % 19.23/19.03 [3124]E(f341(f204(x31241,x31241),f41(x31241)),f41(f861(x31241))) % 19.23/19.03 [3125]E(f60(a1,x31251,f2(a1)),x31251) % 19.23/19.03 [3126]E(f341(f241(a857),f341(a121,x31261)),f341(f242(a857),x31261)) % 19.23/19.03 [3127]E(f341(f266(a857),f341(a121,x31271)),f341(f302(a857),x31271)) % 19.23/19.03 [3128]E(f341(f267(a857),f341(a121,x31281)),f341(f305(a857),x31281)) % 19.23/19.03 [3130]E(f60(a1,f2(a1),x31301),f2(a1)) % 19.23/19.03 [3137]E(f341(f341(f89(a857),x31371),f87(a857)),f341(a121,x31371)) % 19.23/19.03 [3147]E(f341(f303(a857,x31471),f2(a857)),f185(f864(a857,a850))) % 19.23/19.03 [3157]E(f304(a857,f2(a857),x31571),f341(f302(a857),x31571)) % 19.23/19.03 [3202]E(f341(f341(f3(a857),f341(a121,x32021)),f87(a857)),x32021) % 19.23/19.03 [3215]E(f62(f2(a1),x32151),f341(f341(f250(a1,a1),f2(a1)),f2(a1))) % 19.23/19.03 [3265]P85(f341(f341(f242(a857),x32651),f341(a121,x32651))) % 19.23/19.03 [3279]P85(f341(f341(f242(a857),f2(a857)),f341(a121,x32791))) % 19.23/19.03 [3562]E(f341(f341(f3(a108),f341(a5,f341(a121,f341(a22,x35621)))),f87(a108)),x35621) % 19.23/19.03 [3631]P85(f341(f341(f241(a1),f341(f88(a1),f341(f109(a1),x36311))),f2(a1))) % 19.23/19.03 [3783]P85(f341(f341(f242(a1),f341(f88(a1),f341(f109(a1),f341(a121,x37831)))),f2(a1))) % 19.23/19.03 [4413]~E(f248(f864(x44131,a850)),f185(f864(x44131,a850))) % 19.23/19.03 [4466]~P85(f341(f341(f242(a857),x44661),f2(a857))) % 19.23/19.03 [4482]~P85(f341(f341(f242(a1),f341(f109(a1),x44821)),f2(a1))) % 19.23/19.03 [3078]E(f169(x30781,f122(f858(x30781))),f122(f858(x30781))) % 19.23/19.03 [3081]E(f341(f341(f90(a1),a92),x30811),a92) % 19.23/19.03 [3082]E(f341(f341(f89(a1),a92),x30821),x30821) % 19.23/19.03 [3085]E(f341(a114,f341(f109(a1),x30851)),x30851) % 19.23/19.03 [3086]E(f341(f341(f89(a1),x30861),a92),x30861) % 19.23/19.03 [3087]E(f341(f341(f3(a1),x30871),a92),x30871) % 19.23/19.03 [3090]E(f341(f341(f3(a857),x30901),x30901),f2(a857)) % 19.23/19.03 [3095]E(f341(f88(a1),f341(f88(a1),x30951)),x30951) % 19.23/19.03 [3096]E(f341(f50(a857),f341(f266(a857),x30961)),x30961) % 19.23/19.03 [3106]E(f341(f341(f89(a857),f2(a857)),x31061),x31061) % 19.23/19.03 [3107]E(f341(f341(f89(a1),f2(a1)),x31071),x31071) % 19.23/19.03 [3108]E(f341(f341(f90(a857),f87(a857)),x31081),x31081) % 19.23/19.03 [3109]E(f341(f341(f90(a1),f87(a1)),x31091),x31091) % 19.23/19.03 [3110]E(f341(f341(f240(a857),f2(a857)),x31101),x31101) % 19.23/19.03 [3116]E(f341(f341(f90(a857),f2(a857)),x31161),f2(a857)) % 19.23/19.03 [3117]E(f341(f341(f51(a1),f2(a1)),x31171),f2(a1)) % 19.23/19.03 [3118]E(f341(f341(f3(a857),f2(a857)),x31181),f2(a857)) % 19.23/19.03 [3119]E(f341(f341(f245(a857),f2(a857)),x31191),f2(a857)) % 19.23/19.03 [3135]E(f341(f303(a857,f2(a857)),x31351),f341(f266(a857),x31351)) % 19.23/19.03 [3136]E(f341(f341(f90(a1),a106),x31361),f341(f88(a1),x31361)) % 19.23/19.03 [3139]E(f341(a114,f341(f113(a1),x31391)),f341(f113(a857),x31391)) % 19.23/19.03 [3140]E(f341(a22,f341(f113(a108),x31401)),f341(f113(a857),x31401)) % 19.23/19.03 [3141]E(f341(f50(a857),f341(f302(a857),x31411)),f341(a121,x31411)) % 19.23/19.03 [3150]E(f341(f341(f89(a857),f87(a857)),x31501),f341(a121,x31501)) % 19.23/19.03 [3153]E(f341(f112(a1),f341(f109(a1),x31531)),f341(f109(a1),x31531)) % 19.23/19.03 [3154]E(f341(f84(a1),f341(f109(a1),x31541)),f341(f109(a1),x31541)) % 19.23/19.03 [3159]E(f341(f50(x31591),f185(f864(x31591,a850))),f2(a857)) % 19.23/19.03 [3161]E(f341(f341(f51(a857),x31611),f341(a121,f2(a857))),x31611) % 19.23/19.03 [3172]E(f60(a857,x31721,f341(a121,f2(a857))),f2(a857)) % 19.23/19.03 [3173]E(f60(a1,x31731,f341(f113(a1),a106)),f2(a1)) % 19.23/19.03 [3187]E(f341(f341(f51(a1),x31871),f341(f113(a1),a106)),f341(f88(a1),x31871)) % 19.23/19.03 [3191]E(f136(a857,f341(f303(a857,x31911),f2(a857))),f122(a857)) % 19.23/19.03 [3192]E(f341(f341(f3(a1),x31921),f87(a1)),f341(f341(f89(a1),x31921),a106)) % 19.23/19.03 [3193]E(f341(f341(f89(a1),x31931),f87(a1)),f341(f341(f3(a1),x31931),a106)) % 19.23/19.03 [3195]P85(f341(f341(f192(a25),x31951),x31951)) % 19.23/19.03 [3196]P85(f341(f341(f241(a857),x31961),x31961)) % 19.23/19.03 [3197]P85(f341(f341(f241(a1),x31971),x31971)) % 19.23/19.03 [3198]P85(f341(f341(f288(a857),x31981),x31981)) % 19.23/19.03 [3203]E(f341(f88(a1),f341(f113(a1),x32031)),f341(f113(a1),f341(f88(a1),x32031))) % 19.23/19.03 [3204]P85(f341(f71(a857),f341(f302(a857),x32041))) % 19.23/19.03 [3205]P85(f341(f71(a857),f341(f266(a857),x32051))) % 19.23/19.03 [3213]E(f155(x32131,f248(f864(x32131,a850))),f248(f864(f858(x32131),a850))) % 19.23/19.03 [3218]P85(f341(f341(f241(a857),f2(a857)),x32181)) % 19.23/19.03 [3229]E(f341(f341(f89(a857),f120(x32291)),f341(a121,f2(a857))),f120(f341(a121,x32291))) % 19.23/19.03 [3230]E(f341(f265(x32301),f341(f18(a850,x32301),a184)),f185(f864(x32301,a850))) % 19.23/19.03 [3231]E(f341(f265(x32311),f341(f18(a850,x32311),a183)),f248(f864(x32311,a850))) % 19.23/19.03 [3234]E(f341(f341(f311(a857),x32341),f341(f266(a857),x32341)),f341(f266(a857),f341(a121,x32341))) % 19.23/19.03 [3245]E(f341(f341(f89(a1),f87(a1)),f341(f109(a1),x32451)),f341(f109(a1),f341(a121,x32451))) % 19.23/19.03 [3268]E(f185(f864(f863(x32681,x32681),a850)),f269(x32681,f185(f864(x32681,a850)))) % 19.23/19.03 [3269]E(f341(f310(x32691),f248(f864(x32691,a850))),f248(f864(f864(x32691,a850),a850))) % 19.23/19.03 [3270]E(f341(f88(f864(x32701,a850)),f185(f864(x32701,a850))),f248(f864(x32701,a850))) % 19.23/19.03 [3271]E(f341(f88(f864(x32711,a850)),f248(f864(x32711,a850))),f185(f864(x32711,a850))) % 19.23/19.03 [3273]P85(f341(f71(x32731),f185(f864(x32731,a850)))) % 19.23/19.03 [3275]E(f341(f303(a857,x32751),f341(a121,x32751)),f341(f341(f311(a857),x32751),f185(f864(a857,a850)))) % 19.23/19.03 [3276]E(f94(f863(a857,a857),f63(x32761,f2(a857))),f341(f341(f250(a857,a857),f2(a857)),x32761)) % 19.23/19.03 [3290]E(f341(f341(f311(a857),f341(a121,x32901)),f341(f302(a857),x32901)),f341(f302(a857),f341(a121,x32901))) % 19.23/19.03 [3293]P35(x32931,f185(f864(f863(x32931,x32931),a850))) % 19.23/19.03 [3296]P85(f341(f341(f241(a1),f2(a1)),f341(f109(a1),x32961))) % 19.23/19.03 [3304]E(f341(f341(f89(a857),f341(f186(a857),x33041)),f341(a121,f2(a857))),f341(f186(a857),f341(a121,x33041))) % 19.23/19.03 [3410]P37(f341(f312(a857,a1,f109(a1)),x34101)) % 19.23/19.03 [3450]P46(x34501,f185(f864(x34501,a850)),f185(f864(f863(x34501,x34501),a850))) % 19.23/19.03 [3473]E(f341(f341(f250(a1,a1),f341(f113(a1),a106)),f341(f341(f3(a1),x34731),f87(a1))),f65(f341(f113(a1),a106),x34731)) % 19.23/19.03 [3524]P57(x35241,f341(f18(f864(x35241,a850),x35241),f341(f18(a850,x35241),a184))) % 19.23/19.03 [3533]E(f291(a857,f288(a857),x35331,x35331),f341(f341(f311(a857),x35331),f185(f864(a857,a850)))) % 19.23/19.03 [3723]P85(f341(f341(f343(f864(f863(a857,a857),a850)),f342(x37231)),a107)) % 19.23/19.03 [3747]P85(f341(f341(f343(f864(f863(a857,a857),a850)),f341(a117,x37471)),a107)) % 19.23/19.03 [3879]P26(x38791,f864(x38791,a850),f341(f341(f9(x38791,f864(x38791,a850),f864(x38791,a850)),f311(x38791)),f185(f864(x38791,a850))),f248(f864(x38791,a850))) % 19.23/19.03 [4409]~E(f341(f341(f89(a1),x44091),x44091),a106) % 19.23/19.03 [4453]~E(f341(a5,f341(a121,f341(a22,x44531))),f2(a108)) % 19.23/19.03 [4459]~P85(f341(a191,f341(f109(a1),x44591))) % 19.23/19.03 [4462]~P85(f341(f341(f242(a857),x44621),x44621)) % 19.23/19.03 [4475]~P85(f341(f341(f241(a857),f341(a121,x44751)),x44751)) % 19.23/19.03 [3220]E(f341(a114,f341(f88(a1),f341(f109(a1),x32201))),f2(a857)) % 19.23/19.03 [3223]E(f341(f341(f89(a1),f341(f88(a1),x32231)),x32231),f2(a1)) % 19.23/19.03 [3228]E(f341(f50(a1),f341(f303(a1,f2(a1)),x32281)),f341(a114,x32281)) % 19.23/19.03 [3238]E(f341(f341(f251(a857),f341(a121,f2(a857))),x32381),f341(a121,f2(a857))) % 19.23/19.03 [3337]E(f341(f285(x33371),f185(f864(f863(x33371,x33371),a850))),f185(f864(x33371,a850))) % 19.23/19.03 [3345]E(f53(f864(x33451,a850),f185(f864(f864(x33451,a850),a850))),f248(f864(x33451,a850))) % 19.23/19.03 [3346]E(f53(f864(x33461,a850),f248(f864(f864(x33461,a850),a850))),f185(f864(x33461,a850))) % 19.23/19.03 [3347]E(f52(f864(x33471,a850),f185(f864(f864(x33471,a850),a850))),f185(f864(x33471,a850))) % 19.23/19.03 [3348]E(f52(f864(x33481,a850),f248(f864(f864(x33481,a850),a850))),f248(f864(x33481,a850))) % 19.23/19.03 [3353]P85(f341(f341(f288(a857),f341(a121,f2(a857))),x33531)) % 19.23/19.03 [3391]E(f341(f341(f311(f858(x33911)),f122(x33911)),f185(f864(f858(x33911),a850))),f156(x33911,f122(f864(x33911,a850)))) % 19.23/19.03 [3392]E(f341(f341(f311(f858(x33921)),f122(x33921)),f185(f864(f858(x33921),a850))),f155(x33921,f185(f864(x33921,a850)))) % 19.23/19.03 [3434]E(f341(f341(f89(a857),f6(x34341)),f341(a121,f2(a857))),f6(f341(a5,f341(a121,f341(a22,x34341))))) % 19.23/19.03 [3465]E(f341(f50(a1),f341(f312(a857,a1,f109(a1)),x34651)),f341(f50(a857),x34651)) % 19.23/19.03 [3468]P85(f341(f341(f241(a857),x34681),f341(f341(f90(a857),x34681),x34681))) % 19.23/19.03 [3505]E(f341(f312(a1,a857,a114),f304(a1,f2(a1),f341(f109(a1),x35051))),f341(f302(a857),x35051)) % 19.23/19.03 [3519]E(f341(f341(f51(a857),f341(a121,f2(a857))),f341(f113(a857),x35191)),f341(a114,f341(f341(f51(a1),f87(a1)),f341(f113(a1),x35191)))) % 19.23/19.03 [3521]E(f341(f163(a857),f136(a857,f341(f303(a857,f2(a857)),f341(a121,x35211)))),f341(f302(a857),x35211)) % 19.23/19.03 [3522]E(f341(f341(f89(a857),f341(f186(a108),x35221)),f341(a121,f2(a857))),f341(f186(a108),f341(a5,f341(a121,f341(a22,x35221))))) % 19.23/19.03 [3538]E(f341(f312(a1,a857,a114),f341(f312(a857,a1,f109(a1)),x35381)),x35381) % 19.23/19.03 [3567]E(f341(f341(f311(a857),f2(a857)),f341(f312(a857,a857,a121),f341(f266(a857),x35671))),f341(f266(a857),f341(a121,x35671))) % 19.23/19.03 [3573]P52(x35731,x35731,f309(x35731,f185(f864(f863(x35731,x35731),a850)))) % 19.23/19.03 [3579]P85(f341(a191,f341(f88(a1),f341(f109(a1),f341(a121,x35791))))) % 19.23/19.03 [3590]E(f341(f341(f3(f864(a857,a850)),f341(f267(a857),x35901)),f341(f341(f311(a857),x35901),f185(f864(a857,a850)))),f341(f267(a857),f341(a121,x35901))) % 19.23/19.03 [3607]E(f341(f341(f89(a1),f341(f341(f3(a1),a92),x36071)),f341(f341(f3(a1),a92),x36071)),f341(f341(f3(a1),a92),f341(f341(f89(a1),x36071),x36071))) % 19.23/19.03 [3621]E(f341(f341(f311(f864(x36211,a850)),f185(f864(x36211,a850))),f185(f864(f864(x36211,a850),a850))),f341(f310(x36211),f185(f864(x36211,a850)))) % 19.23/19.03 [3650]E(f341(f341(f3(f864(a857,a850)),f341(f305(a857),x36501)),f341(f341(f311(a857),f341(a121,x36501)),f185(f864(a857,a850)))),f341(f305(a857),f341(a121,x36501))) % 19.23/19.03 [3659]E(f341(f341(f311(f861(x36591)),f188(x36591)),f341(f312(x36591,f861(x36591),f235(x36591)),f248(f864(x36591,a850)))),f248(f864(f861(x36591),a850))) % 19.23/19.03 [3759]E(f341(f113(a857),f341(f341(f89(a1),x37591),x37591)),f341(f341(f95(a857,a857),f341(f113(a857),x37591)),f341(f341(f20(a857,a857,a857),f89(a857)),f7(a857)))) % 19.23/19.03 [4146]P16(x41461,f864(x41461,a850),f341(f341(f10(f864(x41461,a850),f864(f864(x41461,a850),f864(x41461,a850)),x41461),f341(f9(f864(x41461,a850),f864(x41461,a850),f864(x41461,a850)),f3(f864(x41461,a850)))),f341(f341(f9(x41461,f864(x41461,a850),f864(x41461,a850)),f311(x41461)),f185(f864(x41461,a850))))) % 19.23/19.03 [4231]E(f341(f265(f863(a1,a1)),f341(f260(a1,a1,a850),f341(f341(f10(f864(a1,a850),f864(a1,a850),a1),f341(f20(a1,a850,a850),f341(f341(f10(a850,f864(a850,a850),a1),a339),f341(f241(a1),x42311)))),f242(a1)))),f115(x42311)) % 19.23/19.03 [4263]E(f341(f265(f863(a1,a1)),f341(f260(a1,a1,a850),f341(f341(f20(a1,f864(a1,a850),f864(a1,a850)),f341(f341(f10(f864(a850,a850),f864(f864(a1,a850),f864(a1,a850)),a1),f10(a850,a850,a1)),f341(f341(f10(a850,f864(a850,a850),a1),a339),f341(f241(a1),x42631)))),f242(a1)))),f116(x42631)) % 19.23/19.03 [4315]E(f341(f265(f863(f864(x43151,a850),f864(x43151,a850))),f341(f260(f864(x43151,a850),f864(x43151,a850),a850),f341(f341(f9(f864(x43151,a850),f864(f864(x43151,a850),a850),f864(f864(x43151,a850),a850)),f341(f341(f10(f864(f864(x43151,a850),f864(a850,a850)),f864(f864(f864(x43151,a850),a850),f864(f864(x43151,a850),a850)),f864(x43151,a850)),f20(f864(x43151,a850),a850,a850)),f341(f341(f10(f864(f864(x43151,a850),a850),f864(f864(x43151,a850),f864(a850,a850)),f864(x43151,a850)),f341(f10(a850,f864(a850,a850),f864(x43151,a850)),a339)),f242(f864(x43151,a850))))),f71(x43151)))),f308(x43151)) % 19.23/19.03 [4479]~P85(f341(f71(f858(x44791)),f248(f864(f858(x44791),a850)))) % 19.23/19.03 [4493]~P85(f341(f341(f241(a1),f2(a1)),f341(f88(a1),f341(f109(a1),f341(a121,x44931))))) % 19.23/19.03 [3369]E(f341(f341(f3(a1),f341(f341(f89(a1),x33691),a106)),a106),x33691) % 19.23/19.03 [3385]E(f341(f163(a857),f136(a857,f341(f303(a857,f2(a857)),x33851))),f341(f266(a857),x33851)) % 19.23/19.03 [3627]E(f341(f341(f89(a1),f341(f341(f89(a1),f87(a1)),x36271)),x36271),f341(f341(f3(a1),f341(f341(f89(a1),x36271),x36271)),a106)) % 19.23/19.03 [3677]E(f341(f287(x36771,x36771),f309(x36771,f185(f864(f863(x36771,x36771),a850)))),f309(x36771,f185(f864(f863(x36771,x36771),a850)))) % 19.23/19.03 [3726]P85(f341(f341(f241(a857),x37261),f341(f341(f90(a857),x37261),f341(f341(f90(a857),x37261),x37261)))) % 19.23/19.03 [4001]P85(f341(f71(a857),f341(f265(a857),f341(f341(f9(a857,a857,a850),f242(a857)),x40011)))) % 19.23/19.03 [4002]P85(f341(f71(a857),f341(f265(a857),f341(f341(f9(a857,a857,a850),f241(a857)),x40021)))) % 19.23/19.03 [4282]E(f341(f265(f863(x42821,x42821)),f341(f341(f10(f864(x42821,a850),a850,f863(x42821,x42821)),f96(x42821)),f341(f341(f9(f863(x42821,x42821),f864(x42821,f863(x42821,x42821)),f864(x42821,a850)),f341(f341(f10(f864(f863(x42821,x42821),a850),f864(f864(x42821,f863(x42821,x42821)),f864(x42821,a850)),f863(x42821,x42821)),f10(f863(x42821,x42821),a850,x42821)),a338)),f341(f341(f20(x42821,x42821,f863(x42821,x42821)),f250(x42821,x42821)),f7(x42821))))),f309(x42821,f185(f864(f863(x42821,x42821),a850)))) % 19.23/19.03 [4481]~E(f341(f341(f3(a1),f341(f341(f89(a1),x44811),x44811)),a106),a92) % 19.23/19.03 [4483]~E(f341(f341(f89(a1),f341(f341(f89(a1),f87(a1)),x44831)),x44831),f2(a1)) % 19.23/19.03 [3771]E(f341(f341(f89(a1),f341(f341(f3(a1),a106),x37711)),f341(f341(f3(a1),a106),x37711)),f341(f341(f3(a1),a106),f341(f341(f3(a1),f341(f341(f89(a1),x37711),x37711)),a106))) % 19.23/19.03 [3887]E(f341(f341(f3(a1),f341(f341(f89(a1),f341(f341(f3(a1),a106),x38871)),f341(f341(f3(a1),a106),x38871))),a106),f341(f341(f3(a1),a106),f341(f341(f89(a1),x38871),x38871))) % 19.23/19.03 [3921]E(f341(f341(f3(a1),f341(f341(f89(a1),f341(f341(f89(a1),x39211),a106)),f341(f341(f89(a1),x39211),a106))),a106),f341(f341(f89(a1),f341(f341(f89(a1),x39211),x39211)),a106)) % 19.23/19.03 [3960]E(f341(f341(f3(a1),f341(f341(f89(a1),f341(f341(f3(a1),a106),x39601)),f341(f341(f3(a1),a106),x39601))),a106),f341(f341(f3(a1),a92),f341(f341(f3(a1),f341(f341(f89(a1),x39601),x39601)),a106))) % 19.23/19.03 [4064]E(f341(a98,f341(f286(f863(a857,a857),f863(a857,a857),a118),f341(f341(f311(f863(a857,a857)),f341(f341(f250(a857,a857),x40641),f2(a857))),f185(f864(f863(a857,a857),a850))))),f341(f109(a1),x40641)) % 19.23/19.03 [4073]E(f341(a98,f341(f286(f863(a857,a857),f863(a857,a857),a118),f341(f341(f311(f863(a857,a857)),f341(f341(f250(a857,a857),f346(x40731)),f370(x40731))),f185(f864(f863(a857,a857),a850))))),x40731) % 19.23/19.03 [4106]E(f341(f265(a1),f341(f341(f20(a1,a850,a850),f341(f341(f10(a850,f864(a850,a850),a1),a339),f341(f241(a1),f2(a1)))),x41061)),f341(f312(a857,a1,f109(a1)),f341(f265(a857),f341(f341(f10(a1,a850,a857),x41061),f109(a1))))) % 19.23/19.03 [4154]P37(f341(f265(a1),f341(f341(f20(a1,a850,a850),f341(f341(f10(a850,f864(a850,a850),a1),a339),f341(f241(a1),f2(a1)))),x41541))) % 19.23/19.03 [4174]P85(f341(f341(f343(f863(f864(f863(a857,a857),a850),f864(f863(a857,a857),a850))),f341(f341(f250(f864(f863(a857,a857),a850),f864(f863(a857,a857),a850)),x41741),f185(f864(f863(a857,a857),a850)))),a80)) % 19.23/19.03 [4180]E(f341(f312(a1,a857,a114),f341(f265(a1),f341(f341(f20(a1,a850,a850),f341(f341(f10(a850,f864(a850,a850),a1),a339),f341(f241(a1),f2(a1)))),f341(f341(f10(a857,a850,a1),x41801),a114)))),f341(f265(a857),x41801)) % 19.23/19.03 [4329]E(f315(a857,f341(f341(f54(f863(a857,a857),f864(a857,a850)),f341(a117,x43291)),f341(f260(a857,a857,f864(a857,a850)),f341(f341(f9(a857,f864(a857,a850),f864(a857,f864(a857,a850))),f341(f341(f10(f864(a857,f864(f864(a857,a850),f864(a857,a850))),f864(f864(a857,a850),f864(a857,f864(a857,a850))),a857),f9(a857,f864(a857,a850),f864(a857,a850))),f341(f341(f10(f864(a857,a857),f864(a857,f864(f864(a857,a850),f864(a857,a850))),a857),f341(f10(a857,f864(f864(a857,a850),f864(a857,a850)),a857),f311(a857))),f3(a857)))),f185(f864(a857,a850)))))),f341(a114,x43291)) % 19.23/19.03 [3814]E(f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),x38141),x38141)),a106)),a106),f341(f341(f89(a1),x38141),x38141)) % 19.23/19.03 [3862]E(f341(f341(f3(a1),f341(f341(f3(a1),f341(f341(f89(a1),x38621),x38621)),a106)),a106),f341(f341(f89(a1),f341(f341(f3(a1),x38621),a106)),f341(f341(f3(a1),x38621),a106))) % 19.23/19.03 [4081]E(f341(f341(f3(a1),f341(f341(f89(a1),f341(f341(f89(a1),f341(f88(a1),x40811)),a106)),f341(f341(f89(a1),f341(f88(a1),x40811)),a106))),a106),f341(f88(a1),f341(f341(f3(a1),f341(f341(f89(a1),x40811),x40811)),a106))) % 19.23/19.03 [4124]E(f341(f341(f89(a857),x41241),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),f341(a121,f341(a121,x41241))) % 19.23/19.03 [4125]E(f341(f341(f90(a857),x41251),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),f341(f341(f89(a857),x41251),x41251)) % 19.23/19.03 [4126]E(f341(f341(f51(a857),f341(f341(f89(a857),x41261),x41261)),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),x41261) % 19.23/19.03 [4207]E(f60(a857,f341(a121,f341(a121,x42071)),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),f60(a857,x42071,f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106))))) % 19.23/19.03 [4345]E(f341(a98,f341(f341(f54(f863(a857,a857),f864(f863(a857,a857),a850)),f341(a117,x43451)),f341(f260(a857,a857,f864(f863(a857,a857),a850)),f341(f341(f10(f864(a857,f864(f863(a857,a857),a850)),f864(a857,f864(f863(a857,a857),a850)),a857),f341(f10(f864(f863(a857,a857),a850),f864(f863(a857,a857),a850),a857),f286(f863(a857,a857),f863(a857,a857),a118))),f341(f341(f9(a857,f864(f863(a857,a857),a850),f864(a857,f864(f863(a857,a857),a850))),f341(f341(f10(f864(a857,f864(f864(f863(a857,a857),a850),f864(f863(a857,a857),a850))),f864(f864(f863(a857,a857),a850),f864(a857,f864(f863(a857,a857),a850))),a857),f9(a857,f864(f863(a857,a857),a850),f864(f863(a857,a857),a850))),f341(f341(f10(f864(a857,f863(a857,a857)),f864(a857,f864(f864(f863(a857,a857),a850),f864(f863(a857,a857),a850))),a857),f341(f10(f863(a857,a857),f864(f864(f863(a857,a857),a850),f864(f863(a857,a857),a850)),a857),f311(f863(a857,a857)))),f341(f9(a857,a857,f863(a857,a857)),f250(a857,a857))))),f185(f864(f863(a857,a857),a850))))))),f341(f88(a1),x43451)) % 19.23/19.03 [4202]E(f341(f341(f89(a857),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),x42021),f341(a121,f341(a121,x42021))) % 19.23/19.03 [4203]E(f341(f341(f90(a857),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),x42031),f341(f341(f89(a857),x42031),x42031)) % 19.23/19.03 [4236]E(f341(f341(f51(a857),f341(a121,f341(a121,x42361))),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),f341(a121,f341(f341(f51(a857),x42361),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))))) % 19.23/19.03 [4287]E(f341(f341(f89(a857),f341(f113(a857),f341(f341(f3(a1),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106))),a106))),x42871),f341(a121,f341(a121,f341(a121,x42871)))) % 19.23/19.03 [4366]E(f341(f260(a1,a1,f863(a1,a1)),f341(f341(f20(a1,f864(a1,f863(a1,a1)),f864(a1,f863(a1,a1))),f341(f341(f10(f864(a1,f864(f863(a1,a1),f863(a1,a1))),f864(f864(a1,f863(a1,a1)),f864(a1,f863(a1,a1))),a1),f20(a1,f863(a1,a1),f863(a1,a1))),f341(f341(f10(f864(a1,f863(a1,a1)),f864(a1,f864(f863(a1,a1),f863(a1,a1))),a1),f341(f20(a1,f863(a1,a1),f864(f863(a1,a1),f863(a1,a1))),f341(f341(f10(a850,f864(f863(a1,a1),f864(f863(a1,a1),f863(a1,a1))),a1),f105(f863(a1,a1))),f341(f341(f10(a1,a850,a1),f341(f241(a1),f2(a1))),f341(f341(f9(a1,a1,a1),f3(a1)),x43661))))),f341(f341(f9(a1,f864(a1,a1),f864(a1,f863(a1,a1))),f341(f341(f10(f864(a1,f863(a1,a1)),f864(f864(a1,a1),f864(a1,f863(a1,a1))),a1),f10(a1,f863(a1,a1),a1)),f341(f341(f10(a1,f864(a1,f863(a1,a1)),a1),f250(a1,a1)),f341(f341(f9(a1,a1,a1),f341(f341(f10(a1,f864(a1,a1),a1),f89(a1)),f341(f90(a1),f341(f113(a1),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))))),f87(a1))))),f341(f341(f9(a1,a1,a1),f3(a1)),x43661))))),f341(f341(f10(a1,f864(a1,f863(a1,a1)),a1),f250(a1,a1)),f341(f90(a1),f341(f113(a1),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106))))))),f58(x43661)) % 19.23/19.03 [3413]P38(a25,x34131,x34132,x34131) % 19.23/19.03 [3072]P15(a1,f168(x30721,x30722)) % 19.23/19.03 [3167]P46(x31671,x31672,f269(x31671,x31672)) % 19.23/19.03 [3168]P52(x31681,x31681,f269(x31681,x31682)) % 19.23/19.03 [3437]P26(x34371,x34371,f7(x34371),x34372) % 19.23/19.03 [3438]P26(x34381,x34381,f41(x34381),x34382) % 19.23/19.03 [3445]P33(x34451,x34452,f122(x34451),f122(x34451)) % 19.23/19.03 [3446]P26(x34461,f861(x34461),f235(x34461),x34462) % 19.23/19.03 [3455]P26(f858(x34551),f858(x34551),f148(x34551),x34552) % 19.23/19.03 [4374]~E(f43(x43741),f42(x43742)) % 19.23/19.03 [4382]~E(f30(x43821,x43822),a25) % 19.23/19.03 [4383]~E(f38(x43831,x43832),a25) % 19.23/19.03 [4384]~E(f37(x43841,x43842),a25) % 19.23/19.03 [3038]E(f341(f7(x30381),x30382),x30382) % 19.23/19.03 [3039]E(f341(f265(x30391),x30392),x30392) % 19.23/19.03 [3041]E(f341(f41(x30411),x30412),x30412) % 19.23/19.03 [3050]E(f341(f189(x30501),x30502),f124(x30501)) % 19.23/19.03 [3060]E(f36(f30(x30601,x30602)),f2(a857)) % 19.23/19.03 [3070]E(f94(x30701,f341(a338,x30702)),x30702) % 19.23/19.03 [3071]E(f99(x30711,f341(a338,x30712)),x30712) % 19.23/19.03 [3088]E(f341(f186(a851),f30(x30881,x30882)),f2(a857)) % 19.23/19.03 [3093]E(f341(f133(x30931,x30932),f122(x30931)),f122(x30931)) % 19.23/19.03 [3112]E(f309(x31121,f309(x31121,x31122)),f309(x31121,x31122)) % 19.23/19.03 [3133]E(f341(f341(f132(x31331),x31332),f122(x31331)),x31332) % 19.23/19.03 [3142]E(f341(f341(f164(x31421),x31422),f122(x31421)),f122(x31421)) % 19.23/19.03 [3143]E(f341(f341(f135(x31431),x31432),f122(x31431)),f122(x31431)) % 19.23/19.03 [3145]E(f236(x31451,x31452,f188(x31451)),f2(a857)) % 19.23/19.03 [3146]E(f150(x31461,x31462,f122(x31461)),f2(a857)) % 19.23/19.03 [3148]E(f157(x31481,x31482,f122(x31481)),f122(x31481)) % 19.23/19.03 [3149]E(f165(x31491,f122(x31491),x31492),f122(x31491)) % 19.23/19.03 [3155]E(f341(f268(x31551,x31551),f269(x31551,x31552)),x31552) % 19.23/19.03 [3156]E(f341(f270(x31561,x31561),f269(x31561,x31562)),x31562) % 19.23/19.03 [3165]P85(f341(a26,f30(x31651,x31652))) % 19.23/19.03 [3166]E(f341(f287(x31661,x31661),f269(x31661,x31662)),f269(x31661,x31662)) % 19.23/19.03 [3179]E(f309(f858(x31791),f152(x31791,x31792)),f153(x31791,f309(x31791,x31792))) % 19.23/19.03 [3181]P85(f341(f134(a1),f168(x31811,x31812))) % 19.23/19.03 [3189]E(f341(f268(x31891,x31891),f309(x31891,x31892)),f248(f864(x31891,a850))) % 19.23/19.03 [3190]E(f341(f270(x31901,x31901),f309(x31901,x31902)),f248(f864(x31901,a850))) % 19.23/19.03 [3201]E(f341(f163(a1),f168(x32011,x32012)),f304(a1,x32011,x32012)) % 19.23/19.03 [3216]P53(x32161,f185(f864(x32161,a850)),x32162) % 19.23/19.03 [3221]E(f341(f259(a1,a1),f61(x32211,x32212)),f60(a1,x32211,x32212)) % 19.23/19.03 [3222]E(f341(f303(a857,x32221),f341(a121,x32222)),f304(a857,x32221,x32222)) % 19.23/19.03 [3249]E(f304(a857,f341(a121,x32491),x32492),f306(a857,x32491,x32492)) % 19.23/19.03 [3252]P46(x32521,f248(f864(x32521,a850)),f309(x32521,x32522)) % 19.23/19.03 [3315]E(f341(f341(f3(a857),x33151),f341(a121,x33152)),f341(f50(a857),f307(a857,x33152,x33151))) % 19.23/19.03 [3370]E(f161(x33701,x33702,f122(x33701)),f341(f341(f250(f858(x33701),f858(x33701)),f122(x33701)),f122(x33701))) % 19.23/19.03 [3389]E(f341(f260(x33891,x33892,f863(x33891,x33892)),f250(x33891,x33892)),f41(f863(x33891,x33892))) % 19.23/19.03 [3394]P85(f341(f341(f343(f858(x33941)),f122(x33941)),f155(x33941,x33942))) % 19.23/19.03 [3395]E(f341(f186(f858(x33951)),f123(x33951,x33952)),f341(f341(f3(a857),f341(f186(f858(x33951)),x33952)),f87(a857))) % 19.23/19.03 [3404]P85(f341(f71(a857),f307(a857,x34041,x34042))) % 19.23/19.03 [3405]P85(f341(f71(a857),f306(a857,x34051,x34052))) % 19.23/19.03 [3406]P85(f341(f71(a857),f304(a857,x34061,x34062))) % 19.23/19.03 [3407]P85(f341(f71(a1),f307(a1,x34071,x34072))) % 19.23/19.03 [3408]P85(f341(f71(a1),f306(a1,x34081,x34082))) % 19.23/19.03 [3409]P85(f341(f71(a1),f304(a1,x34091,x34092))) % 19.23/19.03 [3499]E(f341(f341(f341(f100(x34991),f605(x34991,x34992)),f804(x34991,x34992)),f815(x34991,x34992)),x34992) % 19.23/19.03 [3518]E(f341(f312(a857,a857,a121),f304(a857,x35181,x35182)),f304(a857,f341(a121,x35181),f341(a121,x35182))) % 19.23/19.03 [3535]E(f341(f341(f290(x35351,x35351,x35351),f309(x35351,x35352)),f309(x35351,x35352)),f309(x35351,x35352)) % 19.23/19.03 [3565]E(f341(f341(f250(a1,a1),f341(f341(f51(a1),x35651),x35652)),f60(a1,x35651,x35652)),f61(x35651,x35652)) % 19.23/19.03 [3566]E(f341(f341(f250(a108,a108),f341(f341(f51(a108),x35661),x35662)),f60(a108,x35661,x35662)),f24(x35661,x35662)) % 19.23/19.03 [3594]E(f341(f341(f250(a857,a857),f341(f341(f51(a857),x35941),x35942)),f60(a857,x35941,x35942)),f94(f863(a857,a857),f63(x35941,x35942))) % 19.23/19.03 [3646]P85(f341(f341(f242(a857),f341(f341(f3(a857),x36461),x36462)),f341(a121,x36461))) % 19.23/19.03 [3746]E(f341(f341(f89(a1),f341(f341(f90(a1),x37461),f341(f341(f51(a1),x37462),x37461))),f60(a1,x37462,x37461)),x37462) % 19.23/19.03 [3750]E(f341(f341(f54(a857,f864(f863(f858(x37501),f858(x37501)),a850)),f248(f864(a857,a850))),f139(x37501,x37502)),f141(x37501,x37502)) % 19.23/19.03 [3975]P85(f341(f341(f343(f863(f858(x39751),f858(x39751))),f341(f341(f250(f858(x39751),f858(x39751)),f122(x39751)),f122(x39751))),f153(x39751,x39752))) % 19.23/19.03 [4137]E(f261(x41371,x41371,x41372,x41372,f7(x41371),f7(x41372)),f41(f863(x41371,x41372))) % 19.23/19.03 [4139]E(f261(x41391,x41391,x41392,x41392,f41(x41391),f41(x41392)),f41(f863(x41391,x41392))) % 19.23/19.03 [4392]~E(f341(f235(x43921),x43922),f188(x43921)) % 19.23/19.03 [4410]~P36(x44101,f341(f235(x44101),x44102)) % 19.23/19.03 [3131]E(f341(f239(x31311),f341(f235(x31311),x31312)),x31312) % 19.23/19.03 [3132]E(f341(f148(x31321),f341(f148(x31321),x31322)),x31322) % 19.23/19.03 [3134]E(f341(f341(f135(x31341),f2(a857)),x31342),x31342) % 19.23/19.03 [3144]E(f341(f341(f164(x31441),f2(a857)),x31442),f122(x31441)) % 19.23/19.03 [3151]E(f341(f341(f132(x31511),f122(x31511)),x31512),x31512) % 19.23/19.03 [3158]E(f341(f186(f861(x31581)),f341(f235(x31581),x31582)),f2(a857)) % 19.23/19.03 [3160]E(f52(f864(x31601,a850),f341(f310(x31601),x31602)),x31602) % 19.23/19.03 [3162]E(f341(f163(x31621),f341(f147(x31621),x31622)),f341(f163(x31621),x31622)) % 19.23/19.03 [3163]E(f341(f163(x31631),f341(f148(x31631),x31632)),f341(f163(x31631),x31632)) % 19.23/19.03 [3170]E(f341(f341(f3(a108),x31701),x31702),f341(f341(a4,x31701),x31702)) % 19.23/19.03 [3183]E(f341(f341(f89(a857),x31831),x31832),f341(f341(f89(a857),x31832),x31831)) % 19.23/19.03 [3184]E(f341(f341(f89(a1),x31841),x31842),f341(f341(f89(a1),x31842),x31841)) % 19.23/19.03 [3185]E(f341(f341(f90(a857),x31851),x31852),f341(f341(f90(a857),x31852),x31851)) % 19.23/19.03 [3186]E(f341(f341(f90(a1),x31861),x31862),f341(f341(f90(a1),x31862),x31861)) % 19.23/19.03 [3208]E(f341(f341(f179(x32081,x32081),f2(a857)),x32082),f41(x32081)) % 19.23/19.03 [3209]E(f341(f186(f858(x32091)),f341(f147(x32091),x32092)),f341(f186(f858(x32091)),x32092)) % 19.23/19.03 [3210]E(f341(f186(f858(x32101)),f341(f148(x32101),x32102)),f341(f186(f858(x32101)),x32102)) % 19.23/19.03 [3211]E(f165(x32111,x32112,f185(f864(a857,a850))),f122(x32111)) % 19.23/19.03 [3212]E(f341(f341(f149(x32121,x32121),f7(x32121)),x32122),x32122) % 19.23/19.03 [3214]E(f341(f249(a1,a1),f61(x32141,x32142)),f341(f341(f51(a1),x32141),x32142)) % 19.23/19.03 [3232]E(f36(f37(x32321,x32322)),f341(f341(f89(a857),f36(x32322)),f341(a121,f2(a857)))) % 19.23/19.03 [3233]E(f341(f285(x32331),f341(f287(x32331,x32331),x32332)),f341(f285(x32331),x32332)) % 19.23/19.03 [3237]P85(f341(f71(x32371),f341(f163(x32371),x32372))) % 19.23/19.03 [3244]E(f341(f341(f89(a1),x32441),f341(f88(a1),x32442)),f341(f341(f3(a1),x32441),x32442)) % 19.23/19.03 [3251]P25(x32511,x32512,f185(f864(f856(x32511),a850))) % 19.23/19.03 [3255]E(f341(f312(x32551,x32551,f7(x32551)),x32552),x32552) % 19.23/19.03 [3256]E(f341(f312(x32561,x32561,f41(x32561)),x32562),x32562) % 19.23/19.03 [3257]E(f341(f314(x32571,x32571,f7(x32571)),x32572),x32572) % 19.23/19.03 [3258]E(f341(f314(x32581,x32581,f41(x32581)),x32582),x32582) % 19.23/19.03 [3259]P85(f341(f248(f864(x32591,a850)),x32592)) % 19.23/19.03 [3261]E(f341(f50(a857),f341(f303(a857,x32611),x32612)),f341(f341(f3(a857),x32612),x32611)) % 19.23/19.03 [3262]E(f341(f303(a857,f341(a121,x32621)),x32622),f307(a857,x32621,x32622)) % 19.23/19.03 [3274]E(f341(f341(f311(x32741),x32742),f185(f864(x32741,a850))),f341(f265(x32741),f341(a338,x32742))) % 19.23/19.03 [3280]E(f341(f341(f311(x32801),x32802),f185(f864(x32801,a850))),f234(x32801,f341(f235(x32801),x32802))) % 19.23/19.03 [3282]E(f309(x32821,f341(f287(x32821,x32821),x32822)),f341(f287(x32821,x32821),f309(x32821,x32822))) % 19.23/19.03 [3286]E(f341(f341(f89(a857),f341(a121,x32861)),x32862),f341(f341(f89(a857),x32861),f341(a121,x32862))) % 19.23/19.03 [3287]E(f341(f341(f3(a857),f341(a121,x32871)),f341(a121,x32872)),f341(f341(f3(a857),x32871),x32872)) % 19.23/19.03 [3292]E(f341(f50(a857),f306(a857,x32921,x32922)),f341(f341(f3(a857),x32922),x32921)) % 19.23/19.03 [3301]P35(x33011,f341(f341(f289(a857,x33011),a246),x33012)) % 19.23/19.03 [3303]P15(a857,f136(a857,f341(f303(a857,x33031),x33032))) % 19.23/19.03 [3305]P85(f341(f71(a857),f341(f303(a857,x33051),x33052))) % 19.23/19.03 [3306]P85(f341(f71(a1),f341(f303(a1,x33061),x33062))) % 19.23/19.03 [3308]E(f341(f287(f858(x33081),f858(x33081)),f152(x33081,x33082)),f152(x33081,f341(f287(x33081,x33081),x33082))) % 19.23/19.03 [3309]E(f341(f186(a851),f37(x33091,x33092)),f341(f341(f89(a857),f341(f186(a851),x33092)),f341(a121,f2(a857)))) % 19.23/19.03 [3311]E(f341(f303(a1,x33111),f341(f341(f89(a1),x33112),f87(a1))),f304(a1,x33111,x33112)) % 19.23/19.03 [3314]E(f341(f341(f51(a1),f341(f88(a1),x33141)),f341(f88(a1),x33142)),f341(f341(f51(a1),x33141),x33142)) % 19.23/19.03 [3322]E(f176(x33221,x33222,f341(f18(f861(x33222),x33221),f188(x33222))),f185(f864(x33222,a850))) % 19.23/19.03 [3323]E(f174(x33231,x33232,f341(f18(f861(x33232),x33231),f188(x33232))),f185(f864(x33231,a850))) % 19.23/19.03 [3324]E(f341(f341(f179(f863(x33241,x33241),a850),f87(a857)),x33242),x33242) % 19.23/19.03 [3326]E(f341(f341(f3(f864(x33261,a850)),x33262),f185(f864(x33261,a850))),x33262) % 19.23/19.03 [3327]E(f341(f341(f110(f864(x33271,a850)),x33272),f185(f864(x33271,a850))),x33272) % 19.23/19.03 [3328]E(f341(f341(f111(f864(x33281,a850)),x33282),f248(f864(x33281,a850))),x33282) % 19.23/19.03 [3329]E(f341(f249(a857,a857),f94(f863(a857,a857),f63(x33291,x33292))),f341(f341(f51(a857),x33291),x33292)) % 19.23/19.03 [3335]E(f316(x33351,f341(a23,x33352),f341(f88(a1),f341(a23,x33352))),f341(f341(f319(a1),x33351),x33352)) % 19.23/19.03 [3336]E(f304(a1,f341(f341(f89(a1),x33361),f87(a1)),x33362),f306(a1,x33361,x33362)) % 19.23/19.03 [3341]E(f341(f259(a857,a857),f94(f863(a857,a857),f63(x33411,x33412))),f60(a857,x33411,x33412)) % 19.23/19.03 [3349]E(f317(x33491,f341(a23,x33492),f341(f88(a1),f341(a23,x33492))),f318(a1,x33491,x33492)) % 19.23/19.03 [3352]P85(f341(f341(f343(x33521),x33522),f248(f864(x33521,a850)))) % 19.23/19.03 [3356]E(f341(f341(f3(a857),f341(a121,x33561)),x33562),f341(f50(a857),f304(a857,x33562,x33561))) % 19.23/19.03 [3381]E(f341(f341(f3(f864(x33811,a850)),x33812),f248(f864(x33811,a850))),f185(f864(x33811,a850))) % 19.23/19.03 [3382]E(f341(f341(f110(f864(x33821,a850)),x33822),f248(f864(x33821,a850))),f248(f864(x33821,a850))) % 19.23/19.03 [3383]E(f341(f341(f111(f864(x33831,a850)),x33832),f185(f864(x33831,a850))),f185(f864(x33831,a850))) % 19.23/19.03 [3397]E(f60(a1,f341(f109(a1),x33971),f341(f109(a1),x33972)),f341(f109(a1),f60(a857,x33971,x33972))) % 19.23/19.03 [3398]E(f60(a1,f341(f88(a1),x33981),f341(f88(a1),x33982)),f341(f88(a1),f60(a1,x33981,x33982))) % 19.23/19.03 [3411]E(f341(f186(f858(x34111)),f341(f162(x34111),x34112)),f341(f341(f3(a857),f341(f186(f858(x34111)),x34112)),f87(a857))) % 19.23/19.03 [3439]E(f341(f341(f51(a1),f60(a1,x34391,x34392)),x34392),f2(a1)) % 19.23/19.03 [3448]E(f341(a5,f60(a857,f341(a22,x34481),f341(a22,x34482))),f60(a108,x34481,x34482)) % 19.23/19.03 [3484]E(f341(a5,f341(f341(f89(a857),f341(a22,x34841)),f341(a22,x34842))),f341(f341(f89(a108),x34841),x34842)) % 19.23/19.03 [3485]E(f341(a5,f341(f341(f90(a857),f341(a22,x34851)),f341(a22,x34852))),f341(f341(f90(a108),x34851),x34852)) % 19.23/19.03 [3486]E(f341(a5,f341(f341(f51(a857),f341(a22,x34861)),f341(a22,x34862))),f341(f341(f51(a108),x34861),x34862)) % 19.23/19.03 [3487]E(f341(a5,f341(f341(f3(a857),f341(a22,x34871)),f341(a22,x34872))),f341(f341(f3(a108),x34871),x34872)) % 19.23/19.03 [3496]E(f341(f312(a857,a857,a121),f341(f303(a857,x34961),x34962)),f341(f303(a857,f341(a121,x34961)),f341(a121,x34962))) % 19.23/19.03 [3523]P85(f341(f63(x35231,x35232),f94(f863(a857,a857),f63(x35231,x35232)))) % 19.23/19.03 [3540]E(f341(f341(f89(a857),f341(f341(f89(a857),f36(x35401)),f36(x35402))),f341(a121,f2(a857))),f36(f38(x35401,x35402))) % 19.23/19.03 [3541]E(f60(a857,f341(a121,f60(a857,x35411,x35412)),x35412),f60(a857,f341(a121,x35411),x35412)) % 19.23/19.03 [3555]E(f341(f341(f55(f864(x35551,a850),f864(x35551,a850)),x35552),f7(f864(x35551,a850))),f53(f864(x35551,a850),x35552)) % 19.23/19.03 [3556]E(f341(f341(f54(f864(x35561,a850),f864(x35561,a850)),x35562),f7(f864(x35561,a850))),f52(f864(x35561,a850),x35562)) % 19.23/19.03 [3559]P85(f341(f341(f343(f864(x35591,a850)),x35592),f341(f310(x35591),x35592))) % 19.23/19.03 [3564]E(f60(a1,f341(f88(a1),f60(a1,x35641,x35642)),x35642),f60(a1,f341(f88(a1),x35641),x35642)) % 19.23/19.03 [3575]P85(f341(f341(f241(f864(x35751,a850)),x35752),f248(f864(x35751,a850)))) % 19.23/19.03 [3577]E(f341(f341(f290(x35771,x35771,x35771),f309(x35771,x35772)),f309(x35771,f309(x35771,x35772))),f309(x35771,x35772)) % 19.23/19.03 [3578]E(f341(f341(f110(f864(x35781,a850)),f341(f270(x35781,x35781),x35782)),f341(f268(x35781,x35781),x35782)),f341(f285(x35781),x35782)) % 19.23/19.03 [3600]E(f323(x36001,x36002,f248(f864(x36001,a850)),f248(f864(x36002,a850))),f248(f864(f865(x36001,x36002),a850))) % 19.23/19.03 [3651]P85(f341(f341(f241(a857),f60(a857,x36511,x36512)),x36511)) % 19.23/19.03 [3675]P85(f341(f341(f241(a1),f341(f88(a1),f341(f109(a1),x36751))),f341(f109(a1),x36752))) % 19.23/19.03 [3700]P85(f341(f341(f343(f864(x37001,a850)),f185(f864(x37001,a850))),f341(f310(x37001),x37002))) % 19.23/19.03 [3705]E(f309(x37051,f341(f341(f290(x37051,x37051,x37051),x37052),f309(x37051,x37052))),f309(x37051,x37052)) % 19.23/19.03 [3708]E(f341(f341(f290(x37081,x37081,x37081),f309(x37081,x37082)),x37082),f341(f341(f290(x37081,x37081,x37081),x37082),f309(x37081,x37082))) % 19.23/19.03 [3710]E(f341(a114,f341(f341(f89(a1),f341(f341(f3(a1),x37101),x37102)),f87(a1))),f341(f50(a1),f304(a1,x37102,x37101))) % 19.23/19.03 [3727]E(f341(f268(x37271,x37271),f341(f341(f290(x37271,x37271,x37271),x37272),f309(x37271,x37272))),f341(f268(x37271,x37271),x37272)) % 19.23/19.03 [3728]E(f341(f270(x37281,x37281),f341(f341(f290(x37281,x37281,x37281),x37282),f309(x37281,x37282))),f341(f270(x37281,x37281),x37282)) % 19.23/19.03 [3742]E(f341(f341(f89(a857),f341(f341(f89(a857),f341(f186(a851),x37421)),f341(f186(a851),x37422))),f341(a121,f2(a857))),f341(f186(a851),f38(x37421,x37422))) % 19.23/19.03 [3754]P26(a857,a857,f341(f341(f9(a857,a857,a857),f89(a857)),x37541),x37542) % 19.23/19.03 [3756]P15(a857,f341(f148(a857),f341(f341(f149(f858(x37561),a857),f186(f858(x37561))),f169(x37561,x37562)))) % 19.23/19.03 [3803]P85(f341(f341(f242(a1),f341(f88(a1),f341(f109(a1),f341(a121,x38031)))),f341(f109(a1),x38032))) % 19.23/19.03 [3843]E(f341(f138(f858(x38431),x38431,f341(f9(x38431,f858(x38431),f858(x38431)),f146(x38431)),f122(x38431)),x38432),f341(f148(x38431),x38432)) % 19.23/19.03 [3894]P85(f341(f341(f241(f864(f863(f858(x38941),f858(x38941)),a850)),f153(x38941,x38942)),f309(f858(x38941),f152(x38941,x38942)))) % 19.23/19.03 [3925]P85(f341(f63(x39251,x39252),f341(f341(f250(a857,a857),f341(f341(f51(a857),x39251),x39252)),f60(a857,x39251,x39252)))) % 19.23/19.03 [3936]P85(f341(f341(f241(f864(f863(f858(x39361),f858(x39361)),a850)),f152(x39361,f309(x39361,x39362))),f309(f858(x39361),f152(x39361,x39362)))) % 19.23/19.03 [4166]E(f341(f341(f262(f863(a108,a108),a108,f863(a108,a108),f863(x41661,f863(a108,a108))),f273(f341(f160(a108),f341(f341(f149(f863(a108,x41661),a108),f249(a108,x41661)),x41662)))),f341(f341(f10(x41661,f864(f863(a108,a108),f863(x41661,f863(a108,a108))),a108),f250(x41661,f863(a108,a108))),f274(x41661,x41662))),f272(x41661,x41662)) % 19.23/19.03 [4344]E(f341(f260(f864(f863(x43441,x43441),a850),f864(f863(x43441,x43441),a850),f864(f864(x43442,x43441),f863(f864(f863(x43442,x43442),a850),f864(f863(x43442,x43442),a850)))),f341(f341(f9(f864(f863(x43441,x43441),a850),f864(f864(f863(x43441,x43441),a850),f864(f864(x43442,x43441),f864(f863(x43442,x43442),a850))),f864(f864(f863(x43441,x43441),a850),f864(f864(x43442,x43441),f863(f864(f863(x43442,x43442),a850),f864(f863(x43442,x43442),a850))))),f341(f341(f10(f864(f864(f864(x43442,x43441),f864(f863(x43442,x43442),a850)),f864(f864(x43442,x43441),f863(f864(f863(x43442,x43442),a850),f864(f863(x43442,x43442),a850)))),f864(f864(f864(f863(x43441,x43441),a850),f864(f864(x43442,x43441),f864(f863(x43442,x43442),a850))),f864(f864(f863(x43441,x43441),a850),f864(f864(x43442,x43441),f863(f864(f863(x43442,x43442),a850),f864(f863(x43442,x43442),a850))))),f864(f863(x43441,x43441),a850)),f10(f864(f864(x43442,x43441),f864(f863(x43442,x43442),a850)),f864(f864(x43442,x43441),f863(f864(f863(x43442,x43442),a850),f864(f863(x43442,x43442),a850))),f864(f863(x43441,x43441),a850))),f341(f341(f10(f864(f864(x43442,x43441),f864(f864(f863(x43442,x43442),a850),f863(f864(f863(x43442,x43442),a850),f864(f863(x43442,x43442),a850)))),f864(f864(f864(x43442,x43441),f864(f863(x43442,x43442),a850)),f864(f864(x43442,x43441),f863(f864(f863(x43442,x43442),a850),f864(f863(x43442,x43442),a850)))),f864(f863(x43441,x43441),a850)),f20(f864(x43442,x43441),f864(f863(x43442,x43442),a850),f863(f864(f863(x43442,x43442),a850),f864(f863(x43442,x43442),a850)))),f341(f341(f10(f864(f864(x43442,x43441),f864(f863(x43442,x43442),a850)),f864(f864(x43442,x43441),f864(f864(f863(x43442,x43442),a850),f863(f864(f863(x43442,x43442),a850),f864(f863(x43442,x43442),a850)))),f864(f863(x43441,x43441),a850)),f341(f10(f864(f863(x43442,x43442),a850),f864(f864(f863(x43442,x43442),a850),f863(f864(f863(x43442,x43442),a850),f864(f863(x43442,x43442),a850))),f864(x43442,x43441)),f250(f864(f863(x43442,x43442),a850),f864(f863(x43442,x43442),a850)))),f289(x43441,x43442))))),f289(x43441,x43442))),f83(x43441,x43442)) % 19.23/19.03 [4460]~E(f341(f310(x44601),x44602),f185(f864(f864(x44601,a850),a850))) % 19.23/19.03 [4478]~P85(f341(f341(f343(x44781),x44782),f185(f864(x44781,a850)))) % 19.23/19.03 [4488]~P85(f341(f341(f242(f864(x44881,a850)),x44882),f185(f864(x44881,a850)))) % 19.23/19.03 [3264]E(f341(f341(f3(a857),x32641),f341(f341(f89(a857),x32641),x32642)),f2(a857)) % 19.23/19.03 [3266]E(f341(f341(f110(f864(x32661,a850)),x32662),x32662),x32662) % 19.23/19.03 [3267]E(f341(f341(f111(f864(x32671,a850)),x32672),x32672),x32672) % 19.23/19.03 [3294]E(f341(f341(f3(f864(x32941,a850)),x32942),x32942),f185(f864(x32941,a850))) % 19.23/19.03 [3297]E(f341(f139(x32971,x32972),f2(a857)),f185(f864(f863(f858(x32971),f858(x32971)),a850))) % 19.23/19.03 [3298]E(f341(f341(f89(a857),x32981),f341(a121,x32982)),f341(a121,f341(f341(f89(a857),x32981),x32982))) % 19.23/19.03 [3310]E(f193(f341(f109(a1),x33101),f341(f109(a1),x33102)),f341(f109(a1),f341(f341(f3(a857),x33101),x33102))) % 19.23/19.03 [3313]E(f341(f341(f51(a1),f341(f88(a1),x33131)),x33132),f341(f341(f51(a1),x33131),f341(f88(a1),x33132))) % 19.23/19.03 [3317]E(f341(f50(a1),f341(f303(a1,x33171),x33172)),f341(a114,f341(f341(f3(a1),x33172),x33171))) % 19.23/19.03 [3320]E(f341(f341(f89(a857),f341(a121,x33201)),x33202),f341(a121,f341(f341(f89(a857),x33201),x33202))) % 19.23/19.03 [3325]E(f341(f88(f864(x33251,a850)),f341(f88(f864(x33251,a850)),x33252)),x33252) % 19.23/19.03 [3338]E(f169(x33381,f341(f341(f146(f858(x33381)),f122(x33381)),x33382)),f169(x33381,x33382)) % 19.23/19.03 [3342]E(f341(f341(f89(a857),x33421),f341(f341(f90(a857),x33421),x33422)),f341(f341(f90(a857),x33421),f341(a121,x33422))) % 19.23/19.03 [3350]E(f341(f341(a4,f341(a5,x33501)),f341(a5,x33502)),f341(a5,f341(f341(f3(a857),x33501),x33502))) % 19.23/19.03 [3361]E(f341(f341(f90(a1),f341(f88(a1),x33611)),x33612),f341(f88(a1),f341(f341(f90(a1),x33611),x33612))) % 19.23/19.03 [3363]E(f341(f341(f251(a1),f341(f109(a1),x33631)),x33632),f341(f109(a1),f341(f341(f251(a857),x33631),x33632))) % 19.23/19.03 [3364]E(f341(f341(f89(a108),f341(a5,x33641)),f341(a5,x33642)),f341(a5,f341(f341(f89(a857),x33641),x33642))) % 19.23/19.03 [3365]E(f341(f341(f90(a108),f341(a5,x33651)),f341(a5,x33652)),f341(a5,f341(f341(f90(a857),x33651),x33652))) % 19.23/19.03 [3366]E(f341(f341(f245(a857),f341(a121,x33661)),f341(a121,x33662)),f341(a121,f341(f341(f245(a857),x33661),x33662))) % 19.23/19.03 [3367]E(f341(f341(f240(a857),f341(a121,x33671)),f341(a121,x33672)),f341(a121,f341(f341(f240(a857),x33671),x33672))) % 19.23/19.03 [3373]E(f341(f163(a857),f136(a857,f341(f303(a857,x33731),x33732))),f341(f303(a857,x33731),x33732)) % 19.23/19.03 [3374]E(f315(x33741,f341(f341(f311(x33741),x33742),f185(f864(x33741,a850)))),x33742) % 19.23/19.03 [3379]E(f341(f268(x33791,x33792),f185(f864(f863(x33791,x33792),a850))),f185(f864(x33792,a850))) % 19.23/19.03 [3380]E(f341(f270(x33801,x33802),f185(f864(f863(x33801,x33802),a850))),f185(f864(x33801,a850))) % 19.23/19.03 [3384]E(f341(a114,f341(f341(f3(a1),x33841),x33842)),f341(f50(a1),f306(a1,x33842,x33841))) % 19.23/19.03 [3388]E(f341(f341(f89(a857),x33881),f341(f341(f90(a857),x33882),x33881)),f341(f341(f90(a857),f341(a121,x33882)),x33881)) % 19.23/19.03 [3390]E(f341(f341(f69(x33901),f185(f864(x33901,a850))),x33902),f185(f864(f864(x33901,a850),a850))) % 19.23/19.03 [3399]E(f341(f186(f858(a857)),f136(a857,f341(f303(a857,x33991),x33992))),f341(f341(f3(a857),x33992),x33991)) % 19.23/19.03 [3418]E(f341(f341(f110(f864(x34181,a850)),f185(f864(x34181,a850))),x34182),x34182) % 19.23/19.03 [3419]E(f341(f341(f111(f864(x34191,a850)),f248(f864(x34191,a850))),x34192),x34192) % 19.23/19.03 [3422]E(f341(f341(f89(a1),f341(f88(a1),x34221)),f341(f88(a1),x34222)),f341(f88(a1),f341(f341(f89(a1),x34221),x34222))) % 19.23/19.03 [3425]E(f341(f341(f89(a1),f341(f109(a1),x34251)),f341(f109(a1),x34252)),f341(f109(a1),f341(f341(f89(a857),x34251),x34252))) % 19.23/19.03 [3426]E(f341(f341(f89(a1),f341(f113(a1),x34261)),f341(f113(a1),x34262)),f341(f113(a1),f341(f341(f89(a1),x34261),x34262))) % 19.23/19.03 [3428]E(f341(f341(f90(a1),f341(f109(a1),x34281)),f341(f109(a1),x34282)),f341(f109(a1),f341(f341(f90(a857),x34281),x34282))) % 19.23/19.03 [3429]E(f341(f341(f90(a1),f341(f113(a1),x34291)),f341(f113(a1),x34292)),f341(f113(a1),f341(f341(f90(a1),x34291),x34292))) % 19.23/19.03 [3430]E(f341(f341(f51(a1),f341(f109(a1),x34301)),f341(f109(a1),x34302)),f341(f109(a1),f341(f341(f51(a857),x34301),x34302))) % 19.23/19.03 [3449]E(f341(f341(f8(x34491,a857),f341(f18(a857,x34491),f87(a857))),x34492),f341(f50(x34491),x34492)) % 19.23/19.03 [3460]E(f341(f88(a1),f60(a1,f341(f88(a1),x34601),x34602)),f60(a1,x34601,f341(f88(a1),x34602))) % 19.23/19.03 [3462]E(f341(f163(a1),f168(x34621,f341(f341(f3(a1),x34622),f87(a1)))),f341(f303(a1,x34621),x34622)) % 19.23/19.03 [3466]P85(f341(f341(f241(a857),x34661),f341(f341(f89(a857),x34662),x34661))) % 19.23/19.03 [3467]P85(f341(f341(f241(a857),x34671),f341(f341(f89(a857),x34671),x34672))) % 19.23/19.03 [3470]E(f341(f341(f3(f864(x34701,a850)),f185(f864(x34701,a850))),x34702),f185(f864(x34701,a850))) % 19.23/19.03 [3471]E(f341(f341(f110(f864(x34711,a850)),f248(f864(x34711,a850))),x34712),f248(f864(x34711,a850))) % 19.23/19.03 [3472]E(f341(f341(f111(f864(x34721,a850)),f185(f864(x34721,a850))),x34722),f185(f864(x34721,a850))) % 19.23/19.03 [3477]E(f341(f341(f250(a1,a1),x34771),f341(f88(a1),x34772)),f341(a66,f341(f341(f250(a1,a1),x34771),x34772))) % 19.23/19.03 [3478]E(f341(f303(a1,f341(f341(f89(a1),x34781),f87(a1))),x34782),f307(a1,x34781,x34782)) % 19.23/19.03 [3488]E(f341(f341(f90(a857),x34881),f341(f341(f51(a857),x34882),x34881)),f341(f341(f3(a857),x34882),f60(a857,x34882,x34881))) % 19.23/19.03 [3489]E(f341(f341(f90(a1),x34891),f341(f341(f51(a1),x34892),x34891)),f341(f341(f3(a1),x34892),f60(a1,x34892,x34891))) % 19.23/19.03 [3493]E(f341(f163(a1),f168(f341(f341(f89(a1),x34931),f87(a1)),x34932)),f306(a1,x34931,x34932)) % 19.23/19.03 [3497]P85(f341(f341(f241(f864(x34971,a850)),x34972),x34972)) % 19.23/19.03 [3503]E(f341(f341(f110(f864(x35031,a850)),x35032),f341(f88(f864(x35031,a850)),x35032)),f248(f864(x35031,a850))) % 19.23/19.03 [3504]E(f341(f341(f111(f864(x35041,a850)),x35042),f341(f88(f864(x35041,a850)),x35042)),f185(f864(x35041,a850))) % 19.23/19.03 [3510]E(f341(f341(f3(a857),f341(f341(f3(a857),x35101),f87(a857))),x35102),f341(f341(f3(a857),x35101),f341(a121,x35102))) % 19.23/19.03 [3515]E(f341(f341(f3(f864(x35151,a850)),f248(f864(x35151,a850))),x35152),f341(f88(f864(x35151,a850)),x35152)) % 19.23/19.03 [3516]E(f341(f341(f3(a1),f341(f113(a1),x35161)),f341(f113(a1),x35162)),f341(f113(a1),f341(f341(f89(a1),x35161),f341(f88(a1),x35162)))) % 19.23/19.03 [3528]E(f341(f163(a857),f136(a857,f341(f303(a857,x35281),f341(a121,x35282)))),f304(a857,x35281,x35282)) % 19.23/19.03 [3557]E(f341(f341(f179(f863(x35571,x35571),a850),f2(a857)),x35572),f309(x35571,f185(f864(f863(x35571,x35571),a850)))) % 19.23/19.03 [3561]P85(f341(f134(a857),f136(a857,f341(f303(a857,x35611),x35612)))) % 19.23/19.03 [3576]E(f341(f312(a1,a857,a114),f304(a1,f341(f109(a1),x35761),f341(f109(a1),x35762))),f304(a857,x35761,x35762)) % 19.23/19.03 [3586]E(f181(a857,f2(a857),f7(a857),f341(f341(f3(a857),x35861),x35862)),f341(f341(f3(a857),x35861),f341(a121,x35862))) % 19.23/19.03 [3587]E(f341(a114,f341(f341(f3(a1),x35871),f341(f341(f89(a1),x35872),f87(a1)))),f341(f50(a1),f307(a1,x35872,x35871))) % 19.23/19.03 [3622]E(f341(f341(f149(a857,a857),a121),f136(a857,f341(f303(a857,x36221),x36222))),f136(a857,f341(f303(a857,f341(a121,x36221)),f341(a121,x36222)))) % 19.23/19.03 [3629]E(f341(f163(a1),f168(f341(f341(f89(a1),x36291),f87(a1)),f341(f341(f3(a1),x36292),f87(a1)))),f307(a1,x36291,x36292)) % 19.23/19.03 [3643]P85(f341(f341(f241(f864(x36431,a850)),f185(f864(x36431,a850))),x36432)) % 19.23/19.03 [3647]E(f94(x36471,f341(f341(f9(x36471,x36471,a850),a338),x36472)),x36472) % 19.23/19.03 [3648]E(f99(x36481,f341(f341(f9(x36481,x36481,a850),a338),x36482)),x36482) % 19.23/19.03 [3652]E(f341(f163(a857),f136(a857,f341(f303(a857,f341(a121,x36521)),f341(a121,x36522)))),f306(a857,x36521,x36522)) % 19.23/19.03 [3678]E(f341(f341(f257(x36781,x36782),f248(f864(x36781,a850))),f341(f18(f864(x36782,a850),x36781),f248(f864(x36782,a850)))),f248(f864(f863(x36781,x36782),a850))) % 19.23/19.03 [3714]E(f341(f265(x37141),f341(f341(f10(a850,a850,x37141),a337),x37142)),f341(f88(f864(x37141,a850)),f341(f265(x37141),x37142))) % 19.23/19.03 [3717]E(f341(f265(x37171),f341(f341(f9(x37171,x37171,a850),a338),x37172)),f341(f341(f311(x37171),x37172),f185(f864(x37171,a850)))) % 19.23/19.03 [3724]E(f341(f341(f89(a1),f341(f341(f89(a1),x37241),x37241)),f341(f341(f89(a1),x37242),x37242)),f341(f341(f89(a1),f341(f341(f89(a1),x37241),x37242)),f341(f341(f89(a1),x37241),x37242))) % 19.23/19.03 [3725]E(f341(f341(f3(a1),f341(f341(f89(a1),x37251),x37251)),f341(f341(f89(a1),x37252),x37252)),f341(f341(f89(a1),f341(f341(f3(a1),x37251),x37252)),f341(f341(f3(a1),x37251),x37252))) % 19.23/19.03 [3740]P85(f341(f341(f241(a857),f341(f50(x37401),f341(f163(x37401),x37402))),f341(f186(f858(x37401)),x37402))) % 19.23/19.03 [3751]E(f341(f265(x37511),f341(f341(f9(x37511,f864(x37511,a850),a850),f343(x37511)),x37512)),x37512) % 19.23/19.03 [3767]E(f341(f341(f164(x37671),f341(f341(f3(a857),f341(f186(f858(x37671)),x37672)),f87(a857))),x37672),f123(x37671,x37672)) % 19.23/19.03 [3790]E(f181(a857,f2(a857),f341(f341(f10(a857,a857,a857),a121),f341(f245(a857),x37901)),x37902),f341(f341(f245(a857),f341(a121,x37901)),x37902)) % 19.23/19.03 [3794]E(f52(f864(x37941,a850),f341(f312(f864(f863(x37941,x37941),a850),f864(x37941,a850),f285(x37941)),x37942)),f341(f285(x37941),f52(f864(f863(x37941,x37941),a850),x37942))) % 19.23/19.03 [3795]E(f181(a857,f341(a121,x37951),f341(f341(f10(a857,a857,a857),a121),f341(f240(a857),x37951)),x37952),f341(f341(f240(a857),f341(a121,x37951)),x37952)) % 19.23/19.03 [3797]E(f341(f341(f250(a1,a1),f341(f341(f51(a1),f341(f84(a1),x37971)),f341(f84(a1),x37972))),f60(a1,f341(f84(a1),x37971),f341(f84(a1),x37972))),f68(x37971,x37972)) % 19.23/19.03 [3817]P85(f341(f341(f241(f864(f864(x38171,a850),a850)),x38172),f341(f310(x38171),f52(f864(x38171,a850),x38172)))) % 19.23/19.03 [3848]E(f341(f341(f54(x38481,f864(x38481,a850)),x38482),f341(f341(f9(x38481,f864(x38481,a850),f864(x38481,a850)),f311(x38481)),f185(f864(x38481,a850)))),x38482) % 19.23/19.03 [3849]E(f341(f341(f290(x38491,x38491,x38491),f341(f287(x38491,x38491),x38492)),f309(x38491,f341(f287(x38491,x38491),x38492))),f341(f287(x38491,x38491),f341(f341(f290(x38491,x38491,x38491),x38492),f309(x38491,x38492)))) % 19.23/19.03 [3917]E(f341(f163(x39171),f341(f138(f858(x39171),f858(x39171),f132(x39171),f122(x39171)),x39172)),f341(f341(f54(f858(x39171),f864(x39171,a850)),f341(f163(f858(x39171)),x39172)),f163(x39171))) % 19.23/19.03 [3948]E(f341(f341(f110(f864(f863(x39481,x39481),a850)),f309(x39481,f185(f864(f863(x39481,x39481),a850)))),f341(f341(f290(x39481,x39481,x39481),f309(x39481,x39482)),x39482)),f309(x39481,x39482)) % 19.23/19.03 [3986]E(f341(f341(f172(x39861,x39861),x39862),x39862),f341(f341(f149(x39861,f863(x39861,x39861)),f341(f341(f20(x39861,x39861,f863(x39861,x39861)),f250(x39861,x39861)),f7(x39861))),x39862)) % 19.23/19.03 [4100]E(f341(f138(a857,f858(x41001),f341(f9(f858(x41001),a857,a857),f341(f341(f10(a857,f864(a857,a857),f858(x41001)),f240(a857)),f186(f858(x41001)))),f2(a857)),f341(f148(f858(x41001)),x41002)),f341(f186(f858(f858(x41001))),f169(x41001,x41002))) % 19.23/19.03 [4179]E(f341(f341(f289(f863(a857,f858(x41791)),f858(x41791)),f335(a857,f858(x41791),a246,f141(x41791,x41792))),f341(f341(f20(f858(x41791),f858(x41791),f863(a857,f858(x41791))),f341(f341(f10(a857,f864(f858(x41791),f863(a857,f858(x41791))),f858(x41791)),f250(a857,f858(x41791))),f186(f858(x41791)))),f7(f858(x41791)))),f142(x41791,x41792)) % 19.23/19.03 [4302]E(f341(f265(x43021),f341(f341(f10(f864(f864(x43021,a850),a850),a850,x43021),f97(f864(x43021,a850))),f341(f341(f10(f864(f864(x43021,a850),a850),f864(f864(x43021,a850),a850),x43021),f341(f20(f864(x43021,a850),a850,a850),f341(f341(f10(a850,f864(a850,a850),f864(x43021,a850)),a344),f341(f341(f9(f864(x43021,a850),f864(f864(x43021,a850),a850),a850),f343(f864(x43021,a850))),x43022)))),f343(x43021)))),f53(f864(x43021,a850),x43022)) % 19.23/19.03 [4489]~P85(f341(f341(f242(a1),f341(f109(a1),x44891)),f341(f88(a1),f341(f109(a1),x44892)))) % 19.23/19.03 [3386]E(f341(f341(f3(a857),f341(f341(f89(a857),x33861),x33862)),x33862),x33861) % 19.23/19.03 [3387]E(f341(f341(f3(a857),f341(f341(f89(a857),x33871),x33872)),x33871),x33872) % 19.23/19.03 [3461]E(f341(f341(f89(a857),f341(f341(f3(a857),x34611),x34612)),x34612),f341(f341(f240(a857),x34611),x34612)) % 19.23/19.03 [3563]E(f341(f341(f90(a857),f341(f341(f51(a857),x35631),x35632)),x35632),f341(f341(f3(a857),x35631),f60(a857,x35631,x35632))) % 19.23/19.03 [3591]E(f341(f163(a857),f136(a857,f341(f303(a857,f341(a121,x35911)),x35912))),f307(a857,x35911,x35912)) % 19.23/19.03 [3599]E(f341(f109(a1),f219(f341(a114,f341(f84(a1),x35991)),f341(a114,f341(f84(a1),x35992)))),f341(f341(a220,x35991),x35992)) % 19.23/19.03 [3601]E(f341(f341(f110(f864(x36011,a850)),f341(f88(f864(x36011,a850)),x36012)),x36012),f248(f864(x36011,a850))) % 19.23/19.03 [3602]E(f341(f341(f111(f864(x36021,a850)),f341(f88(f864(x36021,a850)),x36022)),x36022),f185(f864(x36021,a850))) % 19.23/19.03 [3618]P85(f341(f341(f241(a857),f341(f341(f51(a857),x36181),x36182)),x36181)) % 19.23/19.03 [3619]P85(f341(f341(f241(a857),f341(f341(f3(a857),x36191),x36192)),x36191)) % 19.23/19.03 [3644]P85(f341(f341(f242(a857),x36441),f341(a121,f341(f341(f89(a857),x36442),x36441)))) % 19.23/19.03 [3645]P85(f341(f341(f242(a857),x36451),f341(a121,f341(f341(f89(a857),x36451),x36452)))) % 19.23/19.03 [3664]E(f341(f341(f90(a857),f341(a114,f341(f84(a1),x36641))),f341(a114,f341(f84(a1),x36642))),f341(a114,f341(f84(a1),f341(f341(f90(a1),x36641),x36642)))) % 19.23/19.03 [3674]P85(f341(f341(f241(a1),f2(a1)),f341(f341(f251(a1),f341(f84(a1),x36741)),x36742))) % 19.23/19.03 [3745]E(f341(f286(f858(x37451),f858(x37451),f153(x37451,x37452)),f341(f341(f311(f858(x37451)),f122(x37451)),f185(f864(f858(x37451),a850)))),f341(f341(f311(f858(x37451)),f122(x37451)),f185(f864(f858(x37451),a850)))) % 19.23/19.03 [3763]E(f341(f341(f110(f864(f863(x37631,x37631),a850)),f309(x37631,x37632)),f309(x37631,f185(f864(f863(x37631,x37631),a850)))),f309(x37631,x37632)) % 19.23/19.03 [3779]E(f341(f341(f51(a1),f341(f113(a1),f341(f341(f89(a1),x37791),x37791))),f341(f113(a1),f341(f341(f89(a1),x37792),x37792))),f341(f341(f51(a1),f341(f113(a1),x37791)),f341(f113(a1),x37792))) % 19.23/19.03 [3838]E(f341(f341(f251(a1),x38381),f341(f113(a857),f341(f341(f89(a1),x38382),x38382))),f341(f341(f95(a1,a1),f341(f341(f251(a1),x38381),f341(f113(a857),x38382))),f341(f341(f20(a1,a1,a1),f90(a1)),f7(a1)))) % 19.23/19.03 [3844]E(f341(f265(f864(x38441,a850)),f341(f341(f9(f864(x38441,a850),f864(x38441,a850),a850),f241(f864(x38441,a850))),x38442)),f341(f310(x38441),x38442)) % 19.23/19.03 [3893]E(f341(f312(a1,a1,f341(f341(f9(a1,a1,a1),f89(a1)),x38931)),f341(f303(a1,f2(a1)),f341(f341(f3(a1),x38932),x38931))),f341(f303(a1,x38931),x38932)) % 19.23/19.03 [3896]P47(x38961,f341(f341(f3(f864(f863(x38961,x38961),a850)),x38962),f309(x38961,f185(f864(f863(x38961,x38961),a850))))) % 19.23/19.03 [3915]E(f341(f186(f858(x39151)),f341(f138(f858(x39151),f858(x39151),f132(x39151),f122(x39151)),x39152)),f341(f160(a857),f341(f341(f149(f858(x39151),a857),f186(f858(x39151))),x39152))) % 19.23/19.03 [3919]P46(x39191,f248(f864(x39191,a850)),f341(f341(f110(f864(f863(x39191,x39191),a850)),x39192),f309(x39191,f185(f864(f863(x39191,x39191),a850))))) % 19.23/19.03 [3965]E(f181(a857,f2(a857),f341(f341(f10(a857,a857,a857),a121),f341(f341(f9(a857,a857,a857),f245(a857)),x39651)),x39652),f341(f341(f245(a857),x39652),f341(a121,x39651))) % 19.23/19.03 [3968]E(f181(a857,f341(a121,x39681),f341(f341(f10(a857,a857,a857),a121),f341(f341(f9(a857,a857,a857),f240(a857)),x39681)),x39682),f341(f341(f240(a857),x39682),f341(a121,x39681))) % 19.23/19.03 [3971]E(f341(f312(x39711,f858(x39711),f341(f341(f9(x39711,f858(x39711),f858(x39711)),f146(x39711)),f122(x39711))),x39712),f166(x39711,x39712,f341(f341(f311(f858(x39711)),f122(x39711)),f185(f864(f858(x39711),a850))))) % 19.23/19.03 [3972]E(f341(f341(f110(f864(f863(x39721,x39721),a850)),f341(f341(f290(x39721,x39721,x39721),x39722),f309(x39721,x39722))),f309(x39721,f185(f864(f863(x39721,x39721),a850)))),f309(x39721,x39722)) % 19.23/19.03 [3980]P85(f341(f341(f241(f864(f863(x39801,x39801),a850)),f269(x39801,x39802)),f341(f341(f257(x39801,x39801),x39802),f341(f18(f864(x39801,a850),x39801),x39802)))) % 19.23/19.03 [3984]E(f341(f312(a1,a857,a114),f341(f341(f110(f864(a1,a850)),f341(f312(a857,a1,f109(a1)),x39841)),f341(f312(a857,a1,f109(a1)),x39842))),f341(f341(f110(f864(a857,a850)),x39841),x39842)) % 19.23/19.03 [3985]E(f341(f312(a1,a857,a114),f341(f341(f111(f864(a1,a850)),f341(f312(a857,a1,f109(a1)),x39851)),f341(f312(a857,a1,f109(a1)),x39852))),f341(f341(f111(f864(a857,a850)),x39851),x39852)) % 19.23/19.03 [3989]E(f341(f265(x39891),f341(f341(f10(a850,a850,x39891),a337),f341(f341(f9(x39891,f864(x39891,a850),a850),f343(x39891)),x39892))),f341(f88(f864(x39891,a850)),x39892)) % 19.23/19.03 [4016]E(f341(f138(f858(x40161),f858(x40161),f132(x40161),f122(x40161)),f341(f341(f149(f858(x40161),f858(x40161)),f148(x40161)),f341(f148(f858(x40161)),x40162))),f341(f148(x40161),f341(f138(f858(x40161),f858(x40161),f132(x40161),f122(x40161)),x40162))) % 19.23/19.03 [4043]E(f341(f341(f54(a857,f864(f863(x40431,x40431),a850)),f248(f864(a857,a850))),f341(f341(f9(a857,f864(f863(x40431,x40431),a850),f864(f863(x40431,x40431),a850)),f179(f863(x40431,x40431),a850)),x40432)),f309(x40431,x40432)) % 19.23/19.03 [4065]E(f94(x40651,f341(f341(f10(f864(x40651,a850),a850,x40651),f341(a338,x40652)),f341(f341(f9(x40651,f864(x40651,a850),f864(x40651,a850)),f311(x40651)),f185(f864(x40651,a850))))),f315(x40651,x40652)) % 19.23/19.03 [4088]E(f341(f341(f110(f864(f863(x40881,x40881),a850)),x40882),f341(f341(f290(x40881,x40881,x40881),f341(f341(f290(x40881,x40881,x40881),x40882),f309(x40881,x40882))),x40882)),f341(f341(f290(x40881,x40881,x40881),x40882),f309(x40881,x40882))) % 19.23/19.03 [4110]P85(f341(f341(f241(f864(f863(x41101,x41101),a850)),f341(f341(f290(x41101,x41101,x41101),x41102),f309(x41101,x41102))),f341(f341(f257(x41101,x41101),f341(f285(x41101),x41102)),f341(f18(f864(x41101,a850),x41101),f341(f285(x41101),x41102))))) % 19.23/19.03 [4155]E(f341(f265(f858(x41551)),f341(f341(f9(f858(x41551),f864(x41551,a850),a850),f341(f341(f10(f864(x41551,a850),f864(f864(x41551,a850),a850),f858(x41551)),f241(f864(x41551,a850))),f163(x41551))),x41552)),f155(x41551,x41552)) % 19.23/19.03 [4167]E(f341(f151(f858(x41671),x41671,f122(x41671),f341(f341(f10(f858(x41671),f864(f858(x41671),f858(x41671)),x41671),f341(f9(f858(x41671),f858(x41671),f858(x41671)),f132(x41671))),f341(f341(f9(x41671,f858(x41671),f858(x41671)),f146(x41671)),f122(x41671)))),x41672),f341(f147(x41671),x41672)) % 19.23/19.03 [4206]P26(f864(x42061,x42062),f864(f863(x42061,x42062),a850),f341(f341(f10(f864(f863(x42061,x42062),a850),f864(f863(x42061,x42062),a850),f864(x42061,x42062)),f265(f863(x42061,x42062))),f341(f341(f10(f864(x42061,f864(x42062,a850)),f864(f863(x42061,x42062),a850),f864(x42061,x42062)),f260(x42061,x42062,a850)),f341(f10(x42062,f864(x42062,a850),x42061),f341(f9(x42062,x42062,a850),a338)))),f248(f864(f864(x42061,x42062),a850))) % 19.23/19.03 [4211]E(f60(a1,f341(f113(a1),f341(f341(f89(a1),x42111),x42111)),f341(f113(a1),f341(f341(f89(a1),x42112),x42112))),f341(f341(f90(a1),f341(f113(a1),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),f60(a1,f341(f113(a1),x42111),f341(f113(a1),x42112)))) % 19.23/19.03 [4252]E(f341(f341(f54(x42521,f864(f863(x42521,x42521),a850)),x42522),f341(f341(f9(x42521,f864(f863(x42521,x42521),a850),f864(f863(x42521,x42521),a850)),f341(f341(f10(f863(x42521,x42521),f864(f864(f863(x42521,x42521),a850),f864(f863(x42521,x42521),a850)),x42521),f311(f863(x42521,x42521))),f341(f341(f20(x42521,x42521,f863(x42521,x42521)),f250(x42521,x42521)),f7(x42521)))),f185(f864(f863(x42521,x42521),a850)))),f269(x42521,x42522)) % 19.23/19.03 [4260]E(f206(x42601,f341(f341(f250(a1,a1),f341(f88(a1),f341(f341(f82(f863(a1,a1),a1,x42601,f249(a1,a1)),f215(x42601)),x42602))),f341(f341(f82(f863(a1,a1),a1,x42601,f259(a1,a1)),f215(x42601)),x42602))),f229(x42601,x42602)) % 19.23/19.03 [4340]E(f341(f265(f864(x43401,a850)),f341(f341(f10(f864(f864(x43401,a850),a850),a850,f864(x43401,a850)),f96(f864(x43401,a850))),f341(f341(f9(f864(x43401,a850),f864(f864(x43401,a850),a850),f864(f864(x43401,a850),a850)),f341(f341(f10(f864(f864(x43401,a850),f864(a850,a850)),f864(f864(f864(x43401,a850),a850),f864(f864(x43401,a850),a850)),f864(x43401,a850)),f20(f864(x43401,a850),a850,a850)),f341(f341(f10(f864(f864(x43401,a850),a850),f864(f864(x43401,a850),f864(a850,a850)),f864(x43401,a850)),f341(f10(a850,f864(a850,a850),f864(x43401,a850)),a339)),f341(f341(f9(f864(x43401,a850),f864(f864(x43401,a850),f864(x43401,a850)),f864(f864(x43401,a850),a850)),f341(f341(f10(f864(f864(x43401,a850),a850),f864(f864(f864(x43401,a850),f864(x43401,a850)),f864(f864(x43401,a850),a850)),f864(x43401,a850)),f10(f864(x43401,a850),a850,f864(x43401,a850))),a338)),f88(f864(x43401,a850)))))),f341(f341(f10(f864(f864(x43401,a850),a850),a850,f864(x43401,a850)),f341(f343(f864(x43401,a850)),x43402)),f310(x43401))))),f341(f310(x43401),f341(f88(f864(x43401,a850)),x43402))) % 19.23/19.03 [4485]~E(f341(f341(f89(a1),x44851),x44851),f341(f341(f3(a1),f341(f341(f89(a1),x44852),x44852)),a106)) % 19.23/19.03 [4491]~P85(f341(f341(f242(a857),f341(f341(f89(a857),x44911),x44912)),x44912)) % 19.23/19.03 [4492]~P85(f341(f341(f242(a857),f341(f341(f89(a857),x44921),x44922)),x44921)) % 19.23/19.03 [3679]E(f341(f341(f3(a857),x36791),f341(f341(f90(a857),f341(f341(f51(a857),x36791),x36792)),x36792)),f60(a857,x36791,x36792)) % 19.23/19.03 [3680]E(f341(f341(f3(a1),x36801),f341(f341(f90(a1),f341(f341(f51(a1),x36801),x36802)),x36802)),f60(a1,x36801,x36802)) % 19.23/19.03 [3715]E(f341(f341(f149(a857,x37151),f341(f158(x37151),x37152)),f136(a857,f341(f303(a857,f2(a857)),f341(f186(f858(x37151)),x37152)))),x37152) % 19.23/19.03 [3775]E(f341(f286(x37751,x37751,f309(x37751,f185(f864(f863(x37751,x37751),a850)))),x37752),x37752) % 19.23/19.03 [3897]E(f309(x38971,f341(f341(f3(f864(f863(x38971,x38971),a850)),x38972),f309(x38971,f185(f864(f863(x38971,x38971),a850))))),f309(x38971,x38972)) % 19.23/19.03 [3898]E(f309(x38981,f341(f341(f110(f864(f863(x38981,x38981),a850)),x38982),f309(x38981,f185(f864(f863(x38981,x38981),a850))))),f309(x38981,x38982)) % 19.23/19.03 [3952]E(f341(f341(f3(a1),f341(f341(f3(a1),f341(f341(f89(a1),x39521),x39521)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),x39522),x39522)),a106)),f341(f341(f89(a1),f341(f341(f3(a1),x39521),x39522)),f341(f341(f3(a1),x39521),x39522))) % 19.23/19.03 [3994]E(f341(f341(f3(a1),f341(f341(f89(a1),f341(f341(f89(a1),x39941),x39942)),f341(f341(f89(a1),x39941),x39942))),a106),f341(f341(f89(a1),f341(f341(f89(a1),x39941),x39941)),f341(f341(f3(a1),f341(f341(f89(a1),x39942),x39942)),a106))) % 19.23/19.03 [4020]E(f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),x40201),x40201)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),x40202),x40202)),a106)),f341(f341(f89(a1),f341(f341(f89(a1),x40201),f341(f341(f3(a1),x40202),a106))),f341(f341(f89(a1),x40201),f341(f341(f3(a1),x40202),a106)))) % 19.23/19.03 [4031]E(f341(f341(f3(a1),f341(f341(f89(a1),f341(f341(f89(a1),x40311),x40312)),f341(f341(f89(a1),x40311),x40312))),a106),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),x40311),x40311)),a106)),f341(f341(f89(a1),x40312),x40312))) % 19.23/19.03 [4032]E(f341(f341(f3(a1),f341(f341(f89(a1),f341(f341(f3(a1),x40321),x40322)),f341(f341(f3(a1),x40321),x40322))),a106),f341(f341(f3(a1),f341(f341(f3(a1),f341(f341(f89(a1),x40321),x40321)),a106)),f341(f341(f89(a1),x40322),x40322))) % 19.23/19.03 [4085]E(f341(f109(a1),f341(f341(f51(a857),f341(f341(f90(a857),f341(a114,f341(f84(a1),x40851))),f341(a114,f341(f84(a1),x40852)))),f219(f341(a114,f341(f84(a1),x40851)),f341(a114,f341(f84(a1),x40852))))),f221(x40851,x40852)) % 19.23/19.03 [4130]E(f341(f341(f262(f863(a108,a108),a108,f863(a108,a108),f863(x41301,f863(a108,a108))),f273(f341(a5,f341(f186(f858(x41301)),x41302)))),f341(f341(f10(x41301,f864(f863(a108,a108),f863(x41301,f863(a108,a108))),a108),f250(x41301,f863(a108,a108))),f341(f341(f10(a857,x41301,a108),f341(f158(x41301),x41302)),a22))),f279(x41301,x41302)) % 19.23/19.03 [4212]E(f341(f138(a857,f858(x42121),f341(f9(f858(x42121),a857,a857),f341(f341(f10(a857,f864(a857,a857),f858(x42121)),f240(a857)),f186(f858(x42121)))),f2(a857)),f341(f148(f858(x42121)),f169(x42121,x42122))),f341(f186(f858(f858(x42121))),f341(f133(f858(x42121),f341(f341(f10(a850,a850,f858(x42121)),a337),f341(f341(f9(f858(x42121),f858(x42121),a850),a338),f122(x42121)))),x42122))) % 19.23/19.03 [4218]E(f341(f341(f54(a857,f864(x42181,a850)),f248(f864(a857,a850))),f341(f341(f9(a857,f864(a857,f864(x42181,a850)),f864(x42181,a850)),f341(f341(f10(f864(a857,a850),f864(f864(a857,f864(x42181,a850)),f864(x42181,a850)),a857),f54(a857,f864(x42181,a850))),f303(a857,f2(a857)))),x42182)),f341(f341(f54(a857,f864(x42181,a850)),f248(f864(a857,a850))),x42182)) % 19.23/19.03 [4237]P85(f341(f71(a857),f341(f265(a857),f341(f341(f20(a857,a850,a850),f341(f341(f10(a850,f864(a850,a850),a857),a339),x42371)),f341(f341(f9(a857,a857,a850),f242(a857)),x42372))))) % 19.23/19.03 [4349]E(f341(f265(f863(f858(x43491),f858(x43491))),f341(f260(f858(x43491),f858(x43491),a850),f341(f341(f20(f858(x43491),f864(f858(x43491),a850),f864(f858(x43491),a850)),f341(f341(f10(f864(f858(x43491),f864(a850,a850)),f864(f864(f858(x43491),a850),f864(f858(x43491),a850)),f858(x43491)),f20(f858(x43491),a850,a850)),f341(f341(f10(f864(f858(x43491),a850),f864(f858(x43491),f864(a850,a850)),f858(x43491)),f341(f10(a850,f864(a850,a850),f858(x43491)),a340)),f341(f341(f9(f858(x43491),f864(f858(x43491),a857),f864(f858(x43491),a850)),f341(f341(f10(f864(a857,a850),f864(f864(f858(x43491),a857),f864(f858(x43491),a850)),f858(x43491)),f10(a857,a850,f858(x43491))),f341(f341(f10(a857,f864(a857,a850),f858(x43491)),f242(a857)),f186(f858(x43491))))),f186(f858(x43491)))))),f341(f341(f20(f858(x43491),f864(f858(x43491),a850),f864(f858(x43491),a850)),f341(f341(f10(f864(f858(x43491),f864(a850,a850)),f864(f864(f858(x43491),a850),f864(f858(x43491),a850)),f858(x43491)),f20(f858(x43491),a850,a850)),f341(f341(f10(f864(f858(x43491),a850),f864(f858(x43491),f864(a850,a850)),f858(x43491)),f341(f10(a850,f864(a850,a850),f858(x43491)),a339)),f341(f341(f9(f858(x43491),f864(f858(x43491),a857),f864(f858(x43491),a850)),f341(f341(f10(f864(a857,a850),f864(f864(f858(x43491),a857),f864(f858(x43491),a850)),f858(x43491)),f10(a857,a850,f858(x43491))),f341(f341(f10(a857,f864(a857,a850),f858(x43491)),a338),f186(f858(x43491))))),f186(f858(x43491)))))),f341(f341(f9(f858(x43491),f864(f863(f858(x43491),f858(x43491)),a850),f864(f858(x43491),a850)),f341(f341(f10(f864(f858(x43491),f864(f864(f863(f858(x43491),f858(x43491)),a850),a850)),f864(f864(f863(f858(x43491),f858(x43491)),a850),f864(f858(x43491),a850)),f858(x43491)),f9(f858(x43491),f864(f863(f858(x43491),f858(x43491)),a850),a850)),f341(f341(f10(f864(f858(x43491),f863(f858(x43491),f858(x43491))),f864(f858(x43491),f864(f864(f863(f858(x43491),f858(x43491)),a850),a850)),f858(x43491)),f341(f10(f863(f858(x43491),f858(x43491)),f864(f864(f863(f858(x43491),f858(x43491)),a850),a850),f858(x43491)),f343(f863(f858(x43491),f858(x43491))))),f250(f858(x43491),f858(x43491))))),f141(x43491,x43492)))))),f142(x43491,x43492)) % 19.23/19.03 [4023]E(f341(f341(f89(a1),f341(f341(f89(a1),f341(f341(f90(a1),x40231),x40232)),f341(f341(f90(a1),x40231),x40232))),x40232),f341(f341(f90(a1),f341(f341(f3(a1),f341(f341(f89(a1),x40231),x40231)),a106)),x40232)) % 19.23/19.03 [4128]E(f341(a114,f341(a98,f341(f286(f863(a857,a857),f863(a857,a857),a118),f341(f341(f311(f863(a857,a857)),f341(f341(f250(a857,a857),x41281),x41282)),f185(f864(f863(a857,a857),a850)))))),f341(f341(f3(a857),x41281),x41282)) % 19.23/19.03 [4133]E(f341(f341(f290(x41331,x41331,x41331),f341(f341(f110(f864(f863(x41331,x41331),a850)),x41332),f309(x41331,f185(f864(f863(x41331,x41331),a850))))),f309(x41331,f341(f341(f110(f864(f863(x41331,x41331),a850)),x41332),f309(x41331,f185(f864(f863(x41331,x41331),a850)))))),f309(x41331,x41332)) % 19.23/19.03 [4172]E(f274(x41721,f341(f133(f863(a108,x41721),f341(f260(a108,x41721,a850),f341(f341(f10(a850,f864(x41721,a850),a108),f18(a850,x41721)),f341(f242(a108),f2(a108))))),x41722)),f274(x41721,x41722)) % 19.23/19.03 [4173]E(f272(x41731,f341(f133(f863(a108,x41731),f341(f260(a108,x41731,a850),f341(f341(f10(a850,f864(x41731,a850),a108),f18(a850,x41731)),f341(f242(a108),f2(a108))))),x41732)),f272(x41731,x41732)) % 19.23/19.03 [4175]E(f341(f88(a1),f341(a98,f341(f286(f863(a857,a857),f863(a857,a857),a118),f341(f341(f311(f863(a857,a857)),f341(f341(f250(a857,a857),x41751),x41752)),f185(f864(f863(a857,a857),a850)))))),f341(a98,f341(f286(f863(a857,a857),f863(a857,a857),a118),f341(f341(f311(f863(a857,a857)),f341(f341(f250(a857,a857),x41752),x41751)),f185(f864(f863(a857,a857),a850)))))) % 19.23/19.03 [4249]E(f341(f341(f95(a1,a857),f341(f113(a1),f341(f341(f89(a1),x42491),a106))),f341(f341(f20(a1,a857,a857),f341(f341(f9(a1,a857,f864(a857,a857)),f341(f341(f10(a850,f864(a857,f864(a857,a857)),a1),f105(a857)),a191)),f2(a857))),f341(f341(f10(a857,a857,a1),a121),f341(f341(f10(a857,a857,a1),f341(f245(a857),x42492)),a114)))),f341(f341(f245(a857),f341(a121,x42492)),f341(f113(a857),x42491))) % 19.23/19.03 [4250]E(f341(f341(f95(a1,a857),f341(f113(a1),f341(f341(f89(a1),x42501),a106))),f341(f341(f20(a1,a857,a857),f341(f341(f9(a1,a857,f864(a857,a857)),f341(f341(f10(a850,f864(a857,f864(a857,a857)),a1),f105(a857)),a191)),f341(a121,x42502))),f341(f341(f10(a857,a857,a1),a121),f341(f341(f10(a857,a857,a1),f341(f240(a857),x42502)),a114)))),f341(f341(f240(a857),f341(a121,x42502)),f341(f113(a857),x42501))) % 19.23/19.03 [4270]E(f341(f138(f858(x42701),f858(x42701),f132(x42701),f122(x42701)),f341(f341(f149(f858(x42701),f858(x42701)),f151(f858(x42701),x42701,f122(x42701),f341(f341(f10(f858(x42701),f864(f858(x42701),f858(x42701)),x42701),f18(f858(x42701),f858(x42701))),f341(f341(f9(x42701,f858(x42701),f858(x42701)),f146(x42701)),f122(x42701))))),x42702)),f341(f341(f149(f858(x42701),x42701),f137(x42701)),f341(f133(f858(x42701),f341(f341(f10(a850,a850,f858(x42701)),a337),f341(f341(f9(f858(x42701),f858(x42701),a850),a338),f122(x42701)))),x42702))) % 19.23/19.03 [4330]E(f341(f260(a1,a1,a850),f341(f341(f9(a1,f864(a1,a850),f864(a1,a850)),f341(f341(f10(f864(a1,f864(a850,a850)),f864(f864(a1,a850),f864(a1,a850)),a1),f20(a1,a850,a850)),f341(f341(f10(f864(a1,a850),f864(a1,f864(a850,a850)),a1),f341(f10(a850,f864(a850,a850),a1),a339)),f341(f341(f10(f864(a1,a1),f864(a1,a850),a1),f341(f10(a1,a850,a1),f341(a338,x43301))),f341(f341(f10(a1,f864(a1,a1),a1),f89(a1)),f341(f90(a1),x43302)))))),f341(f341(f20(a1,a850,a850),f341(f341(f10(a850,f864(a850,a850),a1),a339),f341(f341(f10(a850,a850,a1),f341(a344,f341(f341(f242(a1),f2(a1)),x43302))),f341(f341(f20(a1,a850,a850),f341(f341(f10(a850,f864(a850,a850),a1),a339),f341(f241(a1),f2(a1)))),f341(f341(f9(a1,a1,a850),f242(a1)),x43302))))),f341(f341(f10(a850,a850,a1),f341(a344,f341(a337,f341(f341(f242(a1),f2(a1)),x43302)))),f341(f341(f20(a1,a850,a850),f341(f341(f10(a850,f864(a850,a850),a1),a339),f341(f242(a1),x43302))),f341(f341(f9(a1,a1,a850),f241(a1)),f2(a1))))))),f64(x43301,x43302)) % 19.23/19.03 [4332]E(f341(f265(x43321),f341(f341(f10(f864(a857,a850),a850,x43321),f96(a857)),f341(f341(f9(x43321,f864(a857,a850),f864(a857,a850)),f341(f341(f10(f864(a857,f864(a850,a850)),f864(f864(a857,a850),f864(a857,a850)),x43321),f20(a857,a850,a850)),f341(f341(f10(f864(a857,a850),f864(a857,f864(a850,a850)),x43321),f341(f10(a850,f864(a850,a850),a857),a339)),f341(f341(f9(x43321,f864(a857,x43321),f864(a857,a850)),f341(f341(f10(f864(x43321,a850),f864(f864(a857,x43321),f864(a857,a850)),x43321),f10(x43321,a850,a857)),a338)),f341(f158(x43321),x43322))))),f341(f341(f9(a857,a857,a850),f242(a857)),f341(f186(f858(x43321)),x43322))))),f341(f163(x43321),x43322)) % 19.23/19.03 [4145]E(f341(f341(f3(a1),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),x41451),a106)),x41452)),f341(f341(f3(a1),f341(f341(f89(a1),x41451),a106)),x41452))),a106),f341(f341(f3(a1),f341(f341(f89(a1),x41451),x41451)),f341(f341(f3(a1),f341(f341(f89(a1),x41452),x41452)),a106))) % 19.23/19.03 [4265]E(f341(f138(f858(f858(x42651)),f858(f858(x42651)),f132(f858(x42651)),f122(f858(x42651))),f341(f341(f149(f858(x42651),f858(f858(x42651))),f151(f858(f858(x42651)),x42651,f122(f858(x42651)),f341(f18(f864(f858(x42651),f858(f858(x42651))),x42651),f341(f341(f9(f858(x42651),f858(f858(x42651)),f858(f858(x42651))),f146(f858(x42651))),f122(f858(x42651)))))),x42652)),f341(f341(f149(f858(x42651),f858(x42651)),f162(x42651)),f341(f133(f858(x42651),f341(f341(f10(a850,a850,f858(x42651)),a337),f341(f341(f9(f858(x42651),f858(x42651),a850),a338),f122(x42651)))),x42652))) % 19.23/19.03 [4275]E(f341(f341(f95(a1,a857),f341(f113(a1),f341(f341(f89(a1),x42751),a106))),f341(f341(f20(a1,a857,a857),f341(f341(f9(a1,a857,f864(a857,a857)),f341(f341(f10(a850,f864(a857,f864(a857,a857)),a1),f105(a857)),a191)),f2(a857))),f341(f341(f10(a857,a857,a1),a121),f341(f341(f9(a1,a857,a857),f341(f341(f10(a857,f864(a857,a857),a1),f245(a857)),a114)),x42752)))),f341(f341(f245(a857),f341(f113(a857),x42751)),f341(a121,x42752))) % 19.23/19.03 [4276]E(f341(f341(f95(a1,a857),f341(f113(a1),f341(f341(f89(a1),x42761),a106))),f341(f341(f20(a1,a857,a857),f341(f341(f9(a1,a857,f864(a857,a857)),f341(f341(f10(a850,f864(a857,f864(a857,a857)),a1),f105(a857)),a191)),f341(a121,x42762))),f341(f341(f10(a857,a857,a1),a121),f341(f341(f9(a1,a857,a857),f341(f341(f10(a857,f864(a857,a857),a1),f240(a857)),a114)),x42762)))),f341(f341(f240(a857),f341(f113(a857),x42761)),f341(a121,x42762))) % 19.23/19.03 [4264]E(f341(f260(x42641,x42641,a850),f341(f341(f20(x42641,a850,f864(x42641,a850)),f341(f341(f10(f864(x42641,f864(a850,a850)),f864(a850,f864(x42641,a850)),x42641),f9(x42641,a850,a850)),f341(f341(f10(f864(x42641,a850),f864(x42641,f864(a850,a850)),x42641),f341(f10(a850,f864(a850,a850),x42641),a339)),a338))),x42642)),f269(x42641,x42642)) % 19.23/19.03 [4308]E(f341(f341(f51(a857),x43081),f341(f341(f89(a857),f341(f113(a857),f341(f341(f3(a1),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106))),a106))),x43082)),f341(f341(f51(a857),x43081),f341(a121,f341(a121,f341(a121,x43082))))) % 19.23/19.03 [4309]E(f60(a857,x43091,f341(f341(f89(a857),f341(f113(a857),f341(f341(f3(a1),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106))),a106))),x43092)),f60(a857,x43091,f341(a121,f341(a121,f341(a121,x43092))))) % 19.23/19.03 [4310]E(f60(a857,f341(f341(f89(a857),f341(f113(a857),f341(f341(f3(a1),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106))),a106))),x43101),x43102),f60(a857,f341(a121,f341(a121,f341(a121,x43101))),x43102)) % 19.23/19.03 [4323]E(f129(f341(x43231,f341(f341(f90(a108),f341(f113(a108),f341(f341(f3(a1),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106))),a106))),x43232))),f341(f203(x43231),x43232)) % 19.23/19.03 [4324]E(f341(f341(f51(a857),f341(f341(f89(a857),f341(f113(a857),f341(f341(f3(a1),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106))),a106))),x43241)),x43242),f341(f341(f51(a857),f341(a121,f341(a121,f341(a121,x43241)))),x43242)) % 19.23/19.03 [3501]P26(x35011,f865(x35012,x35011),f322(x35011,x35012),x35013) % 19.23/19.03 [3502]P26(x35021,f865(x35021,x35022),f313(x35021,x35022),x35023) % 19.23/19.03 [4393]~E(f30(x43931,x43932),f341(a29,x43933)) % 19.23/19.03 [4394]~E(f38(x43941,x43942),f341(a29,x43943)) % 19.23/19.03 [4395]~E(f37(x43951,x43952),f341(a29,x43953)) % 19.23/19.03 [4396]~E(f341(a29,x43961),f30(x43962,x43963)) % 19.23/19.03 [4397]~E(f341(a29,x43971),f38(x43972,x43973)) % 19.23/19.03 [4398]~E(f341(a29,x43981),f37(x43982,x43983)) % 19.23/19.03 [4417]~E(f33(x44171,x44172,x44173),a25) % 19.23/19.03 [4418]~E(f35(x44181,x44182,x44183),a25) % 19.23/19.03 [4419]~E(f34(x44191,x44192,x44193),a25) % 19.23/19.03 [3113]E(f341(f190(x31131,x31132),x31133),f127(x31131,x31132)) % 19.23/19.03 [3114]E(f341(f202(x31141,x31142),x31143),f130(x31141,x31142)) % 19.23/19.03 [3206]E(f341(f341(f149(x32061,x32062),x32063),f122(x32061)),f122(x32062)) % 19.23/19.03 [3207]E(f341(f341(f204(x32071,x32072),x32073),f188(x32071)),f188(x32072)) % 19.23/19.03 [3227]E(f36(f33(x32271,x32272,x32273)),f2(a857)) % 19.23/19.03 [3246]E(f341(f180(x32461,x32462,x32463),f2(a857)),x32462) % 19.23/19.03 [3247]E(f341(f186(a851),f33(x32471,x32472,x32473)),f2(a857)) % 19.23/19.03 [3248]E(f341(f341(f172(x32481,x32482),x32483),f122(x32482)),f122(f863(x32481,x32482))) % 19.23/19.03 [3285]E(f94(x32851,f72(x32851,x32852,x32853)),f341(f73(x32851,x32852),x32853)) % 19.23/19.03 [3354]E(f341(f249(f858(x33541),f858(x33541)),f161(x33541,x33542,x33543)),f341(f133(x33541,x33542),x33543)) % 19.23/19.03 [3431]E(f19(x34311,x34312,x34313,f2(a108)),x34312) % 19.23/19.03 [3432]E(f21(x34321,x34322,x34323,f2(a108)),x34322) % 19.23/19.03 [3433]E(f181(x34331,x34332,x34333,f2(a857)),x34332) % 19.23/19.03 [3440]E(f159(x34401,x34402,x34403,f122(x34401)),f122(x34402)) % 19.23/19.03 [3447]E(f341(f341(f158(x34471),f341(f341(f146(x34471),x34472),x34473)),f2(a857)),x34472) % 19.23/19.03 [3500]P26(x35001,x35002,x35003,f185(f864(x35001,a850))) % 19.23/19.03 [3595]E(f271(x35951,x35952,x35953),f341(f250(f864(a108,f864(a850,f861(f859(x35951)))),f863(a108,a108)),f56(x35951))) % 19.23/19.03 [3654]E(f341(f82(x36541,x36542,x36541,x36543),f41(x36541)),x36543) % 19.23/19.03 [3829]P85(f341(f341(f343(f863(x38291,x38291)),f341(f341(f250(x38291,x38291),x38292),x38292)),f309(x38291,x38293))) % 19.23/19.03 [4495]~P85(f341(f341(f343(f863(f858(x44951),f858(x44951))),f341(f341(f250(f858(x44951),f858(x44951)),x44952),f122(x44951))),f141(x44951,x44953))) % 19.23/19.03 [4496]~P85(f341(f341(f343(f863(f858(x44961),f858(x44961))),f341(f341(f250(f858(x44961),f858(x44961)),x44962),f122(x44961))),f143(x44961,x44963))) % 19.23/19.03 [4497]~P85(f341(f341(f343(f863(f858(x44971),f858(x44971))),f341(f341(f250(f858(x44971),f858(x44971)),x44972),f122(x44971))),f152(x44971,x44973))) % 19.23/19.03 [4498]~P85(f341(f341(f343(f863(f858(x44981),f858(x44981))),f341(f341(f250(f858(x44981),f858(x44981)),f122(x44981)),x44982)),f141(x44981,x44983))) % 19.23/19.03 [4499]~P85(f341(f341(f343(f863(f858(x44991),f858(x44991))),f341(f341(f250(f858(x44991),f858(x44991)),f122(x44991)),x44992)),f152(x44991,x44993))) % 19.23/19.03 [3182]E(f341(f341(f205(x31821),x31822),x31823),f206(x31821,f218(x31822,x31823))) % 19.23/19.03 [3236]E(f341(f287(x32361,x32362),f341(f287(x32362,x32361),x32363)),x32363) % 19.23/19.03 [3253]E(f321(x32531,x32532,f341(f313(x32531,x32532),x32533)),x32533) % 19.23/19.03 [3254]E(f324(x32541,x32542,f341(f322(x32542,x32541),x32543)),x32543) % 19.23/19.03 [3260]E(f341(f341(f172(x32601,x32602),f122(x32601)),x32603),f122(f863(x32601,x32602))) % 19.23/19.03 [3263]E(f165(x32631,x32632,f341(f266(a857),x32633)),f341(f341(f164(x32631),x32633),x32632)) % 19.23/19.03 [3277]E(f341(f186(f865(x32771,x32772)),f341(f322(x32772,x32771),x32773)),f2(a857)) % 19.23/19.03 [3278]E(f341(f186(f865(x32781,x32782)),f341(f313(x32781,x32782),x32783)),f2(a857)) % 19.23/19.03 [3283]E(f341(f268(x32831,x32832),f341(f287(x32832,x32831),x32833)),f341(f270(x32832,x32831),x32833)) % 19.23/19.03 [3284]E(f341(f270(x32841,x32842),f341(f287(x32842,x32841),x32843)),f341(f268(x32842,x32841),x32843)) % 19.23/19.03 [3299]E(f341(f133(x32991,x32992),f341(f148(x32991),x32993)),f341(f148(x32991),f341(f133(x32991,x32992),x32993))) % 19.23/19.03 [3312]E(f341(f341(f135(x33121),x33122),f341(f162(x33121),x33123)),f341(f341(f135(x33121),f341(a121,x33122)),x33123)) % 19.23/19.03 [3330]E(f36(f34(x33301,x33302,x33303)),f341(f341(f89(a857),f36(x33303)),f341(a121,f2(a857)))) % 19.23/19.03 [3331]E(f341(f312(x33311,x33312,x33313),f185(f864(x33311,a850))),f185(f864(x33312,a850))) % 19.23/19.03 [3332]E(f341(f286(x33321,x33322,x33323),f185(f864(x33321,a850))),f185(f864(x33322,a850))) % 19.23/19.03 [3333]E(f341(f314(x33331,x33332,x33333),f185(f864(x33332,a850))),f185(f864(x33331,a850))) % 19.23/19.03 [3334]E(f341(f314(x33341,x33342,x33343),f248(f864(x33342,a850))),f248(f864(x33341,a850))) % 19.23/19.03 [3371]E(f236(x33711,x33712,f341(f235(x33711),x33713)),f341(f341(f89(a857),f341(x33712,x33713)),f341(a121,f2(a857)))) % 19.23/19.03 [3451]E(f341(f186(a851),f34(x34511,x34512,x34513)),f341(f341(f89(a857),f341(f186(a851),x34513)),f341(a121,f2(a857)))) % 19.23/19.03 [3452]E(f341(f312(f863(x34521,x34522),x34522,f259(x34521,x34522)),x34523),f341(f268(x34521,x34522),x34523)) % 19.23/19.03 [3453]E(f341(f312(f863(x34531,x34532),x34531,f249(x34531,x34532)),x34533),f341(f270(x34531,x34532),x34533)) % 19.23/19.03 [3527]E(f341(f341(f250(x35271,x35272),f341(f249(x35271,x35272),x35273)),f341(f259(x35271,x35272),x35273)),x35273) % 19.23/19.03 [3534]E(f341(f341(f260(x35341,x35342,x35341),f18(x35341,x35342)),x35343),f341(f249(x35341,x35342),x35343)) % 19.23/19.03 [3553]E(f175(x35531,x35532,x35533,f341(f18(f861(x35532),x35531),f188(x35532))),x35533) % 19.23/19.03 [3554]E(f175(x35541,x35542,f341(f18(f861(x35542),x35541),f188(x35542)),x35543),x35543) % 19.23/19.03 [3608]E(f36(f35(x36081,x36082,x36083)),f341(f341(f89(a857),f341(f341(f89(a857),f36(x36082)),f36(x36083))),f341(a121,f2(a857)))) % 19.23/19.03 [3658]E(f341(f82(x36581,x36581,x36582,f41(x36581)),x36583),x36583) % 19.23/19.03 [3743]P85(f341(f71(x37431),f174(x37431,x37432,f171(x37431,x37432,x37433)))) % 19.23/19.03 [3766]P85(f341(f341(f192(f30(x37661,x37662)),x37663),f341(f341(f341(a194,x37663),x37661),f341(x37662,x37663)))) % 19.23/19.03 [3768]E(f341(f186(a851),f35(x37681,x37682,x37683)),f341(f341(f89(a857),f341(f341(f89(a857),f341(f186(a851),x37682)),f341(f186(a851),x37683))),f341(a121,f2(a857)))) % 19.23/19.03 [3839]P85(f341(f341(f241(f864(x38391,a850)),f341(f163(x38391),f341(f133(x38391,x38392),x38393))),f341(f163(x38391),x38393))) % 19.23/19.03 [3884]P85(f341(f341(f241(f864(x38841,a850)),f341(f163(x38841),f341(f341(f164(x38841),x38842),x38843))),f341(f163(x38841),x38843))) % 19.23/19.03 [3885]P85(f341(f341(f241(f864(x38851,a850)),f341(f163(x38851),f341(f341(f135(x38851),x38852),x38853))),f341(f163(x38851),x38853))) % 19.23/19.03 [3889]P85(f341(f341(f241(f864(x38891,a850)),f341(f163(x38891),f157(x38891,x38892,x38893))),f341(f163(x38891),x38893))) % 19.23/19.03 [3890]P85(f341(f341(f241(f864(x38901,a850)),f341(f163(x38901),f165(x38901,x38902,x38903))),f341(f163(x38901),x38902))) % 19.23/19.03 [3913]P26(f863(x39131,x39132),f863(x39132,x39131),f341(f260(x39131,x39132,f863(x39132,x39131)),f341(f9(x39132,x39131,f863(x39132,x39131)),f250(x39132,x39131))),x39133) % 19.23/19.03 [3924]E(f341(f341(f341(f179(f858(x39241),f858(x39241)),f60(a857,x39242,f341(f186(f858(x39241)),x39243))),f147(x39241)),x39243),f341(f341(f341(f179(f858(x39241),f858(x39241)),x39242),f147(x39241)),x39243)) % 19.23/19.03 [3969]P85(f341(f341(f343(f863(f858(x39691),f858(x39691))),f341(f341(f250(f858(x39691),f858(x39691)),x39692),x39692)),f153(x39691,f309(x39691,x39693)))) % 19.23/19.03 [4113]E(f94(f863(x41131,x41132),f341(f341(f20(f863(x41131,x41132),x41132,a850),f341(f341(f10(x41131,f864(x41132,a850),f863(x41131,x41132)),x41133),f249(x41131,x41132))),f259(x41131,x41132))),f94(f863(x41131,x41132),f341(f260(x41131,x41132,a850),x41133))) % 19.23/19.03 [4114]E(f99(f863(x41141,x41142),f341(f341(f20(f863(x41141,x41142),x41142,a850),f341(f341(f10(x41141,f864(x41142,a850),f863(x41141,x41142)),x41143),f249(x41141,x41142))),f259(x41141,x41142))),f99(f863(x41141,x41142),f341(f260(x41141,x41142,a850),x41143))) % 19.23/19.03 [4152]E(f341(f341(f289(f863(a857,x41521),x41521),f335(a857,x41521,a246,x41522)),f341(f341(f20(x41521,x41521,f863(a857,x41521)),f341(f341(f10(a857,f864(x41521,f863(a857,x41521)),x41521),f250(a857,x41521)),x41523)),f7(x41521))),f336(x41521,x41523,x41522)) % 19.23/19.03 [4214]E(f341(f261(x42141,x42141,x42142,x42142,f7(x42141),f7(x42142)),x42143),x42143) % 19.23/19.03 [4348]E(f341(f341(f95(a1,x43481),f221(f341(f341(f82(f863(a1,a1),a1,x43481,f259(a1,a1)),f215(x43481)),x43482),f341(f341(f82(f863(a1,a1),a1,x43481,f259(a1,a1)),f215(x43481)),x43483))),f341(f341(f20(a1,a1,x43481),f341(f341(f10(a1,f864(a1,x43481),a1),f205(x43481)),f341(f341(f20(a1,a1,a1),f341(f341(f10(a1,f864(a1,a1),a1),f89(a1)),f341(f341(f10(a1,a1,a1),f341(f90(a1),f341(f341(f82(f863(a1,a1),a1,x43481,f249(a1,a1)),f215(x43481)),x43482))),f341(f341(f9(a1,a1,a1),f51(a1)),f341(f341(f82(f863(a1,a1),a1,x43481,f259(a1,a1)),f215(x43481)),x43482))))),f341(f341(f10(a1,a1,a1),f341(f90(a1),f341(f341(f82(f863(a1,a1),a1,x43481,f249(a1,a1)),f215(x43481)),x43483))),f341(f341(f9(a1,a1,a1),f51(a1)),f341(f341(f82(f863(a1,a1),a1,x43481,f259(a1,a1)),f215(x43481)),x43483)))))),f7(a1))),f232(x43481,x43482,x43483)) % 19.23/19.03 [4412]~E(f341(f341(f146(x44121),x44122),x44123),x44123) % 19.23/19.03 [4421]~E(f341(f341(f146(x44211),x44212),x44213),f122(x44211)) % 19.23/19.03 [4447]~E(f341(f341(f311(x44471),x44472),x44473),f185(f864(x44471,a850))) % 19.23/19.03 [4476]~E(f341(f312(x44761,f864(x44761,a850),x44762),x44763),f341(f310(x44761),x44763)) % 19.23/19.03 [3240]E(f341(f341(f154(x32401,f122(x32401)),x32402),x32403),f122(x32401)) % 19.23/19.03 [3241]E(f341(f137(x32411),f341(f341(f146(x32411),x32412),x32413)),x32412) % 19.23/19.03 [3242]E(f341(f162(x32421),f341(f341(f146(x32421),x32422),x32423)),x32423) % 19.23/19.03 [3288]E(f341(f341(f135(x32881),f87(a857)),f341(f341(f146(x32881),x32882),x32883)),x32883) % 19.23/19.03 [3319]E(f123(x33191,f341(f341(f135(x33191),x33192),x33193)),f341(f341(f135(x33191),x33192),f123(x33191,x33193))) % 19.23/19.03 [3321]E(f341(f341(f154(x33211,x33212),x33213),f341(f341(f158(x33211),x33212),x33213)),x33212) % 19.23/19.03 [3344]E(f341(f341(f311(x33441),x33442),f341(f341(f311(x33441),x33442),x33443)),f341(f341(f311(x33441),x33442),x33443)) % 19.23/19.03 [3357]E(f341(f341(f311(x33571),x33572),f341(f163(x33571),x33573)),f341(f163(x33571),f341(f341(f146(x33571),x33572),x33573))) % 19.23/19.03 [3359]E(f341(f341(f135(x33591),x33592),f341(f162(x33591),x33593)),f341(f162(x33591),f341(f341(f135(x33591),x33592),x33593))) % 19.23/19.03 [3368]E(f341(f341(f164(x33681),f87(a857)),f341(f341(f146(x33681),x33682),x33683)),f341(f341(f146(x33681),x33682),f122(x33681))) % 19.23/19.03 [3401]E(f341(f171(x34011,x34012,f122(f863(x34011,x34012))),x34013),f188(x34012)) % 19.23/19.03 [3416]E(f341(f73(x34161,x34162),f341(f341(f311(x34161),x34163),f185(f864(x34161,a850)))),x34163) % 19.23/19.03 [3463]E(f341(f341(f89(a857),x34631),f341(f341(f89(a857),x34632),x34633)),f341(f341(f89(a857),x34632),f341(f341(f89(a857),x34631),x34633))) % 19.23/19.03 [3464]E(f341(f341(f89(a1),x34641),f341(f341(f89(a1),x34642),x34643)),f341(f341(f89(a1),x34642),f341(f341(f89(a1),x34641),x34643))) % 19.23/19.03 [3469]E(f341(f341(f257(x34691,x34692),f185(f864(x34691,a850))),x34693),f185(f864(f863(x34691,x34692),a850))) % 19.23/19.03 [3491]E(f341(f341(f110(f864(x34911,a850)),x34912),x34913),f341(f341(f110(f864(x34911,a850)),x34913),x34912)) % 19.23/19.03 [3492]E(f341(f341(f111(f864(x34921,a850)),x34922),x34923),f341(f341(f111(f864(x34921,a850)),x34923),x34922)) % 19.23/19.03 [3494]E(f341(f341(f132(x34941),x34942),f341(f341(f146(x34941),x34943),f122(x34941))),f341(f147(x34941),f341(f341(f146(x34941),x34943),x34942))) % 19.23/19.03 [3495]E(f341(f341(f132(x34951),f341(f148(x34951),x34952)),f341(f148(x34951),x34953)),f341(f148(x34951),f341(f341(f132(x34951),x34953),x34952))) % 19.23/19.03 [3506]E(f341(f162(x35061),f341(f341(f164(x35061),f341(a121,x35062)),x35063)),f341(f341(f164(x35061),x35062),f341(f162(x35061),x35063))) % 19.23/19.03 [3513]P85(f341(f341(f343(x35131),x35132),f341(f341(f311(x35131),x35132),x35133))) % 19.23/19.03 [3517]E(f341(f341(f55(x35171,f864(x35172,a850)),f185(f864(x35171,a850))),x35173),f248(f864(x35172,a850))) % 19.23/19.03 [3520]E(f341(f286(x35201,x35201,f269(x35201,x35202)),x35203),f341(f341(f111(f864(x35201,a850)),x35202),x35203)) % 19.23/19.03 [3532]E(f341(f186(f858(x35321)),f341(f341(f146(x35321),x35322),x35323)),f341(f341(f89(a857),f341(f186(f858(x35321)),x35323)),f341(a121,f2(a857)))) % 19.23/19.03 [3536]E(f140(x35361,f341(f341(f132(x35361),x35362),f341(f341(f146(x35361),x35363),f122(x35361)))),x35363) % 19.23/19.03 [3537]E(f123(x35371,f341(f341(f132(x35371),x35372),f341(f341(f146(x35371),x35373),f122(x35371)))),x35372) % 19.23/19.03 [3542]E(f341(f341(f132(x35421),f341(f341(f164(x35421),x35422),x35423)),f341(f341(f135(x35421),x35422),x35423)),x35423) % 19.23/19.03 [3551]E(f341(f341(f3(a857),f341(f341(f89(a857),x35511),x35512)),f341(f341(f89(a857),x35513),x35512)),f341(f341(f3(a857),x35511),x35513)) % 19.23/19.03 [3552]E(f341(f341(f3(a857),f341(f341(f89(a857),x35521),x35522)),f341(f341(f89(a857),x35521),x35523)),f341(f341(f3(a857),x35522),x35523)) % 19.23/19.03 [3558]E(f341(f341(f132(x35581),f341(f148(x35581),x35582)),f341(f341(f146(x35581),x35583),f122(x35581))),f341(f148(x35581),f341(f341(f146(x35581),x35583),x35582))) % 19.23/19.03 [3560]E(f341(f341(f89(a857),f341(f186(f858(x35601)),x35602)),f341(f186(f858(x35601)),x35603)),f341(f186(f858(x35601)),f341(f341(f132(x35601),x35602),x35603))) % 19.23/19.03 [3569]E(f341(f341(f110(f864(x35691,a850)),f341(f163(x35691),x35692)),f341(f163(x35691),x35693)),f341(f163(x35691),f341(f341(f132(x35691),x35692),x35693))) % 19.23/19.03 [3570]E(f60(a857,f341(f341(f90(a857),x35701),x35702),f341(f341(f90(a857),x35701),x35703)),f341(f341(f90(a857),x35701),f60(a857,x35702,x35703))) % 19.23/19.03 [3583]E(f341(f341(f164(x35831),f341(f341(f3(a857),x35832),f87(a857))),f341(f162(x35831),x35833)),f341(f162(x35831),f341(f341(f164(x35831),x35832),x35833))) % 19.23/19.03 [3588]E(f341(f341(f111(f864(x35881,a850)),x35882),f341(f88(f864(x35881,a850)),x35883)),f341(f341(f3(f864(x35881,a850)),x35882),x35883)) % 19.23/19.03 [3589]E(f341(f341(f3(f864(x35891,a850)),x35892),f341(f88(f864(x35891,a850)),x35893)),f341(f341(f111(f864(x35891,a850)),x35892),x35893)) % 19.23/19.03 [3611]E(f341(f341(f257(x36111,x36112),x36113),f341(f18(f864(x36112,a850),x36111),f185(f864(x36112,a850)))),f185(f864(f863(x36111,x36112),a850))) % 19.23/19.03 [3613]E(f341(f341(f89(a857),f341(f341(f90(a857),x36131),x36132)),f341(f341(f90(a857),x36131),x36133)),f341(f341(f90(a857),x36131),f341(f341(f89(a857),x36132),x36133))) % 19.23/19.03 [3614]E(f341(f341(f3(a857),f341(f341(f90(a857),x36141),x36142)),f341(f341(f90(a857),x36141),x36143)),f341(f341(f90(a857),x36141),f341(f341(f3(a857),x36142),x36143))) % 19.23/19.03 [3615]E(f341(f341(f89(a1),f341(f341(f90(a1),x36151),x36152)),f341(f341(f90(a1),x36151),x36153)),f341(f341(f90(a1),x36151),f341(f341(f89(a1),x36152),x36153))) % 19.23/19.03 [3616]E(f341(f341(f3(a1),f341(f341(f90(a1),x36161),x36162)),f341(f341(f90(a1),x36161),x36163)),f341(f341(f90(a1),x36161),f341(f341(f3(a1),x36162),x36163))) % 19.23/19.03 [3617]E(f341(f341(f90(a1),f341(f341(f251(a1),x36171),x36172)),f341(f341(f251(a1),x36171),x36173)),f341(f341(f251(a1),x36171),f341(f341(f89(a857),x36172),x36173))) % 19.23/19.03 [3630]E(f341(f341(f54(x36301,f864(x36302,a850)),x36303),f341(f18(f864(x36302,a850),x36301),f185(f864(x36302,a850)))),f185(f864(x36302,a850))) % 19.23/19.03 [3632]E(f60(a857,f341(f341(f90(a857),x36321),x36322),f341(f341(f90(a857),x36323),x36322)),f341(f341(f90(a857),f60(a857,x36321,x36323)),x36322)) % 19.23/19.03 [3637]E(f60(a1,f341(f341(f90(a1),x36371),f60(a1,x36372,x36373)),x36373),f60(a1,f341(f341(f90(a1),x36371),x36372),x36373)) % 19.23/19.03 [3638]E(f60(a1,f341(f341(f3(a1),x36381),f60(a1,x36382,x36383)),x36383),f60(a1,f341(f341(f3(a1),x36381),x36382),x36383)) % 19.23/19.03 [3639]P85(f341(f341(f241(f864(x36391,a850)),x36392),f341(f341(f311(x36391),x36393),x36392))) % 19.23/19.03 [3663]E(f341(f312(f863(x36631,x36632),x36631,f249(x36631,x36632)),f341(f163(f863(x36631,x36632)),x36633)),f174(x36631,x36632,f171(x36631,x36632,x36633))) % 19.23/19.03 [3720]E(f341(f341(f55(f864(x37201,a850),f864(x37201,a850)),x37202),f341(f110(f864(x37201,a850)),x37203)),f341(f341(f110(f864(x37201,a850)),x37203),f53(f864(x37201,a850),x37202))) % 19.23/19.03 [3721]E(f341(f341(f54(f864(x37211,a850),f864(x37211,a850)),x37212),f341(f111(f864(x37211,a850)),x37213)),f341(f341(f111(f864(x37211,a850)),x37213),f52(f864(x37211,a850),x37212))) % 19.23/19.03 [3731]E(f341(f163(x37311),f341(f341(f341(f179(f858(x37311),f858(x37311)),x37312),f147(x37311)),x37313)),f341(f163(x37311),x37313)) % 19.23/19.03 [3735]E(f341(f341(f164(x37351),f341(f186(f858(x37351)),f167(x37351,x37352,x37353))),x37353),f167(x37351,x37352,x37353)) % 19.23/19.03 [3736]E(f174(x37361,x37362,f341(f341(f10(x37362,f861(x37362),x37361),f235(x37362)),x37363)),f248(f864(x37361,a850))) % 19.23/19.03 [3739]E(f341(f186(f858(x37391)),f341(f341(f341(f179(f858(x37391),f858(x37391)),x37392),f147(x37391)),x37393)),f341(f186(f858(x37391)),x37393)) % 19.23/19.03 [3741]E(f341(f341(f260(x37411,x37412,x37412),f341(f18(f864(x37412,x37412),x37411),f7(x37412))),x37413),f341(f259(x37411,x37412),x37413)) % 19.23/19.03 [3748]E(f60(a1,f341(f341(f3(a1),f60(a1,x37481,x37482)),x37483),x37482),f60(a1,f341(f341(f3(a1),x37481),x37483),x37482)) % 19.23/19.03 [3749]E(f60(a1,f341(f341(f251(a1),f60(a1,x37491,x37492)),x37493),x37492),f60(a1,f341(f341(f251(a1),x37491),x37493),x37492)) % 19.23/19.03 [3752]E(f341(f341(f54(f864(f863(x37521,x37522),a850),f864(x37522,a850)),x37523),f268(x37521,x37522)),f341(f268(x37521,x37522),f52(f864(f863(x37521,x37522),a850),x37523))) % 19.23/19.03 [3753]E(f341(f341(f54(f864(f863(x37531,x37532),a850),f864(x37531,a850)),x37533),f270(x37531,x37532)),f341(f270(x37531,x37532),f52(f864(f863(x37531,x37532),a850),x37533))) % 19.23/19.03 [3781]E(f341(f82(x37811,x37811,x37811,x37812),f341(f341(f179(x37811,x37811),x37813),x37812)),f341(f341(f179(x37811,x37811),f341(a121,x37813)),x37812)) % 19.23/19.03 [3791]E(f237(f861(x37911),x37912,f188(x37911),f341(f341(f10(x37911,f861(x37911),x37912),f235(x37911)),x37913)),f341(f204(x37912,x37911),x37913)) % 19.23/19.03 [3798]E(f341(f341(f135(x37981),f341(f341(f3(a857),f341(f186(f858(x37981)),x37982)),x37983)),f341(f148(x37981),x37982)),f341(f148(x37981),f341(f341(f164(x37981),x37983),x37982))) % 19.23/19.03 [3799]E(f341(f341(f164(x37991),f341(f341(f3(a857),f341(f186(f858(x37991)),x37992)),x37993)),f341(f148(x37991),x37992)),f341(f148(x37991),f341(f341(f135(x37991),x37993),x37992))) % 19.23/19.03 [3802]E(f341(f341(f89(a857),f341(f160(a857),f341(f341(f149(x38021,a857),x38022),x38023))),f341(f186(f858(x38021)),x38023)),f150(x38021,x38022,x38023)) % 19.23/19.03 [3818]E(f341(f147(x38181),f341(f341(f341(f179(f858(x38181),f858(x38181)),x38182),f147(x38181)),x38183)),f341(f341(f341(f179(f858(x38181),f858(x38181)),f341(a121,x38182)),f147(x38181)),x38183)) % 19.23/19.03 [3830]P85(f341(f341(f241(a857),f341(f186(f858(x38301)),f341(f133(x38301,x38302),x38303))),f341(f186(f858(x38301)),x38303))) % 19.23/19.03 [3847]E(f341(f341(f110(f864(f864(x38471,a850),a850)),f341(f310(x38471),x38472)),f341(f312(f864(x38471,a850),f864(x38471,a850),f341(f311(x38471),x38473)),f341(f310(x38471),x38472))),f341(f310(x38471),f341(f341(f311(x38471),x38473),x38472))) % 19.23/19.03 [3865]P25(x38651,x38652,f341(f341(f311(f856(x38651)),f341(f341(f341(f100(x38651),x38653),a25),x38653)),f185(f864(f856(x38651),a850)))) % 19.23/19.03 [3881]P85(f341(f341(f241(a857),f341(f186(f858(x38811)),f167(x38811,x38812,x38813))),f341(f186(f858(x38811)),x38813))) % 19.23/19.03 [3888]E(f341(f270(x38881,x38882),f341(f265(f863(x38881,x38882)),f341(f260(x38881,x38882,a850),x38883))),f341(f265(x38881),f341(f341(f10(f864(x38882,a850),a850,x38881),f96(x38882)),x38883))) % 19.23/19.03 [3901]E(f341(f312(a857,a857,f341(f341(f9(a857,a857,a857),f89(a857)),x39011)),f304(a857,x39012,x39013)),f304(a857,f341(f341(f89(a857),x39012),x39011),f341(f341(f89(a857),x39013),x39011))) % 19.23/19.03 [3916]E(f341(f312(a857,a857,f341(f341(f9(a857,a857,a857),f89(a857)),x39161)),f341(f303(a857,x39162),x39163)),f341(f303(a857,f341(f341(f89(a857),x39162),x39161)),f341(f341(f89(a857),x39163),x39161))) % 19.23/19.03 [3933]E(f341(f341(f172(x39331,x39332),f341(f341(f149(f863(x39331,x39332),x39331),f249(x39331,x39332)),x39333)),f341(f341(f149(f863(x39331,x39332),x39332),f259(x39331,x39332)),x39333)),x39333) % 19.23/19.03 [3938]E(f341(f341(f89(a857),f341(f341(f90(a857),x39381),f60(a857,f341(f341(f51(a857),x39382),x39381),x39383))),f60(a857,x39382,x39381)),f60(a857,x39382,f341(f341(f90(a857),x39381),x39383))) % 19.23/19.03 [3949]P85(f341(f71(f861(x39491)),f341(f312(x39492,f861(x39491),f171(x39492,x39491,x39493)),f248(f864(x39492,a850))))) % 19.23/19.03 [3953]E(f341(f341(f132(x39531),x39532),f341(f138(f858(x39531),f858(x39531),f132(x39531),f122(x39531)),x39533)),f341(f138(f858(x39531),f858(x39531),f132(x39531),x39532),x39533)) % 19.23/19.03 [3973]P85(f341(f341(f343(f863(x39731,x39731)),f341(f341(f250(x39731,x39731),x39732),x39732)),f341(f341(f179(f863(x39731,x39731),a850),f2(a857)),x39733))) % 19.23/19.03 [3979]E(f341(f265(x39791),f341(f341(f10(f864(x39792,a850),a850,x39791),f96(x39792)),f341(f9(x39792,x39791,a850),x39793))),f341(f268(x39792,x39791),f341(f265(f863(x39792,x39791)),f341(f260(x39792,x39791,a850),x39793)))) % 19.23/19.03 [3998]E(f341(f341(f110(f864(x39981,a850)),f341(f341(f54(a857,f864(x39981,a850)),f304(a857,f87(a857),x39982)),x39983)),f341(x39983,f2(a857))),f341(f341(f54(a857,f864(x39981,a850)),f341(f302(a857),x39982)),x39983)) % 19.23/19.03 [4013]E(f341(f138(f858(x40131),f858(x40131),f132(x40131),f122(x40131)),f341(f341(f149(f858(x40131),f858(x40131)),f133(x40131,x40132)),x40133)),f341(f133(x40131,x40132),f341(f138(f858(x40131),f858(x40131),f132(x40131),f122(x40131)),x40133))) % 19.23/19.03 [4018]E(f341(f259(f858(x40181),f858(x40181)),f161(x40181,x40182,x40183)),f341(f133(x40181,f341(f82(a850,a850,x40181,a337),x40182)),x40183)) % 19.23/19.03 [4067]E(f341(f341(f89(a1),f341(f341(f89(a1),f341(f341(f90(a1),x40671),f341(f341(f51(a1),x40672),x40671))),f60(a1,x40672,x40671))),x40673),f341(f341(f89(a1),x40672),x40673)) % 19.23/19.03 [4102]E(f341(f341(f89(a1),f341(f341(f89(a1),f341(f341(f90(a1),f341(f341(f51(a1),x41021),x41022)),x41022)),f60(a1,x41021,x41022))),x41023),f341(f341(f89(a1),x41021),x41023)) % 19.23/19.03 [4131]E(f94(f863(x41311,x41312),f341(f260(x41311,x41312,a850),f341(f341(f10(f864(x41312,f863(x41311,x41312)),f864(x41312,a850),x41311),f341(f10(f863(x41311,x41312),a850,x41312),x41313)),f250(x41311,x41312)))),f94(f863(x41311,x41312),x41313)) % 19.23/19.03 [4132]E(f99(f863(x41321,x41322),f341(f260(x41321,x41322,a850),f341(f341(f10(f864(x41322,f863(x41321,x41322)),f864(x41322,a850),x41321),f341(f10(f863(x41321,x41322),a850,x41322),x41323)),f250(x41321,x41322)))),f99(f863(x41321,x41322),x41323)) % 19.23/19.03 [4163]P85(f341(f341(f241(f864(x41631,a850)),f52(f864(x41631,a850),f341(f341(f111(f864(f864(x41631,a850),a850)),x41632),x41633))),f341(f341(f111(f864(x41631,a850)),f52(f864(x41631,a850),x41632)),f52(f864(x41631,a850),x41633)))) % 19.23/19.03 [4164]E(f341(f148(x41641),f341(f341(f341(f179(f858(x41641),f858(x41641)),f341(f341(f3(a857),f341(f186(f858(x41641)),x41642)),f60(a857,x41643,f341(f186(f858(x41641)),x41642)))),f147(x41641)),x41642)),f341(f341(f341(f179(f858(x41641),f858(x41641)),x41643),f147(x41641)),f341(f148(x41641),x41642))) % 19.23/19.03 [4176]E(f341(f265(x41761),f341(f341(f10(a850,a850,x41761),a337),f341(f341(f9(x41761,f861(x41762),a850),f341(f341(f10(f861(x41762),f864(f861(x41762),a850),x41761),a338),x41763)),f188(x41762)))),f174(x41761,x41762,x41763)) % 19.23/19.03 [4239]E(f341(f265(x42391),f341(f341(f10(f864(x42392,a850),a850,x42391),f96(x42392)),f341(f341(f10(f861(x42391),f864(x42392,a850),x42391),f341(f9(x42392,f861(x42391),a850),f341(f341(f10(f861(x42391),f864(f861(x42391),a850),x42392),a338),x42393))),f235(x42391)))),f176(x42392,x42391,x42393)) % 19.23/19.03 [4490]~P85(f341(f72(x44901,x44902,f185(f864(x44901,a850))),x44903)) % 19.23/19.03 [3507]E(f341(f186(f858(x35071)),f341(f341(f164(x35071),x35072),x35073)),f341(f341(f245(a857),f341(f186(f858(x35071)),x35073)),x35072)) % 19.23/19.03 [3508]E(f341(f186(f858(x35081)),f341(f341(f135(x35081),x35082),x35083)),f341(f341(f3(a857),f341(f186(f858(x35081)),x35083)),x35082)) % 19.23/19.03 [3544]E(f341(f341(f51(a857),f341(f341(f51(a857),x35441),x35442)),x35443),f341(f341(f51(a857),x35441),f341(f341(f90(a857),x35442),x35443))) % 19.23/19.03 [3545]E(f341(f341(f89(a857),f341(f341(f89(a857),x35451),x35452)),x35453),f341(f341(f89(a857),x35451),f341(f341(f89(a857),x35452),x35453))) % 19.23/19.03 [3546]E(f341(f341(f89(a1),f341(f341(f89(a1),x35461),x35462)),x35463),f341(f341(f89(a1),x35461),f341(f341(f89(a1),x35462),x35463))) % 19.23/19.03 [3547]E(f341(f341(f90(a857),f341(f341(f90(a857),x35471),x35472)),x35473),f341(f341(f90(a857),x35471),f341(f341(f90(a857),x35472),x35473))) % 19.23/19.03 [3548]E(f341(f341(f90(a1),f341(f341(f90(a1),x35481),x35482)),x35483),f341(f341(f90(a1),x35481),f341(f341(f90(a1),x35482),x35483))) % 19.23/19.03 [3549]E(f341(f341(f3(a857),f341(f341(f3(a857),x35491),x35492)),x35493),f341(f341(f3(a857),x35491),f341(f341(f89(a857),x35492),x35493))) % 19.23/19.03 [3550]E(f341(f341(f251(a1),f341(f341(f251(a1),x35501),x35502)),x35503),f341(f341(f251(a1),x35501),f341(f341(f90(a857),x35502),x35503))) % 19.23/19.03 [3568]E(f156(x35681,f341(f341(f146(f864(x35681,a850)),x35682),x35683)),f166(x35681,x35682,f156(x35681,x35683))) % 19.23/19.03 [3612]E(f341(f341(f3(a857),f341(f341(f3(a857),x36121),x36122)),x36123),f341(f341(f3(a857),f341(f341(f3(a857),x36121),x36123)),x36122)) % 19.23/19.03 [3620]E(f341(f341(f111(f864(x36201,a850)),x36202),f341(f341(f3(f864(x36201,a850)),x36203),x36202)),f185(f864(x36201,a850))) % 19.23/19.03 [3665]E(f53(f864(x36651,a850),f341(f341(f311(f864(x36651,a850)),x36652),x36653)),f341(f341(f111(f864(x36651,a850)),x36652),f53(f864(x36651,a850),x36653))) % 19.23/19.03 [3666]E(f52(f864(x36661,a850),f341(f341(f311(f864(x36661,a850)),x36662),x36663)),f341(f341(f110(f864(x36661,a850)),x36662),f52(f864(x36661,a850),x36663))) % 19.23/19.03 [3668]E(f341(f341(f89(a857),f341(f341(f90(a857),x36681),x36682)),f341(f341(f90(a857),x36683),x36682)),f341(f341(f90(a857),f341(f341(f89(a857),x36681),x36683)),x36682)) % 19.23/19.03 [3669]E(f341(f341(f3(a857),f341(f341(f90(a857),x36691),x36692)),f341(f341(f90(a857),x36693),x36692)),f341(f341(f90(a857),f341(f341(f3(a857),x36691),x36693)),x36692)) % 19.23/19.03 [3670]E(f341(f341(f89(a1),f341(f341(f90(a1),x36701),x36702)),f341(f341(f90(a1),x36703),x36702)),f341(f341(f90(a1),f341(f341(f89(a1),x36701),x36703)),x36702)) % 19.23/19.03 [3672]E(f341(f341(f3(a1),f341(f341(f90(a1),x36721),x36722)),f341(f341(f90(a1),x36723),x36722)),f341(f341(f90(a1),f341(f341(f3(a1),x36721),x36723)),x36722)) % 19.23/19.03 [3673]E(f341(f341(f245(a857),f341(f341(f3(a857),x36731),x36732)),f341(f341(f3(a857),x36733),x36732)),f341(f341(f3(a857),f341(f341(f245(a857),x36731),x36733)),x36732)) % 19.23/19.03 [3697]E(f341(f341(f110(f864(x36971,a850)),x36972),f341(f341(f3(f864(x36971,a850)),x36973),x36972)),f341(f341(f110(f864(x36971,a850)),x36972),x36973)) % 19.23/19.03 [3698]E(f341(f341(f110(f864(x36981,a850)),x36982),f341(f341(f110(f864(x36981,a850)),x36982),x36983)),f341(f341(f110(f864(x36981,a850)),x36982),x36983)) % 19.23/19.03 [3699]E(f341(f341(f111(f864(x36991,a850)),x36992),f341(f341(f111(f864(x36991,a850)),x36992),x36993)),f341(f341(f111(f864(x36991,a850)),x36992),x36993)) % 19.23/19.03 [3711]E(f341(f341(f290(x37111,x37112,x37112),x37113),f309(x37112,f185(f864(f863(x37112,x37112),a850)))),x37113) % 19.23/19.03 [3716]E(f341(f341(f110(f864(x37161,a850)),f341(f341(f311(x37161),x37162),f185(f864(x37161,a850)))),x37163),f341(f341(f311(x37161),x37162),x37163)) % 19.23/19.03 [3734]E(f341(f341(f3(a857),f341(f341(f3(a857),f341(a121,x37341)),x37342)),f341(a121,x37343)),f341(f341(f3(a857),f341(f341(f3(a857),x37341),x37342)),x37343)) % 19.23/19.03 [3761]E(f341(f341(f111(f864(f864(x37611,a850),a850)),f341(f310(x37611),x37612)),f341(f310(x37611),x37613)),f341(f310(x37611),f341(f341(f111(f864(x37611,a850)),x37612),x37613))) % 19.23/19.03 [3764]E(f341(f341(f110(f864(x37641,a850)),f341(f88(f864(x37641,a850)),x37642)),x37643),f341(f88(f864(x37641,a850)),f341(f341(f3(f864(x37641,a850)),x37642),x37643))) % 19.23/19.03 [3777]E(f341(f341(f311(x37771),x37772),f341(f341(f3(f864(x37771,a850)),x37773),f341(f341(f311(x37771),x37772),f185(f864(x37771,a850))))),f341(f341(f311(x37771),x37772),x37773)) % 19.23/19.03 [3788]P85(f341(f341(f241(f864(x37881,a850)),x37882),f341(f341(f110(f864(x37881,a850)),x37883),x37882))) % 19.23/19.03 [3789]P85(f341(f341(f241(f864(x37891,a850)),x37892),f341(f341(f110(f864(x37891,a850)),x37892),x37893))) % 19.23/19.03 [3792]E(f341(f341(f111(f864(x37921,a850)),f341(f88(f864(x37921,a850)),x37922)),f341(f88(f864(x37921,a850)),x37923)),f341(f88(f864(x37921,a850)),f341(f341(f110(f864(x37921,a850)),x37922),x37923))) % 19.23/19.03 [3793]E(f341(f341(f110(f864(x37931,a850)),f341(f88(f864(x37931,a850)),x37932)),f341(f88(f864(x37931,a850)),x37933)),f341(f88(f864(x37931,a850)),f341(f341(f111(f864(x37931,a850)),x37932),x37933))) % 19.23/19.03 [3806]P85(f341(f341(f241(f864(x38061,a850)),f341(f163(x38061),x38062)),f341(f163(x38061),f341(f341(f146(x38061),x38063),x38062)))) % 19.23/19.03 [3815]E(f341(f341(f110(f864(x38151,a850)),f341(f341(f3(f864(x38151,a850)),x38152),x38153)),f341(f341(f111(f864(x38151,a850)),x38152),x38153)),x38152) % 19.23/19.03 [3867]E(f341(f341(f11(x38671,a1),f341(f341(f10(a857,a1,x38671),f109(a1)),x38672)),x38673),f341(f109(a1),f341(f341(f11(x38671,a857),x38672),x38673))) % 19.23/19.03 [3868]E(f341(f341(f8(x38681,a1),f341(f341(f10(a857,a1,x38681),f109(a1)),x38682)),x38683),f341(f109(a1),f341(f341(f8(x38681,a857),x38682),x38683))) % 19.23/19.03 [3922]E(f341(f88(f864(f863(x39221,x39222),a850)),f341(f341(f257(x39221,x39222),x39223),f341(f18(f864(x39222,a850),x39221),f248(f864(x39222,a850))))),f341(f341(f257(x39221,x39222),f341(f88(f864(x39221,a850)),x39223)),f341(f18(f864(x39222,a850),x39221),f248(f864(x39222,a850))))) % 19.23/19.03 [3923]E(f341(f88(f864(f863(x39231,x39232),a850)),f341(f341(f257(x39231,x39232),f248(f864(x39231,a850))),f341(f18(f864(x39232,a850),x39231),x39233))),f341(f341(f257(x39231,x39232),f248(f864(x39231,a850))),f341(f18(f864(x39232,a850),x39231),f341(f88(f864(x39232,a850)),x39233)))) % 19.23/19.03 [3974]E(f341(f341(f54(f864(x39741,a850),f864(x39741,a850)),x39742),f341(f341(f9(f864(x39741,a850),f864(x39741,a850),f864(x39741,a850)),f111(f864(x39741,a850))),x39743)),f341(f341(f111(f864(x39741,a850)),f52(f864(x39741,a850),x39742)),x39743)) % 19.23/19.03 [3981]E(f341(f138(f858(x39811),f858(x39811),f132(x39811),f122(x39811)),f341(f341(f146(f858(x39811)),x39812),x39813)),f341(f341(f132(x39811),x39812),f341(f138(f858(x39811),f858(x39811),f132(x39811),f122(x39811)),x39813))) % 19.23/19.03 [4004]E(f341(f341(f311(f864(x40041,a850)),f341(f286(x40041,x40041,x40042),f341(f341(f311(x40041),x40043),f185(f864(x40041,a850))))),f185(f864(f864(x40041,a850),a850))),f341(f341(f69(x40041),f341(f341(f311(x40041),x40043),f185(f864(x40041,a850)))),x40042)) % 19.23/19.03 [4014]E(f341(f341(f89(a857),f341(f341(f90(a857),x40141),f341(f341(f51(a857),x40142),x40143))),f341(f341(f51(a857),f341(f341(f90(a857),x40141),f60(a857,x40142,x40143))),x40143)),f341(f341(f51(a857),f341(f341(f90(a857),x40141),x40142)),x40143)) % 19.23/19.03 [4015]E(f341(f341(f89(a1),f341(f341(f90(a1),x40151),f341(f341(f51(a1),x40152),x40153))),f341(f341(f51(a1),f341(f341(f90(a1),x40151),f60(a1,x40152,x40153))),x40153)),f341(f341(f51(a1),f341(f341(f90(a1),x40151),x40152)),x40153)) % 19.23/19.03 [4099]E(f341(f341(f132(x40991),f341(f138(f858(x40991),f858(x40991),f132(x40991),f122(x40991)),x40992)),f341(f138(f858(x40991),f858(x40991),f132(x40991),f122(x40991)),x40993)),f341(f138(f858(x40991),f858(x40991),f132(x40991),f122(x40991)),f341(f341(f132(f858(x40991)),x40992),x40993))) % 19.23/19.03 [4104]E(f341(f341(f250(f858(x41041),f858(x41041)),f341(f133(x41041,x41042),x41043)),f341(f133(x41041,f341(f82(a850,a850,x41041,a337),x41042)),x41043)),f161(x41041,x41042,x41043)) % 19.23/19.03 [4107]E(f341(f341(f89(a857),f341(f341(f89(a857),f341(f341(f51(a857),x41071),x41072)),f341(f341(f51(a857),x41073),x41072))),f341(f341(f51(a857),f341(f341(f89(a857),f60(a857,x41071,x41072)),f60(a857,x41073,x41072))),x41072)),f341(f341(f51(a857),f341(f341(f89(a857),x41071),x41073)),x41072)) % 19.23/19.03 [4108]E(f341(f341(f89(a1),f341(f341(f89(a1),f341(f341(f51(a1),x41081),x41082)),f341(f341(f51(a1),x41083),x41082))),f341(f341(f51(a1),f341(f341(f89(a1),f60(a1,x41081,x41082)),f60(a1,x41083,x41082))),x41082)),f341(f341(f51(a1),f341(f341(f89(a1),x41081),x41083)),x41082)) % 19.23/19.03 [4178]E(f341(f265(x41781),f341(f341(f20(x41781,a850,a850),f341(f341(f10(a850,f864(a850,a850),x41781),a340),f341(f341(f9(x41781,x41781,a850),a338),x41782))),f341(f341(f9(x41781,f864(x41781,a850),a850),f343(x41781)),x41783))),f341(f341(f311(x41781),x41782),x41783)) % 19.23/19.03 [4200]E(f341(f265(x42001),f341(f341(f20(x42001,a850,a850),f341(f341(f10(a850,f864(a850,a850),x42001),a340),f341(f341(f9(x42001,f864(x42001,a850),a850),f343(x42001)),x42002))),f341(f341(f9(x42001,f864(x42001,a850),a850),f343(x42001)),x42003))),f341(f341(f110(f864(x42001,a850)),x42002),x42003)) % 19.23/19.03 [4201]E(f341(f265(x42011),f341(f341(f20(x42011,a850,a850),f341(f341(f10(a850,f864(a850,a850),x42011),a339),f341(f341(f9(x42011,f864(x42011,a850),a850),f343(x42011)),x42012))),f341(f341(f9(x42011,f864(x42011,a850),a850),f343(x42011)),x42013))),f341(f341(f111(f864(x42011,a850)),x42012),x42013)) % 19.23/19.03 [4288]E(f341(f341(f54(x42881,f864(f864(x42881,a850),a850)),x42882),f341(f341(f9(x42881,f864(f864(x42881,a850),a850),f864(f864(x42881,a850),a850)),f341(f341(f10(f864(x42881,a850),f864(f864(f864(x42881,a850),a850),f864(f864(x42881,a850),a850)),x42881),f311(f864(x42881,a850))),f341(f341(f10(f864(x42881,a850),f864(x42881,a850),x42881),f286(x42881,x42881,x42883)),f341(f341(f9(x42881,f864(x42881,a850),f864(x42881,a850)),f311(x42881)),f185(f864(x42881,a850)))))),f185(f864(f864(x42881,a850),a850)))),f341(f341(f69(x42881),x42882),x42883)) % 19.23/19.03 [4290]E(f341(f341(f205(x42901),f341(f341(f90(a1),f341(f341(f82(f863(a1,a1),a1,x42901,f249(a1,a1)),f215(x42901)),x42902)),f341(f341(f82(f863(a1,a1),a1,x42901,f249(a1,a1)),f215(x42901)),x42903))),f341(f341(f90(a1),f341(f341(f82(f863(a1,a1),a1,x42901,f259(a1,a1)),f215(x42901)),x42902)),f341(f341(f82(f863(a1,a1),a1,x42901,f259(a1,a1)),f215(x42901)),x42903))),f230(x42901,x42902,x42903)) % 19.23/19.03 [3686]E(f60(a857,f341(f341(f89(a857),f341(f341(f90(a857),x36861),x36862)),x36863),x36862),f60(a857,x36863,x36862)) % 19.23/19.03 [3733]E(f136(a857,f341(f303(a857,f341(f341(f89(a857),x37331),x37332)),x37333)),f341(f341(f135(a857),x37332),f136(a857,f341(f303(a857,x37331),x37333)))) % 19.23/19.03 [3776]E(f341(f341(f89(a1),f341(f109(a1),x37761)),f341(f341(f89(a1),f341(f109(a1),x37762)),x37763)),f341(f341(f89(a1),f341(f109(a1),f341(f341(f89(a857),x37761),x37762))),x37763)) % 19.23/19.03 [3784]E(f341(f341(f3(f864(x37841,a850)),f341(f341(f3(f864(x37841,a850)),x37842),x37843)),x37843),f341(f341(f3(f864(x37841,a850)),x37842),x37843)) % 19.23/19.03 [3785]E(f341(f341(f110(f864(x37851,a850)),f341(f341(f3(f864(x37851,a850)),x37852),x37853)),x37853),f341(f341(f110(f864(x37851,a850)),x37852),x37853)) % 19.23/19.03 [3807]E(f341(f341(f290(x38071,x38071,x38072),f309(x38071,f185(f864(f863(x38071,x38071),a850)))),x38073),x38073) % 19.23/19.03 [3812]E(f341(f341(f110(f864(x38121,a850)),f341(f285(x38121),x38122)),f341(f285(x38121),x38123)),f341(f285(x38121),f341(f341(f110(f864(f863(x38121,x38121),a850)),x38122),x38123))) % 19.23/19.03 [3821]E(f272(x38211,f341(f341(f146(f863(a108,x38211)),f341(f341(f250(a108,x38211),f2(a108)),x38212)),x38213)),f272(x38211,x38213)) % 19.23/19.03 [3824]E(f341(f341(f111(f864(x38241,a850)),f53(f864(x38241,a850),x38242)),f53(f864(x38241,a850),x38243)),f53(f864(x38241,a850),f341(f341(f110(f864(f864(x38241,a850),a850)),x38242),x38243))) % 19.23/19.03 [3825]E(f341(f341(f110(f864(x38251,a850)),f52(f864(x38251,a850),x38252)),f52(f864(x38251,a850),x38253)),f52(f864(x38251,a850),f341(f341(f110(f864(f864(x38251,a850),a850)),x38252),x38253))) % 19.23/19.03 [3860]E(f341(f341(f290(x38601,x38601,x38601),f341(f341(f179(f863(x38601,x38601),a850),x38602),x38603)),x38603),f341(f341(f179(f863(x38601,x38601),a850),f341(a121,x38602)),x38603)) % 19.23/19.03 [3909]P85(f341(f341(f241(f864(x39091,a850)),f341(f341(f3(f864(x39091,a850)),x39092),x39093)),x39092)) % 19.23/19.03 [3910]P85(f341(f341(f241(f864(x39101,a850)),f341(f341(f111(f864(x39101,a850)),x39102),x39103)),x39103)) % 19.23/19.03 [3911]P85(f341(f341(f241(f864(x39111,a850)),f341(f341(f111(f864(x39111,a850)),x39112),x39113)),x39112)) % 19.23/19.03 [3935]E(f309(x39351,f341(f341(f110(f864(f863(x39351,x39351),a850)),f309(x39351,x39352)),f309(x39351,x39353))),f309(x39351,f341(f341(f110(f864(f863(x39351,x39351),a850)),x39352),x39353))) % 19.23/19.03 [3939]E(f52(f864(x39391,a850),f341(f341(f311(f864(x39391,a850)),x39392),f341(f341(f311(f864(x39391,a850)),x39393),f185(f864(f864(x39391,a850),a850))))),f341(f341(f110(f864(x39391,a850)),x39392),x39393)) % 19.23/19.03 [3940]E(f53(f864(x39401,a850),f341(f341(f311(f864(x39401,a850)),x39402),f341(f341(f311(f864(x39401,a850)),x39403),f185(f864(f864(x39401,a850),a850))))),f341(f341(f111(f864(x39401,a850)),x39402),x39403)) % 19.23/19.03 [3946]E(f341(f341(f290(x39461,x39461,x39461),f341(f341(f179(f863(x39461,x39461),a850),x39462),x39463)),x39463),f341(f341(f290(x39461,x39461,x39461),x39463),f341(f341(f179(f863(x39461,x39461),a850),x39462),x39463))) % 19.23/19.03 [4019]E(f341(f341(f110(f864(x40191,a850)),f341(f265(x40191),f341(f341(f9(x40191,x40191,a850),a338),x40192))),x40193),f341(f341(f311(x40191),x40192),x40193)) % 19.23/19.03 [4021]E(f341(a114,f341(f341(f11(x40211,a1),f341(f341(f10(a857,a1,x40211),f109(a1)),x40212)),x40213)),f341(f341(f11(x40211,a857),x40212),x40213)) % 19.23/19.03 [4022]E(f341(a114,f341(f341(f8(x40221,a1),f341(f341(f10(a857,a1,x40221),f109(a1)),x40222)),x40223)),f341(f341(f8(x40221,a857),x40222),x40223)) % 19.23/19.03 [4096]E(f341(f151(f858(x40961),x40961,f341(f162(x40961),x40962),f341(f18(f864(f858(x40961),f858(x40961)),x40961),f341(f341(f9(f858(x40961),f858(x40961),f858(x40961)),f132(x40961)),x40962))),x40963),f341(f162(x40961),f341(f341(f132(x40961),x40963),x40962))) % 19.23/19.03 [4127]P85(f341(f341(f241(f864(f864(x41271,a850),a850)),f341(f341(f110(f864(f864(x41271,a850),a850)),f341(f310(x41271),x41272)),f341(f310(x41271),x41273))),f341(f310(x41271),f341(f341(f110(f864(x41271,a850)),x41272),x41273)))) % 19.23/19.03 [4219]E(f341(f265(x42191),f341(f341(f20(x42191,a850,a850),f341(f341(f10(a850,f864(a850,a850),x42191),a339),f341(f341(f9(x42191,f864(x42191,a850),a850),f343(x42191)),x42192))),f341(f341(f10(a850,a850,x42191),a337),f341(f341(f9(x42191,f864(x42191,a850),a850),f343(x42191)),x42193)))),f341(f341(f3(f864(x42191,a850)),x42192),x42193)) % 19.23/19.03 [4240]E(f341(f50(a857),f341(f265(a857),f341(f341(f20(a857,a850,a850),f341(f341(f10(a850,f864(a850,a850),a857),a339),f341(f341(f9(a857,a857,a850),f242(a857)),f341(f186(f858(x42401)),x42402)))),f341(f341(f10(x42401,a850,a857),x42403),f341(f158(x42401),x42402))))),f341(f186(f858(x42401)),f341(f133(x42401,x42403),x42402))) % 19.23/19.03 [4242]E(f341(f186(f858(x42421)),f165(x42421,x42422,x42423)),f341(f50(a857),f341(f265(a857),f341(f341(f20(a857,a850,a850),f341(f341(f10(a850,f864(a850,a850),a857),a339),f341(f341(f9(a857,a857,a850),f242(a857)),f341(f186(f858(x42421)),x42422)))),f341(f341(f9(a857,f864(a857,a850),a850),f343(a857)),x42423))))) % 19.23/19.03 [4335]E(f341(f341(f111(f864(f863(f858(x43351),f858(x43351)),a850)),f341(f312(f863(f863(x43351,f858(x43351)),f863(x43351,f858(x43351))),f863(f858(x43351),f858(x43351)),f261(f863(x43351,f858(x43351)),f858(x43351),f863(x43351,f858(x43351)),f858(x43351),f341(f260(x43351,f858(x43351),f858(x43351)),f146(x43351)),f341(f260(x43351,f858(x43351),f858(x43351)),f146(x43351)))),f335(x43351,f858(x43351),x43352,f341(f139(x43351,x43352),x43353)))),f341(f265(f863(f858(x43351),f858(x43351))),f341(f260(f858(x43351),f858(x43351),a850),f341(f341(f9(f858(x43351),f864(f858(x43351),a850),f864(f858(x43351),a850)),f341(f341(f10(f864(a850,a850),f864(f864(f858(x43351),a850),f864(f858(x43351),a850)),f858(x43351)),f10(a850,a850,f858(x43351))),f341(f341(f10(a850,f864(a850,a850),f858(x43351)),a339),f341(f341(f9(f858(x43351),a857,a850),f341(f341(f10(a857,f864(a857,a850),f858(x43351)),a338),f186(f858(x43351)))),f341(a121,x43353))))),f341(f341(f9(f858(x43351),a857,a850),f341(f341(f10(a857,f864(a857,a850),f858(x43351)),a338),f186(f858(x43351)))),f341(a121,x43353)))))),f341(f139(x43351,x43352),f341(a121,x43353))) % 19.23/19.03 [3826]E(f60(a857,f341(a121,f341(f341(f89(a857),f341(f341(f90(a857),x38261),x38262)),x38263)),x38262),f60(a857,f341(a121,x38263),x38262)) % 19.23/19.03 [4086]E(f341(f265(x40861),f341(f341(f20(x40861,a850,a850),f341(f341(f10(a850,f864(a850,a850),x40861),a339),x40862)),x40863)),f341(f341(f111(f864(x40861,a850)),f341(f265(x40861),x40862)),f341(f265(x40861),x40863))) % 19.23/19.03 [4087]E(f341(f265(x40871),f341(f341(f20(x40871,a850,a850),f341(f341(f10(a850,f864(a850,a850),x40871),a340),x40872)),x40873)),f341(f341(f110(f864(x40871,a850)),f341(f265(x40871),x40872)),f341(f265(x40871),x40873))) % 19.23/19.03 [4089]E(f341(f341(f132(x40891),f341(f341(f135(x40891),f60(a857,x40892,f341(f186(f858(x40891)),x40893))),x40893)),f341(f341(f164(x40891),f60(a857,x40892,f341(f186(f858(x40891)),x40893))),x40893)),f341(f341(f341(f179(f858(x40891),f858(x40891)),x40892),f147(x40891)),x40893)) % 19.23/19.03 [4094]E(f341(f265(x40941),f341(f341(f20(x40941,a850,a850),f341(f341(f10(a850,f864(a850,a850),x40941),a344),x40942)),x40943)),f341(f341(f110(f864(x40941,a850)),f341(f88(f864(x40941,a850)),f341(f265(x40941),x40942))),f341(f265(x40941),x40943))) % 19.23/19.03 [4109]E(f341(f341(f89(a857),f341(f186(f858(x41091)),f341(f133(x41091,x41092),x41093))),f341(f186(f858(x41091)),f341(f133(x41091,f341(f341(f10(a850,a850,x41091),a337),x41092)),x41093))),f341(f186(f858(x41091)),x41093)) % 19.23/19.03 [4134]P85(f341(f341(f241(f864(x41341,a850)),f341(f341(f110(f864(x41341,a850)),f53(f864(x41341,a850),x41342)),f53(f864(x41341,a850),x41343))),f53(f864(x41341,a850),f341(f341(f111(f864(f864(x41341,a850),a850)),x41342),x41343)))) % 19.23/19.03 [4150]E(f341(f163(x41501),f341(f133(x41501,f341(f341(f10(a850,a850,x41501),a337),f341(f341(f9(x41501,x41501,a850),a338),x41502))),x41503)),f341(f341(f3(f864(x41501,a850)),f341(f163(x41501),x41503)),f341(f341(f311(x41501),x41502),f185(f864(x41501,a850))))) % 19.23/19.03 [4159]P85(f341(f341(f241(f864(f863(x41591,x41591),a850)),f341(f341(f110(f864(f863(x41591,x41591),a850)),f309(x41591,x41592)),f309(x41591,x41593))),f309(x41591,f341(f341(f110(f864(f863(x41591,x41591),a850)),x41592),x41593)))) % 19.23/19.03 [4183]E(f341(f341(f90(a857),f341(a121,f341(a121,f2(a857)))),f341(f341(f8(a857,a857),f341(f341(f10(a857,a857,a857),f341(f89(a857),x41831)),f341(f341(f9(a857,a857,a857),f90(a857)),x41832))),f341(f266(a857),x41833))),f341(f341(f90(a857),x41833),f341(f341(f89(a857),x41831),f341(f341(f89(a857),x41831),f341(f341(f90(a857),f341(f341(f3(a857),x41833),f87(a857))),x41832))))) % 19.23/19.03 [4193]E(f341(f265(x41931),f341(f341(f20(x41931,a850,a850),f341(f341(f10(a850,f864(a850,a850),x41931),a339),f341(f341(f9(x41931,f864(x41931,a850),a850),f343(x41931)),f341(f163(x41931),x41932)))),x41933)),f341(f163(x41931),f341(f133(x41931,x41933),x41932))) % 19.23/19.03 [4334]E(f341(f265(x43341),f341(f341(f10(f864(a857,a850),a850,x43341),f96(a857)),f341(f341(f9(x43341,f864(a857,a850),f864(a857,a850)),f341(f341(f10(f864(a857,f864(a850,a850)),f864(f864(a857,a850),f864(a857,a850)),x43341),f20(a857,a850,a850)),f341(f341(f10(f864(a857,a850),f864(a857,f864(a850,a850)),x43341),f341(f10(a850,f864(a850,a850),a857),a339)),f341(f341(f9(x43341,f864(a857,x43341),f864(a857,a850)),f341(f341(f10(f864(x43341,a850),f864(f864(a857,x43341),f864(a857,a850)),x43341),f10(x43341,a850,a857)),a338)),f341(f158(x43341),x43342))))),f341(f341(f20(a857,a850,a850),f341(f341(f10(a850,f864(a850,a850),a857),a339),f341(f341(f9(a857,a857,a850),f242(a857)),f341(f186(f858(x43341)),x43342)))),f341(f341(f9(a857,f864(a857,a850),a850),f343(a857)),x43343))))),f341(f163(x43341),f165(x43341,x43342,x43343))) % 19.23/19.03 [4230]E(f341(f265(x42301),f341(f341(f20(x42301,a850,a850),f341(f341(f10(a850,f864(a850,a850),x42301),a344),f341(f341(f10(a850,a850,x42301),a337),f341(f341(f9(x42301,x42301,a850),a338),x42302)))),x42303)),f341(f341(f311(x42301),x42302),f341(f265(x42301),x42303))) % 19.23/19.03 [4261]E(f341(f341(f149(f863(x42611,a857),x42611),f249(x42611,a857)),f341(f133(f863(x42611,a857),f341(f341(f9(f863(x42611,a857),f864(a857,a850),a850),f341(f341(f10(a857,f864(f864(a857,a850),a850),f863(x42611,a857)),f343(a857)),f259(x42611,a857))),x42612)),f341(f341(f172(x42611,a857),x42613),f136(a857,f341(f303(a857,f2(a857)),f341(f186(f858(x42611)),x42613)))))),f165(x42611,x42613,x42612)) % 19.23/19.03 [4289]E(f341(f341(f90(a1),f341(f113(a1),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),f341(f341(f8(a857,a1),f341(f341(f10(a1,a1,a857),f341(f89(a1),x42891)),f341(f341(f9(a857,a1,a1),f341(f341(f10(a1,f864(a1,a1),a857),f90(a1)),f109(a1))),x42892))),f341(f266(a857),x42893))),f341(f341(f90(a1),f341(f109(a1),x42893)),f341(f341(f89(a1),x42891),f341(f341(f89(a1),x42891),f341(f341(f90(a1),f341(f109(a1),f341(f341(f3(a857),x42893),f87(a857)))),x42892))))) % 19.23/19.03 [4328]E(f341(f265(f863(x43281,x43282)),f341(f260(x43281,x43282,a850),f341(f341(f9(x43281,f864(f863(x43282,x43281),a850),f864(x43282,a850)),f341(f341(f10(f864(x43282,f864(f864(f863(x43282,x43281),a850),a850)),f864(f864(f863(x43282,x43281),a850),f864(x43282,a850)),x43281),f9(x43282,f864(f863(x43282,x43281),a850),a850)),f341(f341(f10(f864(x43282,f863(x43282,x43281)),f864(x43282,f864(f864(f863(x43282,x43281),a850),a850)),x43281),f341(f10(f863(x43282,x43281),f864(f864(f863(x43282,x43281),a850),a850),x43282),f343(f863(x43282,x43281)))),f341(f9(x43282,x43281,f863(x43282,x43281)),f250(x43282,x43281))))),x43283))),f341(f287(x43282,x43281),x43283)) % 19.23/19.03 [4362]E(f341(f265(f858(x43621)),f341(f341(f10(f864(x43621,a850),a850,f858(x43621)),f96(x43621)),f341(f341(f10(f864(x43621,f864(f858(x43621),a850)),f864(x43621,a850),f858(x43621)),f341(f10(f864(f858(x43621),a850),a850,x43621),f96(f858(x43621)))),f341(f341(f9(f858(x43621),f864(x43621,f864(f858(x43621),a850)),f864(x43621,f864(f858(x43621),a850))),f341(f341(f10(f864(x43621,f864(f864(f858(x43621),a850),f864(f858(x43621),a850))),f864(f864(x43621,f864(f858(x43621),a850)),f864(x43621,f864(f858(x43621),a850))),f858(x43621)),f20(x43621,f864(f858(x43621),a850),f864(f858(x43621),a850))),f341(f341(f10(f864(x43621,f864(f858(x43621),f864(a850,a850))),f864(x43621,f864(f864(f858(x43621),a850),f864(f858(x43621),a850))),f858(x43621)),f341(f10(f864(f858(x43621),f864(a850,a850)),f864(f864(f858(x43621),a850),f864(f858(x43621),a850)),x43621),f20(f858(x43621),a850,a850))),f341(f341(f10(f864(x43621,f864(f858(x43621),a850)),f864(x43621,f864(f858(x43621),f864(a850,a850))),f858(x43621)),f341(f10(f864(f858(x43621),a850),f864(f858(x43621),f864(a850,a850)),x43621),f341(f10(a850,f864(a850,a850),f858(x43621)),a339))),f341(f341(f9(f858(x43621),f864(x43621,f864(f858(x43621),f858(x43621))),f864(x43621,f864(f858(x43621),a850))),f341(f341(f10(f864(f864(f858(x43621),f858(x43621)),f864(f858(x43621),a850)),f864(f864(x43621,f864(f858(x43621),f858(x43621))),f864(x43621,f864(f858(x43621),a850))),f858(x43621)),f10(f864(f858(x43621),f858(x43621)),f864(f858(x43621),a850),x43621)),f341(f341(f10(f864(f858(x43621),a850),f864(f864(f858(x43621),f858(x43621)),f864(f858(x43621),a850)),f858(x43621)),f10(f858(x43621),a850,f858(x43621))),a338))),f146(x43621)))))),f341(f341(f9(x43621,f864(f858(x43621),a850),f864(f858(x43621),a850)),f341(f341(f10(f864(a850,a850),f864(f864(f858(x43621),a850),f864(f858(x43621),a850)),x43621),f10(a850,a850,f858(x43621))),f341(f341(f10(a850,f864(a850,a850),x43621),a339),f341(f341(f9(x43621,f864(x43621,a850),a850),f343(x43621)),x43622)))),f341(f341(f9(f858(x43621),f864(f858(x43621),a850),a850),f343(f858(x43621))),x43623)))))),f166(x43621,x43622,x43623)) % 19.23/19.03 [4347]E(f341(f341(f95(a1,f863(a1,a1)),f341(f341(f3(a1),x43471),x43472)),f341(f341(f9(a1,f863(a1,a1),f863(a1,a1)),f341(f341(f20(a1,f863(a1,a1),f864(f863(a1,a1),f863(a1,a1))),f341(f341(f10(a850,f864(f863(a1,a1),f864(f863(a1,a1),f863(a1,a1))),a1),f105(f863(a1,a1))),f341(f241(a1),f2(a1)))),f341(f250(a1,a1),f341(f341(f89(a1),f341(f341(f90(a1),f341(f113(a1),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),x43473)),f87(a1))))),f341(f341(f250(a1,a1),f341(f341(f90(a1),f341(f113(a1),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),x43473)),x43471))),f341(f58(x43472),f341(f341(f250(a1,a1),x43473),x43471))) % 19.23/19.03 [4400]~E(f38(x44001,x44002),f30(x44003,x44004)) % 19.23/19.03 [4403]~E(f37(x44031,x44032),f30(x44033,x44034)) % 19.23/19.03 [4404]~E(f37(x44041,x44042),f38(x44043,x44044)) % 19.23/19.03 [4422]~E(f341(a29,x44221),f33(x44222,x44223,x44224)) % 19.23/19.03 [4423]~E(f341(a29,x44231),f35(x44232,x44233,x44234)) % 19.23/19.03 [4424]~E(f341(a29,x44241),f34(x44242,x44243,x44244)) % 19.23/19.03 [4425]~E(f33(x44251,x44252,x44253),f341(a29,x44254)) % 19.23/19.03 [4426]~E(f35(x44261,x44262,x44263),f341(a29,x44264)) % 19.23/19.03 [4427]~E(f34(x44271,x44272,x44273),f341(a29,x44274)) % 19.23/19.03 [3378]E(f341(f341(f341(f81(x33781,x33782),x33783),x33784),f341(x33783,x33784)),x33783) % 19.23/19.03 [3441]E(f341(f341(f252(x34411,x34412,x34413),x34414),f2(a857)),x34412) % 19.23/19.03 [3456]E(f45(x34561,x34562,x34563,f42(x34564)),f341(x34563,x34564)) % 19.23/19.03 [3457]E(f45(x34571,x34572,x34573,f43(x34574)),f341(x34572,x34574)) % 19.23/19.03 [3458]E(f46(x34581,x34582,x34583,f42(x34584)),f341(x34583,x34584)) % 19.23/19.03 [3459]E(f46(x34591,x34592,x34593,f43(x34594)),f341(x34592,x34594)) % 19.23/19.03 [3483]E(f181(x34831,x34832,x34833,f341(a121,x34834)),f341(x34833,x34834)) % 19.23/19.03 [3525]E(f157(x35251,x35252,f157(x35251,x35253,x35254)),f157(x35251,x35253,f157(x35251,x35252,x35254))) % 19.23/19.03 [3641]P38(f30(x36411,x36412),x36413,x36414,f341(f341(f341(a194,x36413),x36411),f341(x36412,x36413))) % 19.23/19.03 [3653]E(f341(f237(x36531,x36532,x36533,x36534),f188(x36532)),x36533) % 19.23/19.03 [3655]E(f341(f151(x36551,x36552,x36553,x36554),f122(x36552)),x36553) % 19.23/19.03 [3656]E(f341(f138(x36561,x36562,x36563,x36564),f122(x36562)),x36564) % 19.23/19.03 [3693]E(f341(f186(f862(x36931,x36932)),f223(x36931,x36932,x36933,x36934)),f2(a857)) % 19.23/19.03 [3718]E(f341(f260(x37181,x37182,x37183),f258(x37181,x37182,x37183,x37184)),x37184) % 19.23/19.03 [3773]E(f341(f237(f861(x37731),x37732,f188(x37731),f341(f18(f861(x37731),x37732),f188(x37731))),f341(x37733,x37734)),f188(x37731)) % 19.23/19.03 [3816]E(f341(f341(f110(f864(x38161,a850)),f174(x38161,x38162,x38163)),f174(x38161,x38162,x38164)),f174(x38161,x38162,f175(x38161,x38162,x38164,x38163))) % 19.23/19.03 [3845]E(f341(f341(f262(x38451,x38452,x38453,f863(x38452,x38453)),x38454),f250(x38452,x38453)),x38454) % 19.23/19.03 [3854]E(f238(x38541,x38542,x38543,x38544,f188(x38542)),x38543) % 19.23/19.03 [3855]E(f177(x38551,x38552,x38553,x38554,f122(x38552)),x38553) % 19.23/19.03 [3856]E(f177(x38561,x38562,x38563,f122(x38561),x38564),x38563) % 19.23/19.03 [4141]P40(x41411,x41412,x41413,x41414,f185(f864(x41411,a850)),x41414) % 19.23/19.03 [4451]~E(f341(f313(x44511,x44512),x44513),f341(f322(x44512,x44511),x44514)) % 19.23/19.03 [3188]E(f341(f341(f18(x31881,x31882),x31883),x31884),x31883) % 19.23/19.03 [3300]E(f341(f341(f204(x33001,x33002),x33003),f341(f235(x33001),x33004)),f341(f235(x33002),f341(x33003,x33004))) % 19.23/19.03 [3475]E(f157(x34751,x34752,f341(f133(x34751,x34753),x34754)),f341(f133(x34751,x34753),f157(x34751,x34752,x34754))) % 19.23/19.03 [3509]E(f341(f341(f74(x35091,x35092,x35093),x35094),f185(f864(x35091,a850))),x35094) % 19.23/19.03 [3531]E(f341(f341(f158(x35311),f341(f341(f146(x35311),x35312),x35313)),f341(a121,x35314)),f341(f341(f158(x35311),x35313),x35314)) % 19.23/19.03 [3593]E(f341(f341(x35931,x35932),f341(f180(x35933,x35934,x35931),x35932)),f341(f180(x35933,x35934,x35931),f341(a121,x35932))) % 19.23/19.03 [3633]E(f258(x36331,x36332,x36333,f341(f260(x36331,x36332,x36333),x36334)),x36334) % 19.23/19.03 [3691]E(f341(f341(f154(x36911,f341(f341(f146(x36911),x36912),x36913)),f2(a857)),x36914),f341(f341(f146(x36911),x36914),x36913)) % 19.23/19.03 [3701]E(f341(f341(f54(f864(x37011,a850),f864(x37012,a850)),x37013),f312(x37011,x37012,x37014)),f341(f312(x37011,x37012,x37014),f52(f864(x37011,a850),x37013))) % 19.23/19.03 [3702]E(f341(f341(f54(f864(x37021,a850),f864(x37022,a850)),x37023),f314(x37022,x37021,x37024)),f341(f314(x37022,x37021,x37024),f52(f864(x37021,a850),x37023))) % 19.23/19.03 [3801]E(f174(x38011,x38012,f178(x38011,x38012,x38013,x38014)),f341(f341(f111(f864(x38011,a850)),f174(x38011,x38012,x38013)),x38014)) % 19.23/19.03 [3820]E(f341(f138(x38201,x38202,f341(f9(x38202,x38201,x38201),x38203),x38204),f341(f148(x38202),f122(x38202))),x38204) % 19.23/19.03 [3866]E(f85(x38661,x38662,x38663,x38664,f185(f864(x38661,a850))),x38663) % 19.23/19.03 [3912]E(f341(f341(f341(f341(f81(x39121,f861(x39122)),f341(f18(f861(x39122),x39121),f188(x39122))),x39123),f188(x39122)),x39124),f188(x39122)) % 19.23/19.03 [4060]E(f328(x40601,x40602,x40603,f341(f341(f10(f865(x40601,x40603),x40602,x40601),x40604),f313(x40601,x40603)),f341(f341(f10(f865(x40601,x40603),x40602,x40603),x40604),f322(x40603,x40601))),x40604) % 19.23/19.03 [4070]E(f341(f260(x40701,x40702,x40703),f341(f341(f10(f864(x40702,f863(x40701,x40702)),f864(x40702,x40703),x40701),f341(f10(f863(x40701,x40702),x40703,x40702),x40704)),f250(x40701,x40702))),x40704) % 19.23/19.03 [3376]E(f341(f259(x33761,x33762),f341(f341(f250(x33761,x33762),x33763),x33764)),x33764) % 19.23/19.03 [3377]E(f341(f249(x33771,x33772),f341(f341(f250(x33771,x33772),x33773),x33774)),x33773) % 19.23/19.03 [3414]E(f341(f186(f858(x34141)),f341(f341(f149(x34142,x34141),x34143),x34144)),f341(f186(f858(x34142)),x34144)) % 19.23/19.03 [3415]E(f341(f186(f858(x34151)),f341(f341(f154(x34151,x34152),x34153),x34154)),f341(f186(f858(x34151)),x34152)) % 19.23/19.03 [3436]E(f341(f341(f135(x34361),f341(a121,x34362)),f341(f341(f146(x34361),x34363),x34364)),f341(f341(f135(x34361),x34362),x34364)) % 19.23/19.03 [3511]E(f341(f341(f311(x35111),x35112),f341(f341(f311(x35111),x35113),x35114)),f341(f341(f311(x35111),x35113),f341(f341(f311(x35111),x35112),x35114))) % 19.23/19.03 [3514]E(f341(f341(f149(x35141,x35142),x35143),f123(x35141,x35144)),f123(x35142,f341(f341(f149(x35141,x35142),x35143),x35144))) % 19.23/19.03 [3529]E(f341(f148(x35291),f341(f341(f149(x35292,x35291),x35293),x35294)),f341(f341(f149(x35292,x35291),x35293),f341(f148(x35292),x35294))) % 19.23/19.03 [3530]E(f341(f341(f149(x35301,x35302),x35303),f341(f162(x35301),x35304)),f341(f162(x35302),f341(f341(f149(x35301,x35302),x35303),x35304))) % 19.23/19.03 [3539]E(f341(f341(f164(x35391),f341(a121,x35392)),f341(f341(f146(x35391),x35393),x35394)),f341(f341(f146(x35391),x35393),f341(f341(f164(x35391),x35392),x35394))) % 19.23/19.03 [3543]E(f341(f163(x35431),f341(f341(f149(x35432,x35431),x35433),x35434)),f341(f312(x35432,x35431,x35433),f341(f163(x35432),x35434))) % 19.23/19.03 [3592]E(f19(x35921,x35922,x35923,f341(a5,f341(a121,f341(a22,x35924)))),f341(x35923,x35924)) % 19.23/19.03 [3596]E(f341(f341(f132(x35961),f341(f133(x35961,x35962),x35963)),f341(f133(x35961,x35962),x35964)),f341(f133(x35961,x35962),f341(f341(f132(x35961),x35963),x35964))) % 19.23/19.03 [3623]E(f341(f287(x36231,x36231),f341(f341(f289(x36232,x36231),x36233),x36234)),f341(f341(f289(x36232,x36231),f341(f287(x36232,x36232),x36233)),x36234)) % 19.23/19.03 [3634]E(f341(f341(f290(x36341,x36342,x36343),x36344),f185(f864(f863(x36342,x36343),a850))),f185(f864(f863(x36341,x36343),a850))) % 19.23/19.03 [3635]E(f341(f341(f164(x36351),f341(f341(f3(a857),x36352),x36353)),f341(f341(f135(x36351),x36353),x36354)),f341(f341(f135(x36351),x36353),f341(f341(f164(x36351),x36352),x36354))) % 19.23/19.03 [3657]E(f341(f341(f341(f282(x36571),x36572),x36573),x36574),f341(f250(f864(a108,f864(a850,f861(f859(x36571)))),f863(a108,a108)),f341(f57(x36571),x36572))) % 19.23/19.03 [3683]E(f53(f864(x36831,a850),f341(f312(x36832,f864(x36831,a850),x36833),x36834)),f341(f341(f55(x36832,f864(x36831,a850)),x36834),x36833)) % 19.23/19.03 [3684]E(f52(f864(x36841,a850),f341(f312(x36842,f864(x36841,a850),x36843),x36844)),f341(f341(f54(x36842,f864(x36841,a850)),x36844),x36843)) % 19.23/19.03 [3685]E(f341(f186(f858(f863(x36851,x36852))),f341(f341(f172(x36851,x36852),x36853),x36854)),f341(f341(f245(a857),f341(f186(f858(x36851)),x36853)),f341(f186(f858(x36852)),x36854))) % 19.23/19.03 [3687]E(f341(f314(x36871,x36872,x36873),f341(f88(f864(x36872,a850)),x36874)),f341(f88(f864(x36871,a850)),f341(f314(x36871,x36872,x36873),x36874))) % 19.23/19.03 [3719]E(f341(f178(x37191,x37192,x37193,f185(f864(x37191,a850))),x37194),f188(x37192)) % 19.23/19.03 [3738]E(f341(f314(x37381,x37382,x37383),f341(f265(x37382),x37384)),f341(f265(x37381),f341(f341(f10(x37382,a850,x37381),x37384),x37383))) % 19.23/19.03 [3755]E(f341(f341(f158(x37551),f341(f341(f132(x37551),x37552),f341(f341(f146(x37551),x37553),x37554))),f341(f186(f858(x37551)),x37552)),x37553) % 19.23/19.03 [3760]E(f341(f178(x37601,x37602,f341(f18(f861(x37602),x37601),f188(x37602)),x37603),x37604),f188(x37602)) % 19.23/19.03 [3782]E(f341(f312(x37821,x37822,x37823),f341(f314(x37821,x37822,x37823),x37824)),f341(f341(f111(f864(x37822,a850)),x37824),f341(f312(x37821,x37822,x37823),f248(f864(x37821,a850))))) % 19.23/19.03 [3800]P85(f341(f341(f343(x38001),f341(x38002,x38003)),f341(f312(x38004,x38001,x38002),f248(f864(x38004,a850))))) % 19.23/19.03 [3808]E(f21(x38081,x38082,x38083,f341(a5,f341(a121,f341(a22,x38084)))),f341(f341(x38083,x38084),f21(x38081,x38082,x38083,x38084))) % 19.23/19.03 [3823]E(f150(x38231,x38232,f341(f341(f146(x38231),x38233),x38234)),f341(f341(f89(a857),f341(f341(f89(a857),f341(x38232,x38233)),f150(x38231,x38232,x38234))),f341(a121,f2(a857)))) % 19.23/19.03 [3836]E(f181(f858(x38361),f341(f341(f146(x38361),x38362),x38363),f341(f341(f9(a857,f858(x38361),f858(x38361)),f135(x38361)),x38363),x38364),f341(f341(f135(x38361),x38364),f341(f341(f146(x38361),x38362),x38363))) % 19.23/19.03 [3837]P26(x38371,f863(x38372,x38371),f345(x38373,x38374,x38372,x38371),f341(f341(f54(x38372,f864(x38371,a850)),x38374),x38373)) % 19.23/19.03 [3846]E(f341(f341(f3(f864(x38461,a850)),f341(f341(f3(f864(x38461,a850)),x38462),x38463)),f341(f341(f311(x38461),x38464),f185(f864(x38461,a850)))),f341(f341(f3(f864(x38461,a850)),x38462),f341(f341(f311(x38461),x38464),x38463))) % 19.23/19.03 [3859]E(f341(f341(f179(f864(x38591,x38592),f864(x38591,x38592)),x38593),f82(x38592,x38592,x38591,x38594)),f82(x38592,x38592,x38591,f341(f341(f179(x38592,x38592),x38593),x38594))) % 19.23/19.03 [3934]E(f341(f341(f341(f179(f858(x39341),f858(x39341)),x39342),f147(x39341)),f341(f341(f341(f179(f858(x39341),f858(x39341)),x39343),f147(x39341)),x39344)),f341(f341(f341(f179(f858(x39341),f858(x39341)),f341(f341(f89(a857),x39342),x39343)),f147(x39341)),x39344)) % 19.23/19.03 [3983]E(f341(f341(f110(f864(f865(x39831,x39832),a850)),f341(f312(x39831,f865(x39831,x39832),f313(x39831,x39832)),x39833)),f341(f312(x39832,f865(x39831,x39832),f322(x39832,x39831)),x39834)),f323(x39831,x39832,x39833,x39834)) % 19.23/19.03 [4024]P85(f341(f341(f241(f864(x40241,a850)),f341(f163(x40241),f341(f341(f154(x40241,x40242),x40243),x40244))),f341(f341(f311(x40241),x40244),f341(f163(x40241),x40242)))) % 19.23/19.03 [4058]E(f341(f341(f54(f864(x40581,a850),f864(f863(x40581,x40582),a850)),x40583),f341(f341(f9(f864(x40581,a850),f864(x40581,f864(x40582,a850)),f864(f863(x40581,x40582),a850)),f257(x40581,x40582)),x40584)),f341(f341(f257(x40581,x40582),f52(f864(x40581,a850),x40583)),x40584)) % 19.23/19.03 [4095]E(f212(x40951,x40952,x40953,f341(f82(x40952,f864(a108,f864(a108,f864(f863(a108,a108),f864(a108,f859(x40952))))),x40951,f211(x40952)),x40954)),f213(x40951,x40952,x40954,x40953)) % 19.23/19.03 [4112]E(f208(x41121,x41122,x41123,f341(f82(x41122,f864(a108,f864(a108,f864(f863(a108,a108),f864(a108,f859(f861(x41122)))))),x41121,f207(x41122)),x41124)),f209(x41121,x41122,x41124,x41123)) % 19.23/19.03 [4116]P85(f341(f76(x41161,x41162,x41163,x41164,f185(f864(x41161,a850))),x41164)) % 19.23/19.03 [4162]E(f341(f341(f54(x41621,f864(x41622,a850)),x41623),f341(f341(f9(x41621,f864(x41622,a850),f864(x41622,a850)),f341(f341(f10(x41622,f864(f864(x41622,a850),f864(x41622,a850)),x41621),f311(x41622)),x41624)),f185(f864(x41622,a850)))),f341(f312(x41621,x41622,x41624),x41623)) % 19.23/19.03 [4168]P85(f341(f341(f241(f864(x41681,a850)),f341(f268(x41682,x41681),f341(f341(f111(f864(f863(x41682,x41681),a850)),x41683),x41684))),f341(f341(f111(f864(x41681,a850)),f341(f268(x41682,x41681),x41683)),f341(f268(x41682,x41681),x41684)))) % 19.23/19.03 [4169]P85(f341(f341(f241(f864(x41691,a850)),f341(f270(x41691,x41692),f341(f341(f111(f864(f863(x41691,x41692),a850)),x41693),x41694))),f341(f341(f111(f864(x41691,a850)),f341(f270(x41691,x41692),x41693)),f341(f270(x41691,x41692),x41694)))) % 19.23/19.03 [4228]P85(f341(f341(f241(f864(f863(x42281,x42282),a850)),f341(f312(x42282,f863(x42281,x42282),f345(x42283,x42284,x42281,x42282)),f341(f341(f54(x42281,f864(x42282,a850)),x42284),x42283))),f341(f341(f257(x42281,x42282),x42284),x42283))) % 19.23/19.03 [4229]E(f280(x42291,x42292,x42293,f341(f82(x42292,f864(a108,f864(a108,f864(f863(a108,a108),f863(f864(a108,f864(a850,f861(f859(x42292)))),f863(a108,a108))))),x42291,f282(x42292)),x42294)),f283(x42291,x42292,x42294,x42293)) % 19.23/19.03 [4267]E(f94(f863(x42671,x42672),f341(f260(x42671,x42672,a850),f341(f341(f9(x42671,f864(x42672,a850),f864(x42672,a850)),f341(f341(f10(f864(a850,a850),f864(f864(x42672,a850),f864(x42672,a850)),x42671),f10(a850,a850,x42672)),f341(f341(f10(a850,f864(a850,a850),x42671),a339),f341(a338,x42673)))),f341(a338,x42674)))),f341(f341(f250(x42671,x42672),x42673),x42674)) % 19.23/19.03 [4268]E(f99(f863(x42681,x42682),f341(f260(x42681,x42682,a850),f341(f341(f9(x42681,f864(x42682,a850),f864(x42682,a850)),f341(f341(f10(f864(a850,a850),f864(f864(x42682,a850),f864(x42682,a850)),x42681),f10(a850,a850,x42682)),f341(f341(f10(a850,f864(a850,a850),x42681),a339),f341(a338,x42683)))),f341(a338,x42684)))),f341(f341(f250(x42681,x42682),x42683),x42684)) % 19.23/19.03 [4338]E(f341(f341(f260(f858(x43381),f858(x43381),f863(f858(x43381),f858(x43381))),f341(f341(f20(f858(x43381),f864(f858(x43381),f863(f858(x43381),f858(x43381))),f864(f858(x43381),f863(f858(x43381),f858(x43381)))),f341(f341(f10(f864(f858(x43381),f864(f863(f858(x43381),f858(x43381)),f863(f858(x43381),f858(x43381)))),f864(f864(f858(x43381),f863(f858(x43381),f858(x43381))),f864(f858(x43381),f863(f858(x43381),f858(x43381)))),f858(x43381)),f20(f858(x43381),f863(f858(x43381),f858(x43381)),f863(f858(x43381),f858(x43381)))),f341(f341(f10(f864(f858(x43381),f863(f858(x43381),f858(x43381))),f864(f858(x43381),f864(f863(f858(x43381),f858(x43381)),f863(f858(x43381),f858(x43381)))),f858(x43381)),f341(f10(f863(f858(x43381),f858(x43381)),f864(f863(f858(x43381),f858(x43381)),f863(f858(x43381),f858(x43381))),f858(x43381)),f341(f105(f863(f858(x43381),f858(x43381))),f341(x43382,x43383)))),f341(f341(f10(f858(x43381),f864(f858(x43381),f863(f858(x43381),f858(x43381))),f858(x43381)),f250(f858(x43381),f858(x43381))),f341(f146(x43381),x43383))))),f341(f341(f9(f858(x43381),f864(f858(x43381),f858(x43381)),f864(f858(x43381),f863(f858(x43381),f858(x43381)))),f341(f341(f10(f864(f858(x43381),f863(f858(x43381),f858(x43381))),f864(f864(f858(x43381),f858(x43381)),f864(f858(x43381),f863(f858(x43381),f858(x43381)))),f858(x43381)),f10(f858(x43381),f863(f858(x43381),f858(x43381)),f858(x43381))),f250(f858(x43381),f858(x43381)))),f341(f146(x43381),x43383)))),f161(x43381,x43382,x43384)),f161(x43381,x43382,f341(f341(f146(x43381),x43383),x43384))) % 19.23/19.03 [4343]E(f341(f138(f864(x43431,f861(x43432)),f863(x43431,x43432),f341(f9(f863(x43431,x43432),f864(x43431,f861(x43432)),f864(x43431,f861(x43432))),f341(f260(x43431,x43432,f864(f864(x43431,f861(x43432)),f864(x43431,f861(x43432)))),f341(f341(f9(x43431,f864(x43432,f861(x43432)),f864(x43432,f864(f864(x43431,f861(x43432)),f864(x43431,f861(x43432))))),f341(f341(f10(f864(f861(x43432),f864(f864(x43431,f861(x43432)),f864(x43431,f861(x43432)))),f864(f864(x43432,f861(x43432)),f864(x43432,f864(f864(x43431,f861(x43432)),f864(x43431,f861(x43432))))),x43431),f10(f861(x43432),f864(f864(x43431,f861(x43432)),f864(x43431,f861(x43432))),x43432)),f341(f341(f10(f864(f864(x43431,f861(x43432)),f864(f861(x43432),f864(x43431,f861(x43432)))),f864(f861(x43432),f864(f864(x43431,f861(x43432)),f864(x43431,f861(x43432)))),x43431),f9(f864(x43431,f861(x43432)),f861(x43432),f864(x43431,f861(x43432)))),f341(f9(f864(x43431,f861(x43432)),x43431,f864(f861(x43432),f864(x43431,f861(x43432)))),f81(x43431,f861(x43432)))))),f235(x43432)))),x43433),f341(f148(f863(x43431,x43432)),x43434)),f175(x43431,x43432,x43433,f171(x43431,x43432,x43434))) % 19.23/19.03 [3454]E(f341(f186(f856(x34541)),f341(f341(f341(f100(x34541),x34542),x34543),x34544)),f2(a857)) % 19.23/19.03 [3571]E(f341(f341(f164(x35711),x35712),f341(f341(f164(x35711),x35713),x35714)),f341(f341(f164(x35711),f341(f341(f245(a857),x35712),x35713)),x35714)) % 19.23/19.03 [3572]E(f341(f341(f135(x35721),x35722),f341(f341(f135(x35721),x35723),x35724)),f341(f341(f135(x35721),f341(f341(f89(a857),x35722),x35723)),x35724)) % 19.23/19.03 [3584]E(f341(f341(f132(x35841),f341(f341(f146(x35841),x35842),x35843)),x35844),f341(f341(f146(x35841),x35842),f341(f341(f132(x35841),x35843),x35844))) % 19.23/19.03 [3585]E(f341(f341(f132(x35851),f341(f341(f132(x35851),x35852),x35853)),x35854),f341(f341(f132(x35851),x35852),f341(f341(f132(x35851),x35853),x35854))) % 19.23/19.03 [3667]E(f341(f341(f158(x36671),f341(f341(f146(x36671),x36672),x36673)),x36674),f181(x36671,x36672,f341(f158(x36671),x36673),x36674)) % 19.23/19.03 [3676]E(f341(f341(f179(x36761,x36761),x36762),f341(f341(f179(x36761,x36761),x36763),x36764)),f341(f341(f179(x36761,x36761),f341(f341(f90(a857),x36763),x36762)),x36764)) % 19.23/19.03 [3704]E(f341(f341(f110(f864(x37041,a850)),x37042),f341(f341(f311(x37041),x37043),x37044)),f341(f341(f311(x37041),x37043),f341(f341(f110(f864(x37041,a850)),x37042),x37044))) % 19.23/19.03 [3722]E(f341(f341(f341(f179(x37221,x37221),x37222),x37223),f341(x37223,x37224)),f341(x37223,f341(f341(f341(f179(x37221,x37221),x37222),x37223),x37224))) % 19.23/19.03 [3729]E(f341(f341(f290(x37291,x37292,x37293),f185(f864(f863(x37291,x37292),a850))),x37294),f185(f864(f863(x37291,x37293),a850))) % 19.23/19.03 [3744]E(f341(f341(f110(f864(x37441,a850)),f341(f341(f311(x37441),x37442),x37443)),x37444),f341(f341(f311(x37441),x37442),f341(f341(f110(f864(x37441,a850)),x37443),x37444))) % 19.23/19.03 [3762]E(f341(f50(f863(x37621,x37622)),f341(f341(f257(x37621,x37622),x37623),f341(f18(f864(x37622,a850),x37621),x37624))),f341(f341(f90(a857),f341(f50(x37621),x37623)),f341(f50(x37622),x37624))) % 19.23/19.03 [3770]E(f341(f341(f111(f864(x37701,a850)),f341(f341(f311(x37701),x37702),x37703)),f341(f341(f311(x37701),x37702),x37704)),f341(f341(f311(x37701),x37702),f341(f341(f111(f864(x37701,a850)),x37703),x37704))) % 19.23/19.03 [3780]E(f175(x37801,x37802,f171(x37801,x37802,x37803),f171(x37801,x37802,x37804)),f171(x37801,x37802,f341(f341(f132(f863(x37801,x37802)),x37804),x37803))) % 19.23/19.03 [3786]E(f341(f341(f110(f864(x37861,a850)),x37862),f341(f341(f110(f864(x37861,a850)),x37863),x37864)),f341(f341(f110(f864(x37861,a850)),x37863),f341(f341(f110(f864(x37861,a850)),x37862),x37864))) % 19.23/19.03 [3787]E(f341(f341(f111(f864(x37871,a850)),x37872),f341(f341(f111(f864(x37871,a850)),x37873),x37874)),f341(f341(f111(f864(x37871,a850)),x37873),f341(f341(f111(f864(x37871,a850)),x37872),x37874))) % 19.23/19.03 [3796]E(f74(x37961,x37962,f341(f341(f10(x37962,f864(x37962,x37962),x37961),x37963),x37964)),f341(f75(x37962,x37961,x37963),x37964)) % 19.23/19.03 [3805]E(f169(x38051,f341(f341(f149(f858(x38052),f858(x38051)),f341(f149(x38052,x38051),x38053)),x38054)),f341(f341(f149(f858(x38052),f858(x38051)),f341(f149(x38052,x38051),x38053)),f169(x38052,x38054))) % 19.23/19.03 [3822]E(f178(x38221,x38222,x38223,f341(f88(f864(x38221,a850)),f341(f341(f311(x38221),x38224),f185(f864(x38221,a850))))),f341(f341(f341(f81(x38221,f861(x38222)),x38223),x38224),f188(x38222))) % 19.23/19.03 [3880]E(f341(f82(x38801,x38801,x38801,f341(f341(f179(x38801,x38801),x38802),x38803)),f341(f341(f179(x38801,x38801),x38804),x38803)),f341(f341(f179(x38801,x38801),f341(f341(f89(a857),x38802),x38804)),x38803)) % 19.23/19.03 [3895]E(f341(f341(f341(f81(x38951,f861(x38952)),f171(x38951,x38952,x38953)),f341(f249(x38951,x38952),x38954)),f341(f235(x38952),f341(f259(x38951,x38952),x38954))),f171(x38951,x38952,f341(f341(f146(f863(x38951,x38952)),x38954),x38953))) % 19.23/19.03 [3904]E(f341(f341(f111(f864(x39041,a850)),f341(f341(f3(f864(x39041,a850)),x39042),x39043)),f341(f341(f3(f864(x39041,a850)),x39042),x39044)),f341(f341(f3(f864(x39041,a850)),x39042),f341(f341(f110(f864(x39041,a850)),x39043),x39044))) % 19.23/19.03 [3905]E(f341(f341(f110(f864(x39051,a850)),f341(f341(f3(f864(x39051,a850)),x39052),x39053)),f341(f341(f3(f864(x39051,a850)),x39052),x39054)),f341(f341(f3(f864(x39051,a850)),x39052),f341(f341(f111(f864(x39051,a850)),x39053),x39054))) % 19.23/19.03 [3906]E(f341(f341(f111(f864(x39061,a850)),f341(f341(f110(f864(x39061,a850)),x39062),x39063)),f341(f341(f110(f864(x39061,a850)),x39062),x39064)),f341(f341(f110(f864(x39061,a850)),x39062),f341(f341(f111(f864(x39061,a850)),x39063),x39064))) % 19.23/19.03 [3907]E(f341(f341(f3(f864(x39071,a850)),f341(f341(f111(f864(x39071,a850)),x39072),x39073)),f341(f341(f111(f864(x39071,a850)),x39072),x39074)),f341(f341(f111(f864(x39071,a850)),x39072),f341(f341(f3(f864(x39071,a850)),x39073),x39074))) % 19.23/19.03 [3908]E(f341(f341(f110(f864(x39081,a850)),f341(f341(f111(f864(x39081,a850)),x39082),x39083)),f341(f341(f111(f864(x39081,a850)),x39082),x39084)),f341(f341(f111(f864(x39081,a850)),x39082),f341(f341(f110(f864(x39081,a850)),x39083),x39084))) % 19.23/19.03 [3914]E(f341(f50(f863(x39141,x39142)),f341(f341(f257(x39141,x39142),f341(f341(f311(x39141),x39143),f185(f864(x39141,a850)))),f341(f18(f864(x39142,a850),x39141),x39144))),f341(f50(x39142),x39144)) % 19.23/19.03 [3950]E(f341(f341(f55(x39501,f864(x39502,a850)),x39503),f341(f341(f10(f864(x39502,a850),f864(x39502,a850),x39501),f88(f864(x39502,a850))),x39504)),f341(f88(f864(x39502,a850)),f341(f341(f54(x39501,f864(x39502,a850)),x39503),x39504))) % 19.23/19.03 [3951]E(f341(f341(f54(x39511,f864(x39512,a850)),x39513),f341(f341(f10(f864(x39512,a850),f864(x39512,a850),x39511),f88(f864(x39512,a850))),x39514)),f341(f88(f864(x39512,a850)),f341(f341(f55(x39511,f864(x39512,a850)),x39513),x39514))) % 19.23/19.03 [3967]E(f341(f341(f290(x39671,x39671,x39671),f341(f341(f179(f863(x39671,x39671),a850),x39672),x39673)),f341(f341(f179(f863(x39671,x39671),a850),x39674),x39673)),f341(f341(f179(f863(x39671,x39671),a850),f341(f341(f89(a857),x39672),x39674)),x39673)) % 19.23/19.03 [3999]E(f341(f341(f55(x39991,f864(f864(x39992,a850),a850)),x39993),f341(f341(f10(f864(x39992,a850),f864(f864(x39992,a850),a850),x39991),f310(x39992)),x39994)),f341(f310(x39992),f341(f341(f55(x39991,f864(x39992,a850)),x39993),x39994))) % 19.23/19.03 [4029]E(f341(f341(f54(f864(x40291,a850),f864(x40292,a850)),x40293),f341(f341(f9(f864(x40291,a850),f864(x40291,f864(x40292,a850)),f864(x40292,a850)),f54(x40291,f864(x40292,a850))),x40294)),f341(f341(f54(x40291,f864(x40292,a850)),f52(f864(x40291,a850),x40293)),x40294)) % 19.23/19.03 [4030]E(f341(f341(f55(f864(x40301,a850),f864(x40302,a850)),x40303),f341(f341(f9(f864(x40301,a850),f864(x40301,f864(x40302,a850)),f864(x40302,a850)),f55(x40301,f864(x40302,a850))),x40304)),f341(f341(f55(x40301,f864(x40302,a850)),f52(f864(x40301,a850),x40303)),x40304)) % 19.23/19.03 [4035]E(f341(f341(f149(x40351,x40352),x40353),f341(f138(f858(x40351),f858(x40351),f132(x40351),f122(x40351)),x40354)),f341(f138(f858(x40352),f858(x40352),f132(x40352),f122(x40352)),f341(f341(f149(f858(x40351),f858(x40352)),f341(f149(x40351,x40352),x40353)),x40354))) % 19.23/19.03 [4037]E(f181(f858(x40371),f122(x40371),f341(f341(f10(f858(x40371),f858(x40371),a857),f341(f146(x40371),x40372)),f341(f341(f9(a857,f858(x40371),f858(x40371)),f164(x40371)),x40373)),x40374),f341(f341(f164(x40371),x40374),f341(f341(f146(x40371),x40372),x40373))) % 19.23/19.03 [4079]P85(f341(f341(f241(f864(x40791,a850)),f341(f312(x40792,x40791,x40793),f341(f314(x40792,x40791,x40793),x40794))),x40794)) % 19.23/19.03 [4082]E(f341(f312(f863(x40821,x40822),f863(x40822,x40821),f341(f260(x40821,x40822,f863(x40822,x40821)),f341(f9(x40822,x40821,f863(x40822,x40821)),f250(x40822,x40821)))),f341(f341(f257(x40821,x40822),x40823),f341(f18(f864(x40822,a850),x40821),x40824))),f341(f341(f257(x40822,x40821),x40824),f341(f18(f864(x40821,a850),x40822),x40823))) % 19.23/19.03 [4091]E(f341(f341(f54(x40911,f864(x40912,a850)),x40913),f341(f341(f10(f864(x40911,a850),f864(x40912,a850),x40911),f286(x40911,x40912,x40914)),f341(f341(f9(x40911,f864(x40911,a850),f864(x40911,a850)),f311(x40911)),f185(f864(x40911,a850))))),f341(f286(x40911,x40912,x40914),x40913)) % 19.23/19.03 [4092]E(f341(f341(f54(x40921,f864(x40922,a850)),x40923),f341(f341(f10(f864(x40921,a850),f864(x40922,a850),x40921),f314(x40922,x40921,x40924)),f341(f341(f9(x40921,f864(x40921,a850),f864(x40921,a850)),f311(x40921)),f185(f864(x40921,a850))))),f341(f314(x40922,x40921,x40924),x40923)) % 19.23/19.03 [4182]E(f341(f341(f111(f864(x41821,a850)),f341(f341(f111(f864(x41821,a850)),f341(f341(f110(f864(x41821,a850)),x41822),x41823)),f341(f341(f110(f864(x41821,a850)),x41823),x41824))),f341(f341(f110(f864(x41821,a850)),x41824),x41822)),f341(f341(f110(f864(x41821,a850)),f341(f341(f110(f864(x41821,a850)),f341(f341(f111(f864(x41821,a850)),x41822),x41823)),f341(f341(f111(f864(x41821,a850)),x41823),x41824))),f341(f341(f111(f864(x41821,a850)),x41824),x41822))) % 19.23/19.03 [4241]E(f341(f138(f858(x42411),f858(x42411),f132(x42411),f122(x42411)),f341(f341(f149(x42412,f858(x42411)),f341(f341(f9(x42412,f858(x42411),f858(x42411)),f341(f341(f10(x42411,f864(f858(x42411),f858(x42411)),x42412),f146(x42411)),x42413)),f122(x42411))),x42414)),f341(f341(f149(x42412,x42411),x42413),x42414)) % 19.23/19.03 [4251]E(f341(f341(f95(a1,x42511),f341(f113(a1),f341(f341(f89(a1),x42512),a106))),f341(f341(f20(a1,x42511,x42511),f341(f341(f9(a1,x42511,f864(x42511,x42511)),f341(f341(f10(a850,f864(x42511,f864(x42511,x42511)),a1),f105(x42511)),a191)),x42513)),f341(f341(f10(a857,x42511,a1),x42514),a114))),f181(x42511,x42513,x42514,f341(f113(a857),x42512))) % 19.23/19.03 [4494]~P85(f341(f341(f185(f864(x44941,f864(x44942,a850))),x44943),x44944)) % 19.23/19.03 [3732]E(f341(f341(f158(x37321),f341(f341(f132(x37321),x37322),x37323)),f341(f341(f89(a857),f341(f186(f858(x37321)),x37322)),x37324)),f341(f341(f158(x37321),x37323),x37324)) % 19.23/19.03 [3737]E(f341(f341(f135(x37371),x37372),f341(f341(f164(x37371),f341(f341(f89(a857),x37373),x37372)),x37374)),f341(f341(f164(x37371),x37373),f341(f341(f135(x37371),x37372),x37374))) % 19.23/19.03 [3834]E(f341(f341(f110(f864(x38341,a850)),f341(f268(x38342,x38341),x38343)),f341(f268(x38342,x38341),x38344)),f341(f268(x38342,x38341),f341(f341(f110(f864(f863(x38342,x38341),a850)),x38343),x38344))) % 19.23/19.03 [3835]E(f341(f341(f110(f864(x38351,a850)),f341(f270(x38351,x38352),x38353)),f341(f270(x38351,x38352),x38354)),f341(f270(x38351,x38352),f341(f341(f110(f864(f863(x38351,x38352),a850)),x38353),x38354))) % 19.23/19.03 [3840]E(f341(f341(f3(f864(x38401,a850)),f341(f341(f111(f864(x38401,a850)),x38402),x38403)),x38404),f341(f341(f111(f864(x38401,a850)),x38402),f341(f341(f3(f864(x38401,a850)),x38403),x38404))) % 19.23/19.03 [3841]E(f341(f341(f110(f864(x38411,a850)),f341(f341(f110(f864(x38411,a850)),x38412),x38413)),x38414),f341(f341(f110(f864(x38411,a850)),x38412),f341(f341(f110(f864(x38411,a850)),x38413),x38414))) % 19.23/19.03 [3842]E(f341(f341(f111(f864(x38421,a850)),f341(f341(f111(f864(x38421,a850)),x38422),x38423)),x38424),f341(f341(f111(f864(x38421,a850)),x38422),f341(f341(f111(f864(x38421,a850)),x38423),x38424))) % 19.23/19.03 [3882]E(f341(f341(f110(f864(f863(x38821,x38822),a850)),f341(f287(x38822,x38821),x38823)),f341(f287(x38822,x38821),x38824)),f341(f287(x38822,x38821),f341(f341(f110(f864(f863(x38822,x38821),a850)),x38823),x38824))) % 19.23/19.03 [3883]E(f341(f341(f111(f864(f863(x38831,x38832),a850)),f341(f287(x38832,x38831),x38833)),f341(f287(x38832,x38831),x38834)),f341(f287(x38832,x38831),f341(f341(f111(f864(f863(x38832,x38831),a850)),x38833),x38834))) % 19.23/19.03 [3954]E(f341(f341(f110(f864(x39541,a850)),f341(f341(f3(f864(x39541,a850)),x39542),x39543)),f341(f341(f3(f864(x39541,a850)),x39544),x39543)),f341(f341(f3(f864(x39541,a850)),f341(f341(f110(f864(x39541,a850)),x39542),x39544)),x39543)) % 19.23/19.03 [3955]E(f341(f341(f111(f864(x39551,a850)),f341(f341(f110(f864(x39551,a850)),x39552),x39553)),f341(f341(f110(f864(x39551,a850)),x39554),x39553)),f341(f341(f110(f864(x39551,a850)),f341(f341(f111(f864(x39551,a850)),x39552),x39554)),x39553)) % 19.23/19.03 [3956]E(f341(f341(f3(f864(x39561,a850)),f341(f341(f111(f864(x39561,a850)),x39562),x39563)),f341(f341(f111(f864(x39561,a850)),x39564),x39563)),f341(f341(f111(f864(x39561,a850)),f341(f341(f3(f864(x39561,a850)),x39562),x39564)),x39563)) % 19.23/19.03 [3957]E(f341(f341(f110(f864(x39571,a850)),f341(f341(f111(f864(x39571,a850)),x39572),x39573)),f341(f341(f111(f864(x39571,a850)),x39574),x39573)),f341(f341(f111(f864(x39571,a850)),f341(f341(f110(f864(x39571,a850)),x39572),x39574)),x39573)) % 19.23/19.03 [3958]E(f341(f341(f3(f864(x39581,a850)),f341(f341(f111(f864(x39581,a850)),x39582),x39583)),f341(f341(f111(f864(x39581,a850)),x39584),x39583)),f341(f341(f3(f864(x39581,a850)),f341(f341(f111(f864(x39581,a850)),x39582),x39583)),x39584)) % 19.23/19.03 [3970]E(f341(f341(f3(f864(x39701,a850)),f341(f341(f3(f864(x39701,a850)),x39702),f341(f341(f311(x39701),x39703),f185(f864(x39701,a850))))),x39704),f341(f341(f3(f864(x39701,a850)),x39702),f341(f341(f311(x39701),x39703),x39704))) % 19.23/19.03 [4026]E(f341(f341(f110(f864(x40261,a850)),f341(f341(f311(x40261),x40262),f341(f341(f311(x40261),x40263),f185(f864(x40261,a850))))),f341(f285(x40261),x40264)),f341(f285(x40261),f341(f341(f311(f863(x40261,x40261)),f341(f341(f250(x40261,x40261),x40262),x40263)),x40264))) % 19.23/19.03 [4053]E(f341(f341(f54(a857,f864(x40531,a850)),f341(f302(a857),x40532)),f341(f341(f10(a857,f864(x40531,a850),a857),x40533),f341(f341(f9(a857,a857,a857),f89(a857)),x40534))),f341(f341(f54(a857,f864(x40531,a850)),f304(a857,x40534,f341(f341(f89(a857),x40532),x40534))),x40533)) % 19.23/19.03 [4054]E(f166(x40541,f341(f286(x40541,x40541,x40542),f341(f341(f311(x40541),x40543),f185(f864(x40541,a850)))),f341(f286(f858(x40541),f858(x40541),f153(x40541,x40542)),f341(f341(f311(f858(x40541)),x40544),f185(f864(f858(x40541),a850))))),f341(f286(f858(x40541),f858(x40541),f153(x40541,x40542)),f341(f341(f311(f858(x40541)),f341(f341(f146(x40541),x40543),x40544)),f185(f864(f858(x40541),a850))))) % 19.23/19.03 [4117]E(f171(x41171,x41172,f341(f341(f149(x41171,f863(x41171,x41172)),f341(f341(f20(x41171,x41172,f863(x41171,x41172)),f250(x41171,x41172)),x41173)),x41174)),f178(x41171,x41172,f341(f82(x41172,f861(x41172),x41171,f235(x41172)),x41173),f341(f163(x41171),x41174))) % 19.23/19.03 [4120]E(f341(f265(x41201),f341(f341(f9(x41201,f864(x41202,a850),a850),f341(f341(f10(x41202,f864(f864(x41202,a850),a850),x41201),f343(x41202)),x41203)),x41204)),f341(f314(x41201,x41202,x41203),x41204)) % 19.23/19.03 [4213]E(f341(f265(x42131),f341(f341(f9(x42131,f864(f863(x42132,x42131),a850),a850),f341(f341(f10(f863(x42132,x42131),f864(f864(f863(x42132,x42131),a850),a850),x42131),f343(f863(x42132,x42131))),f341(f250(x42132,x42131),x42133))),x42134)),f341(f286(x42132,x42131,x42134),f341(f341(f311(x42132),x42133),f185(f864(x42132,a850))))) % 19.23/19.03 [4227]E(f341(f341(f149(f863(x42271,a857),x42271),f249(x42271,a857)),f341(f133(f863(x42271,a857),f341(f341(f10(a857,a850,f863(x42271,a857)),x42272),f341(f341(f10(a857,a857,f863(x42271,a857)),a121),f259(x42271,a857)))),f341(f341(f172(x42271,a857),x42273),x42274))),f341(f341(f149(f863(x42271,a857),x42271),f249(x42271,a857)),f341(f133(f863(x42271,a857),f341(f341(f10(a857,a850,f863(x42271,a857)),x42272),f259(x42271,a857))),f341(f341(f172(x42271,a857),x42273),f341(f341(f149(a857,a857),a121),x42274))))) % 19.23/19.03 [4234]P85(f341(f341(f241(f864(f864(x42341,a850),a850)),f341(f341(f54(x42342,f864(f864(x42341,a850),a850)),x42343),f341(f341(f10(f864(x42341,a850),f864(f864(x42341,a850),a850),x42342),f310(x42341)),x42344))),f341(f310(x42341),f341(f341(f54(x42342,f864(x42341,a850)),x42343),x42344)))) % 19.23/19.03 [4274]E(f341(f341(f95(a1,x42741),f341(f113(a1),f341(f341(f89(a1),x42742),a106))),f341(f341(f20(a1,x42741,x42741),f341(f341(f9(a1,x42741,f864(x42741,x42741)),f341(f341(f10(a850,f864(x42741,f864(x42741,x42741)),a1),f105(x42741)),a191)),x42743)),f341(f341(f20(a1,x42741,x42741),f341(f341(f10(a857,f864(x42741,x42741),a1),x42744),a114)),f341(f341(f10(a857,x42741,a1),f180(x42741,x42743,x42744)),a114)))),f341(f180(x42741,x42743,x42744),f341(f113(a857),x42742))) % 19.23/19.03 [4277]E(f341(f341(f149(x42771,x42772),f341(f82(f861(x42772),x42772,x42771,f239(x42772)),x42773)),f341(f133(x42771,f341(f341(f10(a850,a850,x42771),a337),f341(f341(f9(x42771,f861(x42772),a850),f341(f341(f10(f861(x42772),f864(f861(x42772),a850),x42771),a338),x42773)),f188(x42772)))),x42774)),f159(x42771,x42772,x42773,x42774)) % 19.23/19.03 [4298]E(f341(f265(f863(x42981,x42982)),f341(f260(x42981,x42982,a850),f341(f341(f9(x42981,f864(x42982,a850),f864(x42982,a850)),f341(f341(f10(f864(a850,a850),f864(f864(x42982,a850),f864(x42982,a850)),x42981),f10(a850,a850,x42982)),f341(f341(f10(a850,f864(a850,a850),x42981),a339),f341(f341(f9(x42981,f864(x42981,a850),a850),f343(x42981)),x42983)))),f341(f341(f9(x42982,f864(x42982,a850),a850),f343(x42982)),x42984)))),f231(x42981,x42982,x42983,x42984)) % 19.23/19.03 [4331]E(f341(f341(f54(x43311,f864(f863(x43311,x43312),a850)),x43313),f341(f341(f20(x43311,f864(x43312,f864(f863(x43311,x43312),a850)),f864(f863(x43311,x43312),a850)),f341(f341(f10(f864(x43312,a850),f864(f864(x43312,f864(f863(x43311,x43312),a850)),f864(f863(x43311,x43312),a850)),x43311),f54(x43312,f864(f863(x43311,x43312),a850))),x43314)),f341(f341(f9(x43311,f864(f863(x43311,x43312),a850),f864(x43312,f864(f863(x43311,x43312),a850))),f341(f341(f10(f864(x43312,f864(f864(f863(x43311,x43312),a850),f864(f863(x43311,x43312),a850))),f864(f864(f863(x43311,x43312),a850),f864(x43312,f864(f863(x43311,x43312),a850))),x43311),f9(x43312,f864(f863(x43311,x43312),a850),f864(f863(x43311,x43312),a850))),f341(f341(f10(f864(x43312,f863(x43311,x43312)),f864(x43312,f864(f864(f863(x43311,x43312),a850),f864(f863(x43311,x43312),a850))),x43311),f341(f10(f863(x43311,x43312),f864(f864(f863(x43311,x43312),a850),f864(f863(x43311,x43312),a850)),x43312),f311(f863(x43311,x43312)))),f250(x43311,x43312)))),f185(f864(f863(x43311,x43312),a850))))),f341(f341(f257(x43311,x43312),x43313),x43314)) % 19.23/19.03 [3891]E(f341(f341(f132(x38911),f341(f341(f164(x38911),x38912),x38913)),f341(f341(f164(x38911),f341(f341(f3(a857),x38912),f341(f186(f858(x38911)),x38913))),x38914)),f341(f341(f164(x38911),x38912),f341(f341(f132(x38911),x38913),x38914))) % 19.23/19.03 [3892]E(f341(f341(f132(x38921),f341(f341(f135(x38921),x38922),x38923)),f341(f341(f135(x38921),f341(f341(f3(a857),x38922),f341(f186(f858(x38921)),x38923))),x38924)),f341(f341(f135(x38921),x38922),f341(f341(f132(x38921),x38923),x38924))) % 19.23/19.03 [3943]E(f341(f341(f89(a857),f341(f341(f90(a857),x39431),x39432)),f341(f341(f89(a857),f341(f341(f90(a857),x39433),x39432)),x39434)),f341(f341(f89(a857),f341(f341(f90(a857),f341(f341(f89(a857),x39431),x39433)),x39432)),x39434)) % 19.23/19.03 [4147]P85(f341(f341(f241(f864(x41471,a850)),f341(f341(f3(f864(x41471,a850)),f341(f268(x41472,x41471),x41473)),f341(f268(x41472,x41471),x41474))),f341(f268(x41472,x41471),f341(f341(f3(f864(f863(x41472,x41471),a850)),x41473),x41474)))) % 19.23/19.03 [4148]P85(f341(f341(f241(f864(x41481,a850)),f341(f341(f3(f864(x41481,a850)),f341(f270(x41481,x41482),x41483)),f341(f270(x41481,x41482),x41484))),f341(f270(x41481,x41482),f341(f341(f3(f864(f863(x41481,x41482),a850)),x41483),x41484)))) % 19.23/19.03 [4253]E(f341(f341(f89(a1),f341(a98,f341(f286(f863(a857,a857),f863(a857,a857),a118),f341(f341(f311(f863(a857,a857)),f341(f341(f250(a857,a857),x42531),x42532)),f185(f864(f863(a857,a857),a850)))))),f341(a98,f341(f286(f863(a857,a857),f863(a857,a857),a118),f341(f341(f311(f863(a857,a857)),f341(f341(f250(a857,a857),x42533),x42534)),f185(f864(f863(a857,a857),a850)))))),f341(a98,f341(f286(f863(a857,a857),f863(a857,a857),a118),f341(f341(f311(f863(a857,a857)),f341(f341(f250(a857,a857),f341(f341(f89(a857),x42531),x42533)),f341(f341(f89(a857),x42532),x42534))),f185(f864(f863(a857,a857),a850)))))) % 19.23/19.03 [4293]E(f341(f341(f90(a1),f341(a98,f341(f286(f863(a857,a857),f863(a857,a857),a118),f341(f341(f311(f863(a857,a857)),f341(f341(f250(a857,a857),x42931),x42932)),f185(f864(f863(a857,a857),a850)))))),f341(a98,f341(f286(f863(a857,a857),f863(a857,a857),a118),f341(f341(f311(f863(a857,a857)),f341(f341(f250(a857,a857),x42933),x42934)),f185(f864(f863(a857,a857),a850)))))),f341(a98,f341(f286(f863(a857,a857),f863(a857,a857),a118),f341(f341(f311(f863(a857,a857)),f341(f341(f250(a857,a857),f341(f341(f89(a857),f341(f341(f90(a857),x42931),x42933)),f341(f341(f90(a857),x42932),x42934))),f341(f341(f89(a857),f341(f341(f90(a857),x42931),x42934)),f341(f341(f90(a857),x42932),x42933)))),f185(f864(f863(a857,a857),a850)))))) % 19.23/19.03 [4313]E(f341(f265(x43131),f341(f341(f10(f864(x43132,a850),a850,x43131),f97(x43132)),f341(f341(f10(f864(x43132,a850),f864(x43132,a850),x43131),f341(f20(x43132,a850,a850),f341(f341(f10(a850,f864(a850,a850),x43132),a344),f341(f341(f9(x43132,f864(x43132,a850),a850),f343(x43132)),x43133)))),f341(f341(f9(x43131,f864(x43132,f864(x43131,a850)),f864(x43132,a850)),f341(f341(f10(f864(f864(x43131,a850),a850),f864(f864(x43132,f864(x43131,a850)),f864(x43132,a850)),x43131),f10(f864(x43131,a850),a850,x43132)),f343(x43131))),x43134)))),f341(f341(f55(x43132,f864(x43131,a850)),x43133),x43134)) % 19.23/19.03 [4346]E(f341(f341(f290(x43461,x43461,x43461),f341(f341(f311(f863(x43461,x43461)),f341(f341(f250(x43461,x43461),x43462),x43463)),x43464)),f309(x43461,f341(f341(f311(f863(x43461,x43461)),f341(f341(f250(x43461,x43461),x43462),x43463)),x43464))),f341(f341(f110(f864(f863(x43461,x43461),a850)),f341(f341(f290(x43461,x43461,x43461),x43464),f309(x43461,x43464))),f341(f265(f863(x43461,x43461)),f341(f260(x43461,x43461,a850),f341(f341(f9(x43461,f864(x43461,a850),f864(x43461,a850)),f341(f341(f10(f864(a850,a850),f864(f864(x43461,a850),f864(x43461,a850)),x43461),f10(a850,a850,x43461)),f341(f341(f10(a850,f864(a850,a850),x43461),a339),f341(f341(f9(x43461,f864(f863(x43461,x43461),a850),a850),f341(f341(f10(f863(x43461,x43461),f864(f864(f863(x43461,x43461),a850),a850),x43461),f343(f863(x43461,x43461))),f341(f341(f9(x43461,x43461,f863(x43461,x43461)),f250(x43461,x43461)),x43462))),f309(x43461,x43464))))),f341(f341(f9(x43461,f864(f863(x43461,x43461),a850),a850),f341(f341(f10(f863(x43461,x43461),f864(f864(f863(x43461,x43461),a850),a850),x43461),f343(f863(x43461,x43461))),f341(f250(x43461,x43461),x43463))),f309(x43461,x43464))))))) % 19.23/19.03 [4149]E(f341(f133(x41491,f341(f341(f20(x41491,a850,a850),f341(f341(f10(a850,f864(a850,a850),x41491),a339),x41492)),x41493)),x41494),f341(f133(x41491,x41493),f341(f133(x41491,x41492),x41494))) % 19.23/19.03 [4247]E(f341(f341(f132(x42471),f341(f341(f341(f105(f858(x42471)),f341(f341(f343(a857),f2(a857)),x42472)),f341(f341(f146(x42471),x42473),f122(x42471))),f122(x42471))),f165(x42471,x42474,f341(f265(a857),f341(f341(f9(a857,f864(a857,a850),a850),f341(f341(f10(a857,f864(f864(a857,a850),a850),a857),f343(a857)),a121)),x42472)))),f165(x42471,f341(f341(f146(x42471),x42473),x42474),x42472)) % 19.23/19.03 [4341]E(f341(f265(f863(x43411,x43412)),f341(f341(f10(f864(a857,a850),a850,f863(x43411,x43412)),f96(a857)),f341(f341(f9(f863(x43411,x43412),f864(a857,a850),f864(a857,a850)),f341(f341(f10(f864(a857,f864(a850,a850)),f864(f864(a857,a850),f864(a857,a850)),f863(x43411,x43412)),f20(a857,a850,a850)),f341(f341(f10(f864(a857,a850),f864(a857,f864(a850,a850)),f863(x43411,x43412)),f341(f10(a850,f864(a850,a850),a857),a339)),f341(f341(f9(f863(x43411,x43412),f864(a857,f863(x43411,x43412)),f864(a857,a850)),f341(f341(f10(f864(f863(x43411,x43412),a850),f864(f864(a857,f863(x43411,x43412)),f864(a857,a850)),f863(x43411,x43412)),f10(f863(x43411,x43412),a850,a857)),a338)),f341(f341(f20(a857,x43412,f863(x43411,x43412)),f341(f341(f10(x43411,f864(x43412,f863(x43411,x43412)),a857),f250(x43411,x43412)),f341(f158(x43411),x43413))),f341(f158(x43412),x43414)))))),f341(f341(f9(a857,a857,a850),f242(a857)),f341(f341(f245(a857),f341(f186(f858(x43411)),x43413)),f341(f186(f858(x43412)),x43414)))))),f341(f163(f863(x43411,x43412)),f341(f341(f172(x43411,x43412),x43413),x43414))) % 19.23/19.03 [4266]E(f341(f265(f863(x42661,x42662)),f341(f260(x42661,x42662,a850),f341(f341(f9(x42661,f864(x42662,a850),f864(x42662,a850)),f341(f341(f10(f864(a850,a850),f864(f864(x42662,a850),f864(x42662,a850)),x42661),f10(a850,a850,x42662)),f341(f341(f10(a850,f864(a850,a850),x42661),a339),x42663))),x42664))),f341(f341(f257(x42661,x42662),f341(f265(x42661),x42663)),f341(f18(f864(x42662,a850),x42661),f341(f265(x42662),x42664)))) % 19.23/19.03 [4269]E(f341(f265(f863(x42691,x42692)),f341(f260(x42691,x42692,a850),f341(f341(f20(x42691,f864(x42692,a850),f864(x42692,a850)),f341(f341(f10(f864(a850,a850),f864(f864(x42692,a850),f864(x42692,a850)),x42691),f10(a850,a850,x42692)),f341(f341(f10(a850,f864(a850,a850),x42691),a339),x42693))),x42694))),f341(f341(f257(x42691,x42692),f341(f265(x42691),x42693)),f341(f341(f10(f864(x42692,a850),f864(x42692,a850),x42691),f265(x42692)),x42694))) % 19.23/19.03 [4284]E(f341(f265(x42841),f341(f341(f10(f864(x42842,a850),a850,x42841),f97(x42842)),f341(f341(f10(f864(x42842,a850),f864(x42842,a850),x42841),f341(f20(x42842,a850,a850),f341(f341(f10(a850,f864(a850,a850),x42842),a344),f341(f341(f9(x42842,f864(x42842,a850),a850),f343(x42842)),x42843)))),x42844))),f341(f341(f55(x42842,f864(x42841,a850)),x42843),f341(f341(f10(f864(x42841,a850),f864(x42841,a850),x42842),f265(x42841)),f341(f9(x42841,x42842,a850),x42844)))) % 19.23/19.03 [4326]E(f341(f341(f149(f863(x43261,a857),x43261),f249(x43261,a857)),f341(f133(f863(x43261,a857),f341(f341(f9(f863(x43261,a857),f864(a857,a850),a850),f341(f341(f10(a857,f864(f864(a857,a850),a850),f863(x43261,a857)),f343(a857)),f259(x43261,a857))),x43262)),f341(f341(f172(x43261,a857),x43263),f136(a857,f341(f303(a857,x43264),f341(f341(f89(a857),x43264),f341(f186(f858(x43261)),x43263))))))),f341(f341(f149(f863(x43261,a857),x43261),f249(x43261,a857)),f341(f133(f863(x43261,a857),f341(f341(f9(f863(x43261,a857),f864(a857,a850),a850),f341(f341(f10(a857,f864(f864(a857,a850),a850),f863(x43261,a857)),f343(a857)),f341(f341(f9(f863(x43261,a857),a857,a857),f341(f341(f10(a857,f864(a857,a857),f863(x43261,a857)),f89(a857)),f259(x43261,a857))),x43264))),x43262)),f341(f341(f172(x43261,a857),x43263),f136(a857,f341(f303(a857,f2(a857)),f341(f186(f858(x43261)),x43263))))))) % 19.23/19.03 [4327]E(f341(a121,f341(f341(f240(a857),f341(f186(f858(x43271)),x43272)),f341(f138(a857,f858(x43273),f341(f9(f858(x43273),a857,a857),f341(f341(f10(a857,f864(a857,a857),f858(x43273)),f240(a857)),f341(f341(f9(f858(x43273),a857,a857),f341(f341(f10(a857,f864(a857,a857),f858(x43273)),f3(a857)),f186(f858(x43273)))),f341(a121,f2(a857))))),f2(a857)),f341(f148(f858(x43273)),f341(f133(f858(x43273),f341(f341(f10(a850,a850,f858(x43273)),a337),f341(f341(f9(f858(x43273),f858(x43273),a850),a338),f122(x43273)))),x43274))))),f341(f341(f240(a857),f341(a121,f341(f186(f858(x43271)),x43272))),f341(f138(a857,f858(x43273),f341(f9(f858(x43273),a857,a857),f341(f341(f10(a857,f864(a857,a857),f858(x43273)),f240(a857)),f186(f858(x43273)))),f2(a857)),f341(f148(f858(x43273)),x43274)))) % 19.23/19.03 [4283]E(f341(f341(f132(x42831),f165(x42831,x42832,x42833)),f165(x42831,x42834,f341(f265(a857),f341(f341(f9(a857,f864(a857,a850),a850),f341(f341(f10(a857,f864(f864(a857,a850),a850),a857),f343(a857)),f341(f341(f9(a857,a857,a857),f89(a857)),f341(f186(f858(x42831)),x42832)))),x42833)))),f165(x42831,f341(f341(f132(x42831),x42832),x42834),x42833)) % 19.23/19.03 [4333]E(f341(f341(f146(f858(x43331)),f341(f341(f146(x43331),x43332),f341(f138(f858(x43331),f858(x43331),f132(x43331),f122(x43331)),f341(f341(f149(f858(x43331),f858(x43331)),f151(f858(x43331),x43331,f122(x43331),f341(f341(f10(f858(x43331),f864(f858(x43331),f858(x43331)),x43331),f18(f858(x43331),f858(x43331))),f341(f341(f9(x43331,f858(x43331),f858(x43331)),f146(x43331)),f122(x43331))))),x43333)))),f169(x43331,f341(f341(f146(f858(x43331)),x43334),f341(f138(f858(f858(x43331)),f858(f858(x43331)),f132(f858(x43331)),f122(f858(x43331))),f341(f341(f149(f858(x43331),f858(f858(x43331))),f151(f858(f858(x43331)),x43331,f122(f858(x43331)),f341(f18(f864(f858(x43331),f858(f858(x43331))),x43331),f341(f341(f9(f858(x43331),f858(f858(x43331)),f858(f858(x43331))),f146(f858(x43331))),f122(f858(x43331)))))),x43333))))),f169(x43331,f341(f341(f146(f858(x43331)),f341(f341(f146(x43331),x43332),x43334)),x43333))) % 19.23/19.03 [4342]E(f341(f265(f863(x43421,x43421)),f341(f260(x43421,x43421,a850),f341(f341(f9(x43421,f864(f863(x43422,x43422),a850),f864(x43421,a850)),f341(f341(f10(f864(x43421,f864(f864(f863(x43422,x43422),a850),a850)),f864(f864(f863(x43422,x43422),a850),f864(x43421,a850)),x43421),f9(x43421,f864(f863(x43422,x43422),a850),a850)),f341(f341(f10(f864(x43421,f863(x43422,x43422)),f864(x43421,f864(f864(f863(x43422,x43422),a850),a850)),x43421),f341(f10(f863(x43422,x43422),f864(f864(f863(x43422,x43422),a850),a850),x43421),f343(f863(x43422,x43422)))),f341(f341(f9(x43421,f864(x43421,x43422),f864(x43421,f863(x43422,x43422))),f341(f341(f10(f864(x43422,f863(x43422,x43422)),f864(f864(x43421,x43422),f864(x43421,f863(x43422,x43422))),x43421),f10(x43422,f863(x43422,x43422),x43421)),f341(f341(f10(x43422,f864(x43422,f863(x43422,x43422)),x43421),f250(x43422,x43422)),x43423))),x43423)))),x43424))),f341(f341(f289(x43422,x43421),x43424),x43423)) % 19.23/19.03 [4428]~E(f30(x44281,x44282),f33(x44283,x44284,x44285)) % 19.23/19.03 [4429]~E(f30(x44291,x44292),f35(x44293,x44294,x44295)) % 19.23/19.03 [4430]~E(f30(x44301,x44302),f34(x44303,x44304,x44305)) % 19.23/19.03 [4431]~E(f38(x44311,x44312),f33(x44313,x44314,x44315)) % 19.23/19.03 [4432]~E(f38(x44321,x44322),f35(x44323,x44324,x44325)) % 19.23/19.03 [4433]~E(f38(x44331,x44332),f34(x44333,x44334,x44335)) % 19.23/19.03 [4434]~E(f37(x44341,x44342),f33(x44343,x44344,x44345)) % 19.23/19.03 [4435]~E(f37(x44351,x44352),f35(x44353,x44354,x44355)) % 19.23/19.03 [4436]~E(f37(x44361,x44362),f34(x44363,x44364,x44365)) % 19.23/19.03 [4437]~E(f33(x44371,x44372,x44373),f30(x44374,x44375)) % 19.23/19.03 [4438]~E(f33(x44381,x44382,x44383),f38(x44384,x44385)) % 19.23/19.03 [4439]~E(f33(x44391,x44392,x44393),f37(x44394,x44395)) % 19.23/19.03 [4440]~E(f35(x44401,x44402,x44403),f30(x44404,x44405)) % 19.23/19.03 [4441]~E(f35(x44411,x44412,x44413),f38(x44414,x44415)) % 19.23/19.03 [4442]~E(f35(x44421,x44422,x44423),f37(x44424,x44425)) % 19.23/19.03 [4443]~E(f34(x44431,x44432,x44433),f30(x44434,x44435)) % 19.23/19.03 [4444]~E(f34(x44441,x44442,x44443),f38(x44444,x44445)) % 19.23/19.03 [4445]~E(f34(x44451,x44452,x44453),f37(x44454,x44455)) % 19.23/19.03 [3832]E(f341(f175(x38321,x38322,x38323,x38324),x38325),f341(f237(f861(x38322),x38322,f341(x38323,x38325),f235(x38322)),f341(x38324,x38325))) % 19.23/19.03 [3918]E(f175(x39181,x39182,f175(x39181,x39182,x39183,x39184),x39185),f175(x39181,x39182,x39183,f175(x39181,x39182,x39184,x39185))) % 19.23/19.03 [4101]E(f341(f341(f110(f864(x41011,a850)),f341(f163(x41011),f341(f341(f164(x41011),f341(f186(f858(x41012)),x41013)),x41014))),f174(x41011,x41012,x41015)),f174(x41011,x41012,f177(x41011,x41012,x41015,x41014,x41013))) % 19.23/19.03 [3662]E(f341(f341(f260(x36621,x36622,x36623),x36624),x36625),f341(f341(x36624,f341(f249(x36621,x36622),x36625)),f341(f259(x36621,x36622),x36625))) % 19.23/19.03 [3688]E(f341(f237(x36881,x36882,x36883,x36884),f341(f235(x36882),x36885)),f341(x36884,x36885)) % 19.23/19.03 [3696]E(f341(f341(f341(f75(x36961,x36962,x36963),x36964),x36965),f185(f864(x36962,a850))),x36965) % 19.23/19.03 [3712]E(f341(f325(x37121,x37122,x37123,x37124),f341(f313(x37121,x37123),x37125)),f341(x37124,x37125)) % 19.23/19.03 [3713]E(f341(f326(x37131,x37132,x37133,x37134),f341(f322(x37131,x37133),x37135)),f341(x37134,x37135)) % 19.23/19.03 [3863]E(f238(x38631,x38632,x38633,x38634,f341(f235(x38632),x38635)),f341(x38634,x38635)) % 19.23/19.03 [3899]E(f327(x38991,x38992,x38993,x38994,f341(f322(x38992,x38991),x38995)),f341(f341(f89(a857),f341(x38994,x38995)),f341(a121,f2(a857)))) % 19.23/19.03 [3900]E(f327(x39001,x39002,x39003,x39004,f341(f313(x39001,x39002),x39005)),f341(f341(f89(a857),f341(x39003,x39005)),f341(a121,f2(a857)))) % 19.23/19.03 [3976]E(f341(f82(f861(x39761),f861(x39762),f861(x39763),f341(f204(x39761,x39762),x39764)),f341(f204(x39763,x39761),x39765)),f341(f204(x39763,x39762),f341(f82(x39761,x39762,x39763,x39764),x39765))) % 19.23/19.03 [3978]E(f341(f82(f858(x39781),f858(x39782),f858(x39783),f341(f149(x39781,x39782),x39784)),f341(f149(x39783,x39781),x39785)),f341(f149(x39783,x39782),f341(f82(x39781,x39782,x39783,x39784),x39785))) % 19.23/19.03 [4057]E(f94(x40571,f76(x40572,x40571,x40573,x40574,x40575)),f341(f341(f74(x40572,x40571,x40573),x40574),x40575)) % 19.23/19.03 [4093]E(f341(f341(f89(a857),f341(f341(f89(a857),f341(x40931,f341(f249(x40932,x40933),x40934))),f341(x40935,f341(f259(x40932,x40933),x40934)))),f341(a121,f2(a857))),f264(x40932,x40933,x40931,x40935,x40934)) % 19.23/19.03 [4279]E(f159(x42791,x42792,f341(f341(f9(x42791,f861(x42792),f861(x42792)),f341(f341(f20(x42791,f861(x42792),f864(f861(x42792),f861(x42792))),f341(f341(f10(a850,f864(f861(x42792),f864(f861(x42792),f861(x42792))),x42791),f105(f861(x42792))),x42793)),f341(f341(f10(x42792,f861(x42792),x42791),f235(x42792)),x42794))),f188(x42792)),x42795),f341(f341(f149(x42791,x42792),x42794),f341(f133(x42791,x42793),x42795))) % 19.23/19.03 [4487]~E(f341(f341(f341(f81(x44871,f861(x44872)),x44873),x44874),f341(f235(x44872),x44875)),f341(f18(f861(x44872),x44871),f188(x44872))) % 19.23/19.03 [3597]E(f341(f341(f164(x35971),x35972),f341(f341(f149(x35973,x35971),x35974),x35975)),f341(f341(f149(x35973,x35971),x35974),f341(f341(f164(x35973),x35972),x35975))) % 19.23/19.03 [3598]E(f341(f341(f135(x35981),x35982),f341(f341(f149(x35983,x35981),x35984),x35985)),f341(f341(f149(x35983,x35981),x35984),f341(f341(f135(x35983),x35982),x35985))) % 19.23/19.03 [3628]E(f341(f341(f149(x36281,x36282),x36283),f341(f341(f146(x36281),x36284),x36285)),f341(f341(f146(x36282),f341(x36283,x36284)),f341(f341(f149(x36281,x36282),x36283),x36285))) % 19.23/19.03 [3692]E(f341(f312(x36921,x36922,x36923),f341(f341(f311(x36921),x36924),x36925)),f341(f341(f311(x36922),f341(x36923,x36924)),f341(f312(x36921,x36922,x36923),x36925))) % 19.23/19.03 [3757]E(f341(f341(f172(x37571,x37572),f341(f341(f164(x37571),x37573),x37574)),f341(f341(f164(x37572),x37573),x37575)),f341(f341(f164(f863(x37571,x37572)),x37573),f341(f341(f172(x37571,x37572),x37574),x37575))) % 19.23/19.03 [3758]E(f341(f341(f172(x37581,x37582),f341(f341(f135(x37581),x37583),x37584)),f341(f341(f135(x37582),x37583),x37585)),f341(f341(f135(f863(x37581,x37582)),x37583),f341(f341(f172(x37581,x37582),x37584),x37585))) % 19.23/19.03 [3769]E(f341(f341(f154(x37691,f341(f341(f146(x37691),x37692),x37693)),f341(a121,x37694)),x37695),f341(f341(f146(x37691),x37692),f341(f341(f154(x37691,x37693),x37694),x37695))) % 19.23/19.03 [3772]E(f341(f237(f861(x37721),x37722,f188(x37721),x37723),f341(f341(f18(f861(x37722),x37724),f188(x37722)),x37725)),f188(x37721)) % 19.23/19.03 [3774]E(f341(f341(f132(x37741),f341(f341(f149(x37742,x37741),x37743),x37744)),f341(f341(f149(x37742,x37741),x37743),x37745)),f341(f341(f149(x37742,x37741),x37743),f341(f341(f132(x37742),x37744),x37745))) % 19.23/19.03 [3778]E(f341(f341(x37781,x37782),f341(f341(f252(x37783,x37784,x37781),x37782),x37785)),f341(f341(f252(x37783,x37784,x37781),x37782),f341(a121,x37785))) % 19.23/19.03 [3819]E(f341(f341(f290(x38191,x38192,x38193),f341(f287(x38192,x38191),x38194)),f341(f287(x38193,x38192),x38195)),f341(f287(x38193,x38191),f341(f341(f290(x38193,x38192,x38191),x38195),x38194))) % 19.23/19.03 [3850]E(f341(f341(f341(f179(f858(x38501),f858(x38501)),x38502),f147(x38501)),f341(f341(f149(x38503,x38501),x38504),x38505)),f341(f341(f149(x38503,x38501),x38504),f341(f341(f341(f179(f858(x38503),f858(x38503)),x38502),f147(x38503)),x38505))) % 19.23/19.03 [3851]E(f341(f341(f262(x38511,x38512,x38511,x38513),f341(f250(x38512,x38511),x38514)),x38515),f341(x38515,x38514)) % 19.23/19.03 [3877]E(f150(x38771,x38772,f341(f341(f149(x38773,x38771),x38774),x38775)),f150(x38773,f341(f82(x38771,a857,x38773,x38772),x38774),x38775)) % 19.23/19.03 [3941]E(f341(f341(f82(f861(x39411),f861(x39412),x39413,f341(f204(x39411,x39412),x39414)),f341(f18(f861(x39411),x39413),f188(x39411))),x39415),f188(x39412)) % 19.23/19.03 [3942]E(f167(f863(x39421,x39422),f341(f82(x39422,a850,f863(x39421,x39422),x39423),f259(x39421,x39422)),f341(f341(f172(x39421,x39422),x39424),x39425)),f341(f341(f172(x39421,x39422),x39424),f167(x39422,x39423,x39425))) % 19.23/19.03 [3947]E(f341(f312(x39471,x39472,f341(f341(f10(x39473,x39472,x39471),x39474),x39475)),f248(f864(x39471,a850))),f341(f312(x39473,x39472,x39474),f341(f312(x39471,x39473,x39475),f248(f864(x39471,a850))))) % 19.23/19.03 [3961]E(f167(f863(x39611,x39612),f341(f82(x39611,a850,f863(x39611,x39612),x39613),f249(x39611,x39612)),f341(f341(f172(x39611,x39612),x39614),x39615)),f341(f341(f172(x39611,x39612),f167(x39611,x39613,x39614)),x39615)) % 19.23/19.03 [3982]E(f341(f341(f110(f864(x39821,a850)),f341(f314(x39821,x39822,x39823),f341(f341(f311(x39822),x39824),f185(f864(x39822,a850))))),f341(f314(x39821,x39822,x39823),x39825)),f341(f314(x39821,x39822,x39823),f341(f341(f311(x39822),x39824),x39825))) % 19.23/19.03 [4042]E(f341(f341(f149(x40421,x40422),x40423),f167(x40421,f341(f82(x40422,a850,x40421,x40424),x40423),x40425)),f167(x40422,x40424,f341(f341(f149(x40421,x40422),x40423),x40425))) % 19.23/19.03 [4049]E(f341(f138(x40491,x40492,f341(f9(x40492,x40491,x40491),f341(f9(x40491,x40492,x40491),x40493)),x40494),f341(f148(x40492),f341(f148(x40492),x40495))),f341(f138(x40491,x40492,x40493,x40494),x40495)) % 19.23/19.03 [4050]E(f341(f341(f341(f81(x40501,f861(x40502)),f178(x40501,x40502,x40503,x40504)),x40505),f341(x40503,x40505)),f178(x40501,x40502,x40503,f341(f341(f311(x40501),x40505),x40504))) % 19.23/19.03 [4059]E(f341(f328(x40591,x40592,x40593,f341(f18(x40592,x40591),x40594),f341(f18(x40592,x40593),x40594)),x40595),x40594) % 19.23/19.03 [4118]E(f341(f237(f858(x41181),x41181,f159(x41182,x41181,x41183,x41184),f341(f341(f9(x41181,f858(x41181),f858(x41181)),f146(x41181)),f159(x41182,x41181,x41183,x41184))),f341(x41183,x41185)),f159(x41182,x41181,x41183,f341(f341(f146(x41182),x41185),x41184))) % 19.23/19.03 [4157]P85(f341(f341(f241(f864(x41571,a850)),f341(f312(x41572,x41571,x41573),f341(f341(f111(f864(x41572,a850)),x41574),x41575))),f341(f341(f111(f864(x41571,a850)),f341(f312(x41572,x41571,x41573),x41574)),f341(f312(x41572,x41571,x41573),x41575)))) % 19.23/19.03 [4158]P85(f341(f341(f241(f864(x41581,a850)),f341(f286(x41582,x41581,x41583),f341(f341(f111(f864(x41582,a850)),x41584),x41585))),f341(f341(f111(f864(x41581,a850)),f341(f286(x41582,x41581,x41583),x41584)),f341(f286(x41582,x41581,x41583),x41585)))) % 19.23/19.03 [4254]E(f341(f259(x42541,x42542),f341(f261(x42543,x42541,x42542,x42542,x42544,f41(x42542)),x42545)),f341(f259(x42543,x42542),x42545)) % 19.23/19.03 [4255]E(f341(f249(x42551,x42552),f341(f261(x42551,x42551,x42553,x42552,f41(x42551),x42554),x42555)),f341(f249(x42551,x42553),x42555)) % 19.23/19.03 [4337]P25(x43371,x43372,f341(f341(f311(f856(x43371)),f341(f341(f341(f100(x43371),f341(f341(f9(x43371,f864(a855,a855),f864(a855,a850)),f341(f341(f10(f864(a855,a850),f864(f864(a855,a855),f864(a855,a850)),x43371),f10(a855,a850,a855)),x43373)),f341(f341(f20(a855,a857,a855),f341(f341(f9(a855,a852,f864(a857,a855)),a194),x43374)),x43375))),f30(x43374,x43375)),x43373)),f185(f864(f856(x43371),a850)))) % 19.23/19.03 [4339]E(f341(f138(f864(x43391,f861(x43392)),f863(x43391,x43392),f341(f341(f10(f864(x43391,f864(x43392,f864(x43391,f861(x43392)))),f864(f863(x43391,x43392),f864(x43391,f861(x43392))),f864(x43391,f861(x43392))),f260(x43391,x43392,f864(x43391,f861(x43392)))),f341(f341(f9(f864(x43391,f861(x43392)),f864(x43392,f861(x43392)),f864(x43391,f864(x43392,f864(x43391,f861(x43392))))),f341(f341(f10(f864(x43391,f864(f864(x43392,f861(x43392)),f864(x43392,f864(x43391,f861(x43392))))),f864(f864(x43392,f861(x43392)),f864(x43391,f864(x43392,f864(x43391,f861(x43392))))),f864(x43391,f861(x43392))),f9(x43391,f864(x43392,f861(x43392)),f864(x43392,f864(x43391,f861(x43392))))),f341(f341(f10(f864(x43391,f864(f861(x43392),f864(x43391,f861(x43392)))),f864(x43391,f864(f864(x43392,f861(x43392)),f864(x43392,f864(x43391,f861(x43392))))),f864(x43391,f861(x43392))),f341(f10(f864(f861(x43392),f864(x43391,f861(x43392))),f864(f864(x43392,f861(x43392)),f864(x43392,f864(x43391,f861(x43392)))),x43391),f10(f861(x43392),f864(x43391,f861(x43392)),x43392))),f81(x43391,f861(x43392))))),f235(x43392))),x43393),f341(f341(f172(x43391,x43392),x43394),x43395)),f177(x43391,x43392,x43393,x43394,x43395)) % 19.23/19.03 [3442]E(f341(f341(f341(f341(f207(x34421),x34422),x34423),x34424),x34425),f190(x34421,x34422)) % 19.23/19.03 [3443]E(f341(f341(f341(f341(f211(x34431),x34432),x34433),x34434),x34435),f202(x34431,x34432)) % 19.23/19.03 [3490]E(f102(x34901,x34902,f341(f341(f341(f100(x34901),x34903),x34904),x34905)),f2(a857)) % 19.23/19.03 [3580]E(f341(f341(f341(f341(f81(x35801,x35802),x35803),x35804),x35805),x35804),x35805) % 19.23/19.03 [3809]E(f341(f341(f54(x38091,f864(x38092,a850)),f341(f341(f311(x38091),x38093),x38094)),x38095),f341(f341(f110(f864(x38092,a850)),f341(x38095,x38093)),f341(f341(f54(x38091,f864(x38092,a850)),x38094),x38095))) % 19.23/19.03 [3810]E(f341(f341(f55(x38101,f864(x38102,a850)),f341(f341(f311(x38101),x38103),x38104)),x38105),f341(f341(f111(f864(x38102,a850)),f341(x38105,x38103)),f341(f341(f55(x38101,f864(x38102,a850)),x38104),x38105))) % 19.23/19.03 [3870]E(f341(f341(f110(f864(x38701,a850)),f341(f312(x38702,x38701,x38703),x38704)),f341(f312(x38702,x38701,x38703),x38705)),f341(f312(x38702,x38701,x38703),f341(f341(f110(f864(x38702,a850)),x38704),x38705))) % 19.23/19.03 [3871]E(f341(f341(f110(f864(x38711,a850)),f341(f286(x38712,x38711,x38713),x38714)),f341(f286(x38712,x38711,x38713),x38715)),f341(f286(x38712,x38711,x38713),f341(f341(f110(f864(x38712,a850)),x38714),x38715))) % 19.23/19.03 [3872]E(f341(f341(f3(f864(x38721,a850)),f341(f314(x38721,x38722,x38723),x38724)),f341(f314(x38721,x38722,x38723),x38725)),f341(f314(x38721,x38722,x38723),f341(f341(f3(f864(x38722,a850)),x38724),x38725))) % 19.23/19.03 [3873]E(f341(f341(f110(f864(x38731,a850)),f341(f314(x38731,x38732,x38733),x38734)),f341(f314(x38731,x38732,x38733),x38735)),f341(f314(x38731,x38732,x38733),f341(f341(f110(f864(x38732,a850)),x38734),x38735))) % 19.23/19.03 [3874]E(f341(f341(f111(f864(x38741,a850)),f341(f314(x38741,x38742,x38743),x38744)),f341(f314(x38741,x38742,x38743),x38745)),f341(f314(x38741,x38742,x38743),f341(f341(f111(f864(x38742,a850)),x38744),x38745))) % 19.23/19.03 [3876]E(f178(x38761,x38762,f178(x38761,x38762,x38763,x38764),x38765),f178(x38761,x38762,x38763,f341(f341(f111(f864(x38761,a850)),x38764),x38765))) % 19.23/19.03 [3878]E(f125(x38781,x38782,f341(x38783,x38784),f341(f341(f9(x38781,a108,f859(x38782)),x38785),x38784)),f341(f200(x38781,x38782,x38783,x38785),x38784)) % 19.23/19.03 [3937]E(f341(f341(f154(x39371,f341(f341(f132(x39371),x39372),f341(f341(f146(x39371),x39373),x39374))),f341(f186(f858(x39371)),x39372)),x39375),f341(f341(f132(x39371),x39372),f341(f341(f146(x39371),x39375),x39374))) % 19.23/19.03 [3945]E(f341(f341(f55(x39451,f864(x39452,a850)),x39453),f341(f341(f10(f864(x39452,a850),f864(x39452,a850),x39451),f341(f311(x39452),x39454)),x39455)),f341(f341(f311(x39452),x39454),f341(f341(f55(x39451,f864(x39452,a850)),x39453),x39455))) % 19.23/19.03 [4017]E(f178(x40171,x40172,f341(f341(f341(f81(x40171,f861(x40172)),x40173),x40174),f341(f235(x40172),x40175)),f341(f88(f864(x40171,a850)),f341(f341(f311(x40171),x40174),f185(f864(x40171,a850))))),f178(x40171,x40172,x40173,f341(f88(f864(x40171,a850)),f341(f341(f311(x40171),x40174),f185(f864(x40171,a850)))))) % 19.23/19.03 [4105]E(f341(f341(f149(x41051,x41052),x41053),f341(f133(x41051,f341(f82(x41052,a850,x41051,x41054),x41053)),x41055)),f341(f133(x41052,x41054),f341(f341(f149(x41051,x41052),x41053),x41055))) % 19.23/19.03 [4111]E(f341(f186(f858(x41111)),f341(f133(x41111,x41112),f341(f341(f149(x41113,x41111),x41114),x41115))),f341(f186(f858(x41113)),f341(f133(x41113,f341(f82(x41111,a850,x41113,x41112),x41114)),x41115))) % 19.23/19.03 [4246]E(f341(f341(f110(f864(x42461,a850)),f341(f341(f3(f864(x42461,a850)),f174(x42461,x42462,x42463)),f341(f265(x42461),f341(f341(f9(x42461,f864(x42461,a850),a850),f343(x42461)),f341(f341(f3(f864(x42461,a850)),x42464),f174(x42461,x42462,x42465)))))),f341(f265(x42461),f341(f341(f9(x42461,f864(x42461,a850),a850),f343(x42461)),f341(f341(f111(f864(x42461,a850)),x42464),f174(x42461,x42462,x42465))))),f174(x42461,x42462,f85(x42461,f861(x42462),x42463,x42465,x42464))) % 19.23/19.03 [4318]E(f341(f151(f858(f863(x43181,x43182)),x43182,f122(f863(x43181,x43182)),f341(f341(f9(x43182,f864(f858(x43182),f858(f863(x43181,x43182))),f864(f858(x43182),f858(f863(x43181,x43182)))),f341(f341(f10(f864(f858(f863(x43181,x43182)),f858(f863(x43181,x43182))),f864(f864(f858(x43182),f858(f863(x43181,x43182))),f864(f858(x43182),f858(f863(x43181,x43182)))),x43182),f10(f858(f863(x43181,x43182)),f858(f863(x43181,x43182)),f858(x43182))),f341(f341(f10(f863(x43181,x43182),f864(f858(f863(x43181,x43182)),f858(f863(x43181,x43182))),x43182),f146(f863(x43181,x43182))),f341(f250(x43181,x43182),x43183)))),f341(f172(x43181,x43182),x43184))),x43185),f341(f341(f172(x43181,x43182),f341(f341(f146(x43181),x43183),x43184)),x43185)) % 19.23/19.03 [3804]E(f341(f341(f154(x38041,f341(f341(f154(x38041,x38042),x38043),x38044)),x38043),x38045),f341(f341(f154(x38041,x38042),x38043),x38045)) % 19.23/19.03 [3852]E(f341(f268(x38521,x38522),f341(f341(f311(f863(x38521,x38522)),f341(f341(f250(x38521,x38522),x38523),x38524)),x38525)),f341(f341(f311(x38522),x38524),f341(f268(x38521,x38522),x38525))) % 19.23/19.03 [3853]E(f341(f270(x38531,x38532),f341(f341(f311(f863(x38531,x38532)),f341(f341(f250(x38531,x38532),x38533),x38534)),x38535)),f341(f341(f311(x38531),x38533),f341(f270(x38531,x38532),x38535))) % 19.23/19.03 [3902]E(f128(x39021,x39022,f341(x39023,x39024),f341(f341(f9(x39021,a108,f859(f861(x39022))),x39025),x39024)),f341(f198(x39021,x39022,x39023,x39025),x39024)) % 19.23/19.03 [3930]E(f341(f341(f3(f864(f863(x39301,x39302),a850)),f341(f341(f257(x39301,x39302),x39303),x39304)),f341(f341(f257(x39301,x39302),x39305),x39304)),f341(f341(f257(x39301,x39302),f341(f341(f3(f864(x39301,a850)),x39303),x39305)),x39304)) % 19.23/19.03 [3931]E(f341(f341(f110(f864(f863(x39311,x39312),a850)),f341(f341(f257(x39311,x39312),x39313),x39314)),f341(f341(f257(x39311,x39312),x39315),x39314)),f341(f341(f257(x39311,x39312),f341(f341(f110(f864(x39311,a850)),x39313),x39315)),x39314)) % 19.23/19.03 [3932]E(f341(f341(f111(f864(f863(x39321,x39322),a850)),f341(f341(f257(x39321,x39322),x39323),x39324)),f341(f341(f257(x39321,x39322),x39325),x39324)),f341(f341(f257(x39321,x39322),f341(f341(f111(f864(x39321,a850)),x39323),x39325)),x39324)) % 19.23/19.03 [3995]E(f341(f341(f110(f864(x39951,a850)),f341(f341(f54(x39952,f864(x39951,a850)),x39953),x39954)),f341(f341(f54(x39952,f864(x39951,a850)),x39955),x39954)),f341(f341(f54(x39952,f864(x39951,a850)),f341(f341(f110(f864(x39952,a850)),x39953),x39955)),x39954)) % 19.23/19.03 [3996]E(f341(f341(f111(f864(x39961,a850)),f341(f341(f55(x39962,f864(x39961,a850)),x39963),x39964)),f341(f341(f55(x39962,f864(x39961,a850)),x39965),x39964)),f341(f341(f55(x39962,f864(x39961,a850)),f341(f341(f110(f864(x39962,a850)),x39963),x39965)),x39964)) % 19.23/19.03 [4010]E(f341(f341(f54(x40101,f864(x40102,a850)),x40103),f341(f341(f10(f864(x40102,a850),f864(x40102,a850),x40101),f341(f3(f864(x40102,a850)),x40104)),x40105)),f341(f341(f3(f864(x40102,a850)),x40104),f341(f341(f55(x40101,f864(x40102,a850)),x40103),x40105))) % 19.23/19.03 [4011]E(f341(f341(f54(x40111,f864(x40112,a850)),x40113),f341(f341(f10(f864(x40112,a850),f864(x40112,a850),x40111),f341(f111(f864(x40112,a850)),x40114)),x40115)),f341(f341(f111(f864(x40112,a850)),x40114),f341(f341(f54(x40111,f864(x40112,a850)),x40113),x40115))) % 19.23/19.03 [4012]E(f341(f341(f55(x40121,f864(x40122,a850)),x40123),f341(f341(f10(f864(x40122,a850),f864(x40122,a850),x40121),f341(f110(f864(x40122,a850)),x40124)),x40125)),f341(f341(f110(f864(x40122,a850)),x40124),f341(f341(f55(x40121,f864(x40122,a850)),x40123),x40125))) % 19.23/19.03 [4071]E(f181(f858(x40711),f341(f341(f146(x40711),x40712),x40713),f341(f341(f10(f858(x40711),f858(x40711),a857),f341(f146(x40711),x40714)),f341(f341(f9(a857,x40711,f858(x40711)),f154(x40711,x40713)),x40712)),x40715),f341(f341(f154(x40711,f341(f341(f146(x40711),x40714),x40713)),x40715),x40712)) % 19.23/19.03 [4074]E(f341(f341(f54(x40741,f864(f863(x40742,x40743),a850)),x40744),f341(f341(f10(f864(f863(x40743,x40742),a850),f864(f863(x40742,x40743),a850),x40741),f287(x40743,x40742)),x40745)),f341(f287(x40743,x40742),f341(f341(f54(x40741,f864(f863(x40743,x40742),a850)),x40744),x40745))) % 19.23/19.03 [4075]E(f341(f341(f55(x40751,f864(f863(x40752,x40753),a850)),x40754),f341(f341(f10(f864(f863(x40753,x40752),a850),f864(f863(x40752,x40753),a850),x40751),f287(x40753,x40752)),x40755)),f341(f287(x40753,x40752),f341(f341(f55(x40751,f864(f863(x40753,x40752),a850)),x40754),x40755))) % 19.23/19.03 [4129]E(f174(x41291,x41292,f341(f341(f20(x41291,f861(x41293),f861(x41292)),f341(f341(f10(f864(x41293,x41292),f864(f861(x41293),f861(x41292)),x41291),f204(x41293,x41292)),x41294)),x41295)),f174(x41291,x41293,x41295)) % 19.23/19.03 [4181]P85(f341(f341(f241(f864(x41811,a850)),f341(f341(f3(f864(x41811,a850)),f341(f312(x41812,x41811,x41813),x41814)),f341(f312(x41812,x41811,x41813),x41815))),f341(f312(x41812,x41811,x41813),f341(f341(f3(f864(x41812,a850)),x41814),x41815)))) % 19.23/19.03 [4322]E(f341(f151(f858(f863(x43221,x43222)),x43221,f122(f863(x43221,x43222)),f341(f341(f9(x43221,f864(f858(x43221),f858(f863(x43221,x43222))),f864(f858(x43221),f858(f863(x43221,x43222)))),f341(f341(f10(f864(f858(f863(x43221,x43222)),f858(f863(x43221,x43222))),f864(f864(f858(x43221),f858(f863(x43221,x43222))),f864(f858(x43221),f858(f863(x43221,x43222)))),x43221),f10(f858(f863(x43221,x43222)),f858(f863(x43221,x43222)),f858(x43221))),f341(f341(f10(f863(x43221,x43222),f864(f858(f863(x43221,x43222)),f858(f863(x43221,x43222))),x43221),f146(f863(x43221,x43222))),f341(f341(f9(x43221,x43222,f863(x43221,x43222)),f250(x43221,x43222)),x43223)))),f341(f341(f9(f858(x43221),f858(x43222),f858(f863(x43221,x43222))),f172(x43221,x43222)),x43224))),x43225),f341(f341(f172(x43221,x43222),x43225),f341(f341(f146(x43222),x43223),x43224))) % 19.23/19.03 [4036]E(f341(f341(f110(f864(x40361,a850)),f341(f286(x40362,x40361,x40363),x40364)),f341(f286(x40362,x40361,x40365),x40364)),f341(f286(x40362,x40361,f341(f341(f110(f864(f863(x40362,x40361),a850)),x40363),x40365)),x40364)) % 19.23/19.03 [4077]E(f341(f341(f132(f863(x40771,x40772)),f341(f341(f172(x40771,x40772),x40773),f341(f341(f164(x40772),f341(f186(f858(x40771)),x40773)),x40774))),f341(f341(f172(x40771,x40772),x40775),f341(f341(f135(x40772),f341(f186(f858(x40771)),x40773)),x40774))),f341(f341(f172(x40771,x40772),f341(f341(f132(x40771),x40773),x40775)),x40774)) % 19.23/19.03 [4184]E(f341(f341(f257(x41841,x41842),x41843),f341(f341(f20(x41841,f864(x41842,a850),f864(x41842,a850)),f341(f341(f10(f864(x41842,a850),f864(f864(x41842,a850),f864(x41842,a850)),x41841),f3(f864(x41842,a850))),x41844)),x41845)),f341(f341(f3(f864(f863(x41841,x41842),a850)),f341(f341(f257(x41841,x41842),x41843),x41844)),f341(f341(f257(x41841,x41842),x41843),x41845))) % 19.23/19.03 [4185]E(f341(f341(f257(x41851,x41852),x41853),f341(f341(f20(x41851,f864(x41852,a850),f864(x41852,a850)),f341(f341(f10(f864(x41852,a850),f864(f864(x41852,a850),f864(x41852,a850)),x41851),f110(f864(x41852,a850))),x41854)),x41855)),f341(f341(f110(f864(f863(x41851,x41852),a850)),f341(f341(f257(x41851,x41852),x41853),x41854)),f341(f341(f257(x41851,x41852),x41853),x41855))) % 19.23/19.03 [4186]E(f341(f341(f257(x41861,x41862),x41863),f341(f341(f20(x41861,f864(x41862,a850),f864(x41862,a850)),f341(f341(f10(f864(x41862,a850),f864(f864(x41862,a850),f864(x41862,a850)),x41861),f111(f864(x41862,a850))),x41864)),x41865)),f341(f341(f111(f864(f863(x41861,x41862),a850)),f341(f341(f257(x41861,x41862),x41863),x41864)),f341(f341(f257(x41861,x41862),x41863),x41865))) % 19.23/19.03 [4190]E(f341(f341(f54(x41901,f864(x41902,a850)),x41903),f341(f341(f9(x41901,f864(x41902,a850),f864(x41902,a850)),f341(f341(f10(f864(x41902,a850),f864(f864(x41902,a850),f864(x41902,a850)),x41901),f3(f864(x41902,a850))),x41904)),x41905)),f341(f341(f3(f864(x41902,a850)),f341(f341(f54(x41901,f864(x41902,a850)),x41903),x41904)),x41905)) % 19.23/19.03 [4191]E(f341(f341(f54(x41911,f864(x41912,a850)),x41913),f341(f341(f9(x41911,f864(x41912,a850),f864(x41912,a850)),f341(f341(f10(f864(x41912,a850),f864(f864(x41912,a850),f864(x41912,a850)),x41911),f111(f864(x41912,a850))),x41914)),x41915)),f341(f341(f111(f864(x41912,a850)),f341(f341(f54(x41911,f864(x41912,a850)),x41913),x41914)),x41915)) % 19.23/19.03 [4192]E(f341(f341(f55(x41921,f864(x41922,a850)),x41923),f341(f341(f9(x41921,f864(x41922,a850),f864(x41922,a850)),f341(f341(f10(f864(x41922,a850),f864(f864(x41922,a850),f864(x41922,a850)),x41921),f110(f864(x41922,a850))),x41924)),x41925)),f341(f341(f110(f864(x41922,a850)),f341(f341(f55(x41921,f864(x41922,a850)),x41923),x41924)),x41925)) % 19.23/19.03 [4196]E(f341(f341(f54(x41961,f864(x41962,a850)),x41963),f341(f341(f20(x41961,f864(x41962,a850),f864(x41962,a850)),f341(f341(f10(f864(x41962,a850),f864(f864(x41962,a850),f864(x41962,a850)),x41961),f110(f864(x41962,a850))),x41964)),x41965)),f341(f341(f110(f864(x41962,a850)),f341(f341(f54(x41961,f864(x41962,a850)),x41963),x41964)),f341(f341(f54(x41961,f864(x41962,a850)),x41963),x41965))) % 19.23/19.03 [4197]E(f341(f341(f55(x41971,f864(x41972,a850)),x41973),f341(f341(f20(x41971,f864(x41972,a850),f864(x41972,a850)),f341(f341(f10(f864(x41972,a850),f864(f864(x41972,a850),f864(x41972,a850)),x41971),f111(f864(x41972,a850))),x41974)),x41975)),f341(f341(f111(f864(x41972,a850)),f341(f341(f55(x41971,f864(x41972,a850)),x41973),x41974)),f341(f341(f55(x41971,f864(x41972,a850)),x41973),x41975))) % 19.23/19.03 [4209]E(f341(f341(f54(x42091,f864(x42092,a850)),x42093),f341(f341(f20(x42091,f864(x42092,a850),f864(x42092,a850)),f341(f341(f10(f864(x42092,a850),f864(f864(x42092,a850),f864(x42092,a850)),x42091),f110(f864(x42092,a850))),x42094)),x42095)),f341(f341(f110(f864(x42092,a850)),f52(f864(x42092,a850),f341(f312(x42091,f864(x42092,a850),x42094),x42093))),f52(f864(x42092,a850),f341(f312(x42091,f864(x42092,a850),x42095),x42093)))) % 19.23/19.03 [4210]E(f341(f341(f55(x42101,f864(x42102,a850)),x42103),f341(f341(f20(x42101,f864(x42102,a850),f864(x42102,a850)),f341(f341(f10(f864(x42102,a850),f864(f864(x42102,a850),f864(x42102,a850)),x42101),f111(f864(x42102,a850))),x42104)),x42105)),f341(f341(f111(f864(x42102,a850)),f53(f864(x42102,a850),f341(f312(x42101,f864(x42102,a850),x42104),x42103))),f53(f864(x42102,a850),f341(f312(x42101,f864(x42102,a850),x42105),x42103)))) % 19.23/19.03 [4119]E(f341(f341(f132(f863(x41191,x41192)),f341(f341(f172(x41191,x41192),f341(f341(f164(x41191),f341(f186(f858(x41192)),x41193)),x41194)),x41193)),f341(f341(f172(x41191,x41192),f341(f341(f135(x41191),f341(f186(f858(x41192)),x41193)),x41194)),x41195)),f341(f341(f172(x41191,x41192),x41194),f341(f341(f132(x41192),x41193),x41195))) % 19.23/19.03 [4235]E(f94(x42351,f341(f341(f20(x42351,a850,a850),f341(f341(f10(a850,f864(a850,a850),x42351),a339),f341(f341(f9(x42351,f864(x42351,a850),a850),f343(x42351)),x42352))),f341(f341(f9(x42351,x42353,a850),f341(f341(f10(x42353,f864(x42353,a850),x42351),a338),x42354)),x42355))),f341(f86(x42351,x42353,x42352,x42354),x42355)) % 19.23/19.03 [4285]E(f341(f341(f95(a1,x42851),f341(f113(a1),f341(f341(f89(a1),x42852),a106))),f341(f341(f20(a1,x42851,x42851),f341(f341(f9(a1,x42851,f864(x42851,x42851)),f341(f341(f10(a850,f864(x42851,f864(x42851,x42851)),a1),f105(x42851)),a191)),f181(x42851,x42853,x42854,x42855))),f341(f341(f10(a857,x42851,a1),x42854),f341(f341(f9(a1,a857,a857),f341(f341(f10(a857,f864(a857,a857),a1),f89(a857)),a114)),x42855)))),f181(x42851,x42853,x42854,f341(f341(f89(a857),f341(f113(a857),x42852)),x42855))) % 19.23/19.03 [4319]E(f171(x43191,x43192,f341(f341(f149(f863(x43191,x43193),f863(x43191,x43192)),f341(f260(x43191,x43193,f863(x43191,x43192)),f341(f341(f9(x43191,f864(x43193,x43192),f864(x43193,f863(x43191,x43192))),f341(f341(f10(f864(x43192,f863(x43191,x43192)),f864(f864(x43193,x43192),f864(x43193,f863(x43191,x43192))),x43191),f10(x43192,f863(x43191,x43192),x43193)),f250(x43191,x43192))),x43194))),x43195)),f341(f82(f861(x43193),f861(x43192),x43191,f341(f204(x43193,x43192),x43194)),f171(x43191,x43193,x43195))) % 19.23/19.03 [4278]E(f174(x42781,x42782,f341(f341(f20(x42781,f861(x42782),f861(x42782)),f341(f341(f20(x42781,f861(x42782),f864(f861(x42782),f861(x42782))),f341(f341(f10(a850,f864(f861(x42782),f864(f861(x42782),f861(x42782))),x42781),f105(f861(x42782))),x42783)),x42784)),x42785)),f341(f341(f110(f864(x42781,a850)),f341(f341(f111(f864(x42781,a850)),f174(x42781,x42782,x42784)),f341(f265(x42781),x42783))),f341(f341(f111(f864(x42781,a850)),f174(x42781,x42782,x42785)),f341(f265(x42781),f341(f341(f10(a850,a850,x42781),a337),x42783))))) % 19.23/19.03 [4317]E(f341(f341(f95(a1,x43171),f341(f113(a1),f341(f341(f89(a1),x43172),a106))),f341(f341(f20(a1,x43171,x43171),f341(f341(f9(a1,x43171,f864(x43171,x43171)),f341(f341(f10(a850,f864(x43171,f864(x43171,x43171)),a1),f105(x43171)),a191)),f341(f180(x43171,x43173,x43174),x43175))),f341(f341(f20(a1,x43171,x43171),f341(f341(f10(a857,f864(x43171,x43171),a1),x43174),f341(f341(f9(a1,a857,a857),f341(f341(f10(a857,f864(a857,a857),a1),f89(a857)),a114)),x43175))),f341(f341(f10(a857,x43171,a1),f180(x43171,x43173,x43174)),f341(f341(f9(a1,a857,a857),f341(f341(f10(a857,f864(a857,a857),a1),f89(a857)),a114)),x43175))))),f341(f180(x43171,x43173,x43174),f341(f341(f89(a857),f341(f113(a857),x43172)),x43175))) % 19.23/19.03 [4365]E(f341(f265(f863(x43651,x43652)),f341(f260(x43651,x43652,a850),f341(f341(f10(f864(x43652,f864(x43653,a850)),f864(x43652,a850),x43651),f341(f10(f864(x43653,a850),a850,x43652),f96(x43653))),f341(f341(f9(x43651,f864(x43652,f864(x43653,a850)),f864(x43652,f864(x43653,a850))),f341(f341(f10(f864(f864(x43653,a850),f864(x43653,a850)),f864(f864(x43652,f864(x43653,a850)),f864(x43652,f864(x43653,a850))),x43651),f10(f864(x43653,a850),f864(x43653,a850),x43652)),f341(f341(f10(f864(x43653,f864(a850,a850)),f864(f864(x43653,a850),f864(x43653,a850)),x43651),f20(x43653,a850,a850)),f341(f341(f10(f864(x43653,a850),f864(x43653,f864(a850,a850)),x43651),f341(f10(a850,f864(a850,a850),x43653),a339)),f341(f341(f9(x43651,f864(f863(x43651,x43653),a850),f864(x43653,a850)),f341(f341(f10(f864(x43653,f864(f864(f863(x43651,x43653),a850),a850)),f864(f864(f863(x43651,x43653),a850),f864(x43653,a850)),x43651),f9(x43653,f864(f863(x43651,x43653),a850),a850)),f341(f341(f10(f864(x43653,f863(x43651,x43653)),f864(x43653,f864(f864(f863(x43651,x43653),a850),a850)),x43651),f341(f10(f863(x43651,x43653),f864(f864(f863(x43651,x43653),a850),a850),x43653),f343(f863(x43651,x43653)))),f250(x43651,x43653)))),x43654))))),f341(f341(f9(x43652,f864(f863(x43653,x43652),a850),f864(x43653,a850)),f341(f341(f10(f864(x43653,f864(f864(f863(x43653,x43652),a850),a850)),f864(f864(f863(x43653,x43652),a850),f864(x43653,a850)),x43652),f9(x43653,f864(f863(x43653,x43652),a850),a850)),f341(f341(f10(f864(x43653,f863(x43653,x43652)),f864(x43653,f864(f864(f863(x43653,x43652),a850),a850)),x43652),f341(f10(f863(x43653,x43652),f864(f864(f863(x43653,x43652),a850),a850),x43653),f343(f863(x43653,x43652)))),f341(f9(x43653,x43652,f863(x43653,x43652)),f250(x43653,x43652))))),x43655))))),f341(f341(f290(x43651,x43653,x43652),x43654),x43655)) % 19.23/19.03 [4468]~E(f35(x44681,x44682,x44683),f33(x44684,x44685,x44686)) % 19.23/19.03 [4471]~E(f34(x44711,x44712,x44713),f33(x44714,x44715,x44716)) % 19.23/19.03 [4472]~E(f34(x44721,x44722,x44723),f35(x44724,x44725,x44726)) % 19.23/19.03 [3962]E(f226(x39621,x39622,x39623,x39624,f223(x39621,x39622,x39625,x39626)),f341(f341(x39624,x39625),x39626)) % 19.23/19.03 [3963]E(f227(x39631,x39632,x39633,x39634,f223(x39631,x39632,x39635,x39636)),f341(f341(x39634,x39635),x39636)) % 19.23/19.03 [4103]E(f177(x41031,x41032,f175(x41031,x41032,x41033,x41034),x41035,x41036),f175(x41031,x41032,x41033,f177(x41031,x41032,x41034,x41035,x41036))) % 19.23/19.03 [4225]E(f341(f82(f863(x42251,x42252),x42252,f863(x42253,x42254),f259(x42251,x42252)),f261(x42253,x42251,x42254,x42252,x42255,x42256)),f341(f82(x42254,x42252,f863(x42253,x42254),x42256),f259(x42253,x42254))) % 19.23/19.03 [4226]E(f341(f82(f863(x42261,x42262),x42261,f863(x42263,x42264),f249(x42261,x42262)),f261(x42263,x42261,x42264,x42262,x42265,x42266)),f341(f82(x42263,x42261,f863(x42263,x42264),x42265),f249(x42263,x42264))) % 19.23/19.03 [3828]E(f341(f341(f82(x38281,x38282,x38283,x38284),x38285),x38286),f341(x38284,f341(x38285,x38286))) % 19.23/19.03 [4025]E(f228(x40251,x40252,x40253,x40254,f223(x40251,x40252,x40255,x40256)),f341(f341(f89(a857),f341(f341(f89(a857),f341(x40253,x40255)),f341(x40254,x40256))),f341(a121,f2(a857)))) % 19.23/19.03 [4047]E(f341(f328(x40471,x40472,x40473,x40474,x40475),f341(f322(x40473,x40471),x40476)),f341(x40475,x40476)) % 19.23/19.03 [4048]E(f341(f328(x40481,x40482,x40483,x40484,x40485),f341(f313(x40481,x40483),x40486)),f341(x40484,x40486)) % 19.23/19.03 [4142]E(f329(x41421,x41422,x41423,x41424,x41425,f341(f322(x41423,x41421),x41426)),f341(x41425,x41426)) % 19.23/19.03 [4143]E(f329(x41431,x41432,x41433,x41434,x41435,f341(f313(x41431,x41433),x41436)),f341(x41434,x41436)) % 19.23/19.03 [3626]E(f341(f341(f260(x36261,x36262,x36263),x36264),f341(f341(f250(x36261,x36262),x36265),x36266)),f341(f341(x36264,x36265),x36266)) % 19.23/19.03 [3689]E(f341(f341(f341(f10(x36891,x36892,x36893),x36894),x36895),x36896),f341(x36894,f341(x36895,x36896))) % 19.23/19.03 [3690]E(f341(f341(f341(f9(x36901,x36902,x36903),x36904),x36905),x36906),f341(f341(x36904,x36906),x36905)) % 19.23/19.03 [3706]E(f341(f341(f341(f20(x37061,x37062,x37063),x37064),x37065),x37066),f341(f341(x37064,x37066),f341(x37065,x37066))) % 19.23/19.03 [3730]E(f341(f151(x37301,x37302,x37303,x37304),f341(f341(f146(x37302),x37305),x37306)),f341(f341(x37304,x37305),x37306)) % 19.23/19.03 [3831]E(f341(f341(f146(f863(x38311,x38312)),f341(f341(f250(x38311,x38312),x38313),x38314)),f341(f341(f172(x38311,x38312),x38315),x38316)),f341(f341(f172(x38311,x38312),f341(f341(f146(x38311),x38313),x38315)),f341(f341(f146(x38312),x38314),x38316))) % 19.23/19.03 [3833]E(f341(f341(f149(x38331,x38332),x38333),f341(f341(f154(x38331,x38334),x38335),x38336)),f341(f341(f154(x38332,f341(f341(f149(x38331,x38332),x38333),x38334)),x38335),f341(x38333,x38336))) % 19.23/19.03 [3858]E(f341(f341(f258(x38581,x38582,x38583,x38584),x38585),x38586),f341(x38584,f341(f341(f250(x38581,x38582),x38585),x38586))) % 19.23/19.03 [3875]E(f341(f138(x38751,x38752,x38753,x38754),f341(f341(f146(x38752),x38755),x38756)),f341(f138(x38751,x38752,x38753,f341(f341(x38753,x38754),x38755)),x38756)) % 19.23/19.03 [3903]E(f263(x39031,x39032,x39033,x39034,f341(f341(f250(x39031,x39032),x39035),x39036)),f341(f341(x39034,x39035),x39036)) % 19.23/19.03 [3988]E(f341(f341(f54(x39881,f864(x39882,a850)),x39883),f341(f82(x39884,f864(x39882,a850),x39881,x39885),x39886)),f341(f341(f54(x39884,f864(x39882,a850)),f341(f312(x39881,x39884,x39886),x39883)),x39885)) % 19.23/19.03 [4039]E(f341(f341(f149(x40391,x40392),x40393),f341(f341(f149(x40394,x40391),x40395),x40396)),f341(f341(f149(x40394,x40392),f341(f82(x40391,x40392,x40394,x40393),x40395)),x40396)) % 19.23/19.03 [4041]E(f341(f341(f204(x40411,x40412),x40413),f341(f341(f204(x40414,x40411),x40415),x40416)),f341(f341(f204(x40414,x40412),f341(f82(x40411,x40412,x40414,x40413),x40415)),x40416)) % 19.23/19.03 [4045]E(f341(f312(x40451,x40452,f341(f82(x40453,x40452,x40451,x40454),x40455)),x40456),f341(f312(x40453,x40452,x40454),f341(f312(x40451,x40453,x40455),x40456))) % 19.23/19.03 [4046]E(f341(f314(x40461,x40462,f341(f82(x40463,x40462,x40461,x40464),x40465)),x40466),f341(f314(x40461,x40463,x40465),f341(f314(x40463,x40462,x40464),x40466))) % 19.23/19.03 [4076]E(f175(x40761,x40762,x40763,f341(f341(f341(f81(x40761,f861(x40762)),x40764),x40765),f341(f235(x40762),x40766))),f341(f341(f341(f81(x40761,f861(x40762)),f175(x40761,x40762,x40763,x40764)),x40765),f341(f235(x40762),x40766))) % 19.23/19.03 [4078]E(f341(f138(x40781,x40782,x40783,f341(f138(x40781,x40782,x40783,x40784),x40785)),x40786),f341(f138(x40781,x40782,x40783,x40784),f341(f341(f132(x40782),x40785),x40786))) % 19.23/19.03 [4215]E(f341(f261(x42151,x42151,x42152,x42153,f41(x42151),x42154),f341(f341(f250(x42151,x42152),x42155),x42156)),f341(f341(f250(x42151,x42153),x42155),f341(x42154,x42156))) % 19.23/19.03 [4216]E(f341(f261(x42161,x42162,x42163,x42163,x42164,f41(x42163)),f341(f341(f250(x42161,x42163),x42165),x42166)),f341(f341(f250(x42162,x42163),f341(x42164,x42165)),x42166)) % 19.23/19.03 [4301]E(f341(f341(f149(f863(x43011,x43012),f863(x43011,x43013)),f341(f260(x43011,x43012,f863(x43011,x43013)),f341(f341(f9(x43011,f864(x43012,x43013),f864(x43012,f863(x43011,x43013))),f341(f341(f10(f864(x43013,f863(x43011,x43013)),f864(f864(x43012,x43013),f864(x43012,f863(x43011,x43013))),x43011),f10(x43013,f863(x43011,x43013),x43012)),f250(x43011,x43013))),x43014))),f341(f341(f172(x43011,x43012),x43015),x43016)),f341(f341(f172(x43011,x43013),x43015),f341(f341(f149(x43012,x43013),x43014),x43016))) % 19.23/19.03 [3694]E(f103(x36941,x36942,x36943,f341(f341(f341(f100(x36941),x36944),x36945),x36946)),f341(f341(f341(x36943,x36944),x36945),x36946)) % 19.23/19.03 [3695]E(f104(x36951,x36952,x36953,f341(f341(f341(f100(x36951),x36954),x36955),x36956)),f341(f341(f341(x36953,x36954),x36955),x36956)) % 19.23/19.03 [3886]E(f341(f341(f82(x38861,x38862,x38863,f341(f18(x38862,x38861),x38864)),x38865),x38866),x38864) % 19.23/19.03 [3920]E(f341(f312(x39201,x39202,x39203),f341(f312(x39204,x39201,x39205),x39206)),f341(f312(x39204,x39202,f341(f341(f10(x39201,x39202,x39204),x39203),x39205)),x39206)) % 19.23/19.03 [3926]E(f341(f341(f54(x39261,f864(x39262,a850)),f341(f312(x39263,x39261,x39264),x39265)),x39266),f341(f341(f54(x39263,f864(x39262,a850)),x39265),f341(f341(f10(x39261,f864(x39262,a850),x39263),x39266),x39264))) % 19.23/19.03 [3927]E(f341(f341(f55(x39271,f864(x39272,a850)),f341(f312(x39273,x39271,x39274),x39275)),x39276),f341(f341(f55(x39273,f864(x39272,a850)),x39275),f341(f341(f10(x39271,f864(x39272,a850),x39273),x39276),x39274))) % 19.23/19.03 [3928]E(f341(f341(f54(x39281,f864(x39282,a850)),x39283),f341(f341(f10(x39284,f864(x39282,a850),x39281),x39285),x39286)),f341(f341(f54(x39284,f864(x39282,a850)),f341(f312(x39281,x39284,x39286),x39283)),x39285)) % 19.23/19.03 [3929]E(f341(f341(f55(x39291,f864(x39292,a850)),x39293),f341(f341(f10(x39294,f864(x39292,a850),x39291),x39295),x39296)),f341(f341(f55(x39294,f864(x39292,a850)),f341(f312(x39291,x39294,x39296),x39293)),x39295)) % 19.23/19.03 [3990]E(f341(f341(f54(x39901,f864(x39902,a850)),x39903),f341(f341(f10(f864(x39904,a850),f864(x39902,a850),x39901),f312(x39904,x39902,x39905)),x39906)),f341(f312(x39904,x39902,x39905),f341(f341(f54(x39901,f864(x39904,a850)),x39903),x39906))) % 19.23/19.03 [3991]E(f341(f341(f54(x39911,f864(x39912,a850)),x39913),f341(f341(f10(f864(x39914,a850),f864(x39912,a850),x39911),f286(x39914,x39912,x39915)),x39916)),f341(f286(x39914,x39912,x39915),f341(f341(f54(x39911,f864(x39914,a850)),x39913),x39916))) % 19.23/19.03 [3992]E(f341(f341(f54(x39921,f864(x39922,a850)),x39923),f341(f341(f10(f864(x39924,a850),f864(x39922,a850),x39921),f314(x39922,x39924,x39925)),x39926)),f341(f314(x39922,x39924,x39925),f341(f341(f54(x39921,f864(x39924,a850)),x39923),x39926))) % 19.23/19.03 [3993]E(f341(f341(f55(x39931,f864(x39932,a850)),x39933),f341(f341(f10(f864(x39934,a850),f864(x39932,a850),x39931),f314(x39932,x39934,x39935)),x39936)),f341(f314(x39932,x39934,x39935),f341(f341(f55(x39931,f864(x39934,a850)),x39933),x39936))) % 19.23/19.03 [4084]E(f341(f138(x40841,x40842,f341(f9(x40842,x40841,x40841),x40843),x40844),f341(f148(x40842),f341(f341(f146(x40842),x40845),x40846))),f341(f341(x40843,x40845),f341(f138(x40841,x40842,f341(f9(x40842,x40841,x40841),x40843),x40844),f341(f148(x40842),x40846)))) % 19.23/19.03 [4144]E(f341(f341(f20(f863(x41441,x41442),x41442,x41443),f341(f341(f10(x41444,f864(x41442,x41443),f863(x41441,x41442)),x41445),f341(f341(f10(x41441,x41444,f863(x41441,x41442)),x41446),f249(x41441,x41442)))),f259(x41441,x41442)),f341(f260(x41441,x41442,x41443),f341(f341(f10(x41444,f864(x41442,x41443),x41441),x41445),x41446))) % 19.23/19.03 [4151]E(f341(f138(x41511,x41512,f341(f9(x41512,x41511,x41511),x41513),f341(f138(x41511,x41512,f341(f9(x41512,x41511,x41511),x41513),x41514),f341(f148(x41512),x41515))),f341(f148(x41512),x41516)),f341(f138(x41511,x41512,f341(f9(x41512,x41511,x41511),x41513),x41514),f341(f148(x41512),f341(f341(f132(x41512),x41516),x41515)))) % 19.23/19.03 [4153]E(f341(f341(f149(f863(x41531,x41532),f863(x41533,x41532)),f341(f260(x41531,x41532,f863(x41533,x41532)),f341(f341(f10(x41533,f864(x41532,f863(x41533,x41532)),x41531),f250(x41533,x41532)),x41534))),f341(f341(f172(x41531,x41532),x41535),x41536)),f341(f341(f172(x41533,x41532),f341(f341(f149(x41531,x41533),x41534),x41535)),x41536)) % 19.23/19.03 [4199]P85(f341(f341(f241(f864(x41991,a850)),f341(f286(x41992,x41991,x41993),f341(f341(f55(x41994,f864(x41992,a850)),x41995),x41996))),f341(f341(f55(x41994,f864(x41991,a850)),x41995),f341(f341(f10(f864(x41992,a850),f864(x41991,a850),x41994),f286(x41992,x41991,x41993)),x41996)))) % 19.23/19.03 [4003]E(f341(f341(f172(x40031,x40032),f341(f341(f154(x40031,x40033),x40034),f341(f249(x40031,x40032),x40035))),f341(f341(f154(x40032,x40036),x40034),f341(f259(x40031,x40032),x40035))),f341(f341(f154(f863(x40031,x40032),f341(f341(f172(x40031,x40032),x40033),x40036)),x40034),x40035)) % 19.23/19.03 [4066]E(f341(f341(f110(f864(f863(x40661,x40662),a850)),f341(f341(f290(x40661,x40663,x40662),x40664),x40665)),f341(f341(f290(x40661,x40663,x40662),x40664),x40666)),f341(f341(f290(x40661,x40663,x40662),x40664),f341(f341(f110(f864(f863(x40663,x40662),a850)),x40665),x40666))) % 19.23/19.03 [4165]E(f341(f341(f311(f863(x41651,x41652)),f341(f341(f250(x41651,x41652),x41653),x41654)),f341(f341(f110(f864(f863(x41651,x41652),a850)),f341(f341(f257(x41651,x41652),x41655),f341(f18(f864(x41652,a850),x41651),f341(f341(f311(x41652),x41654),x41656)))),f341(f341(f257(x41651,x41652),f341(f341(f311(x41651),x41653),x41655)),f341(f18(f864(x41652,a850),x41651),x41656)))),f341(f341(f257(x41651,x41652),f341(f341(f311(x41651),x41653),x41655)),f341(f18(f864(x41652,a850),x41651),f341(f341(f311(x41652),x41654),x41656)))) % 19.23/19.03 [4238]E(f341(f341(f111(f864(x42381,a850)),f341(f314(x42381,x42382,f341(f82(f863(x42382,x42383),x42382,x42381,f249(x42382,x42383)),x42384)),x42385)),f341(f314(x42381,x42383,f341(f82(f863(x42382,x42383),x42383,x42381,f259(x42382,x42383)),x42384)),x42386)),f341(f314(x42381,f863(x42382,x42383),x42384),f341(f341(f257(x42382,x42383),x42385),f341(f18(f864(x42383,a850),x42382),x42386)))) % 19.23/19.03 [3987]E(f341(f341(f341(f81(x39871,x39872),f341(f341(f341(f81(x39871,x39872),x39873),x39874),x39875)),x39874),x39876),f341(f341(f341(f81(x39871,x39872),x39873),x39874),x39876)) % 19.23/19.03 [4090]E(f341(f341(f110(f864(f863(x40901,x40902),a850)),f341(f341(f290(x40901,x40903,x40902),x40904),x40905)),f341(f341(f290(x40901,x40903,x40902),x40906),x40905)),f341(f341(f290(x40901,x40903,x40902),f341(f341(f110(f864(f863(x40901,x40903),a850)),x40904),x40906)),x40905)) % 19.23/19.03 [4223]E(f341(f341(f54(x42231,f864(x42232,a850)),x42233),f341(f341(f9(x42231,f864(x42234,f864(x42232,a850)),f864(x42232,a850)),f341(f341(f10(f864(x42234,a850),f864(f864(x42234,f864(x42232,a850)),f864(x42232,a850)),x42231),f54(x42234,f864(x42232,a850))),x42235)),x42236)),f341(f341(f54(x42234,f864(x42232,a850)),f341(f341(f54(x42231,f864(x42234,a850)),x42233),x42235)),x42236)) % 19.23/19.03 [4224]E(f341(f341(f55(x42241,f864(x42242,a850)),x42243),f341(f341(f9(x42241,f864(x42244,f864(x42242,a850)),f864(x42242,a850)),f341(f341(f10(f864(x42244,a850),f864(f864(x42244,f864(x42242,a850)),f864(x42242,a850)),x42241),f55(x42244,f864(x42242,a850))),x42245)),x42246)),f341(f341(f55(x42244,f864(x42242,a850)),f341(f341(f54(x42241,f864(x42244,a850)),x42243),x42245)),x42246)) % 19.23/19.03 [4273]E(f341(f260(x42731,x42732,f863(x42733,x42734)),f341(f341(f9(x42731,f864(x42732,x42734),f864(x42732,f863(x42733,x42734))),f341(f341(f10(f864(x42734,f863(x42733,x42734)),f864(f864(x42732,x42734),f864(x42732,f863(x42733,x42734))),x42731),f10(x42734,f863(x42733,x42734),x42732)),f341(f341(f10(x42733,f864(x42734,f863(x42733,x42734)),x42731),f250(x42733,x42734)),x42735))),x42736)),f261(x42731,x42733,x42732,x42734,x42735,x42736)) % 19.23/19.03 [4198]E(f341(f341(f341(f81(x41981,f861(x41982)),f178(x41981,x41982,x41983,f341(f341(f3(f864(x41981,a850)),x41984),f341(f341(f311(x41981),x41985),f185(f864(x41981,a850)))))),x41985),x41986),f341(f341(f341(f81(x41981,f861(x41982)),f178(x41981,x41982,x41983,x41984)),x41985),x41986)) % 19.23/19.03 [4296]E(f341(f312(x42961,x42962,f341(f341(f20(x42961,x42962,x42962),f341(f341(f20(x42961,x42962,f864(x42962,x42962)),f341(f341(f10(a850,f864(x42962,f864(x42962,x42962)),x42961),f105(x42962)),x42963)),x42964)),x42965)),x42966),f341(f341(f110(f864(x42962,a850)),f341(f312(x42961,x42962,x42964),f341(f341(f111(f864(x42961,a850)),x42966),f341(f265(x42961),x42963)))),f341(f312(x42961,x42962,x42965),f341(f341(f111(f864(x42961,a850)),x42966),f341(f265(x42961),f341(f341(f10(a850,a850,x42961),a337),x42963)))))) % 19.23/19.03 [4307]E(f341(f312(x43071,f863(x43072,x43073),f341(f341(f20(x43071,x43073,f863(x43072,x43073)),f341(f341(f10(x43072,f864(x43073,f863(x43072,x43073)),x43071),f250(x43072,x43073)),x43074)),x43075)),x43076),f341(f341(f257(x43072,x43073),f341(f312(x43071,x43072,x43074),x43076)),f341(f341(f10(f864(x43071,a850),f864(x43073,a850),x43072),f312(x43071,x43073,x43075)),f341(f341(f9(x43072,f864(x43071,a850),f864(x43071,a850)),f341(f341(f10(f864(x43071,a850),f864(f864(x43071,a850),f864(x43071,a850)),x43072),f111(f864(x43071,a850))),f341(f341(f10(f864(x43072,a850),f864(x43071,a850),x43072),f314(x43071,x43072,x43074)),f341(f341(f9(x43072,f864(x43072,a850),f864(x43072,a850)),f311(x43072)),f185(f864(x43072,a850)))))),x43076)))) % 19.23/19.03 [4256]E(f341(f259(x42561,x42562),f341(f261(x42563,x42561,x42564,x42562,x42565,x42566),x42567)),f341(x42566,f341(f259(x42563,x42564),x42567))) % 19.23/19.03 [4257]E(f341(f249(x42571,x42572),f341(f261(x42573,x42571,x42574,x42572,x42575,x42576),x42577)),f341(x42575,f341(f249(x42573,x42574),x42577))) % 19.23/19.03 [3964]E(f341(f341(f172(x39641,x39642),f341(f341(f154(x39641,x39643),x39644),x39645)),f341(f341(f154(x39642,x39646),x39644),x39647)),f341(f341(f154(f863(x39641,x39642),f341(f341(f172(x39641,x39642),x39643),x39646)),x39644),f341(f341(f250(x39641,x39642),x39645),x39647))) % 19.23/19.03 [4034]E(f341(f341(f341(f262(x40341,x40342,x40343,x40344),x40345),x40346),x40347),f341(f341(f260(x40342,x40343,x40344),x40346),f341(x40345,x40347))) % 19.23/19.03 [4044]E(f341(f341(f341(f262(x40441,x40442,x40443,x40444),x40445),x40446),x40447),f341(f341(x40446,f341(f249(x40442,x40443),f341(x40445,x40447))),f341(f259(x40442,x40443),f341(x40445,x40447)))) % 19.23/19.03 [4080]E(f177(x40801,x40802,f341(f341(f341(f81(x40801,f861(x40802)),x40803),x40804),f341(f235(x40802),x40805)),x40806,x40807),f177(x40801,x40802,x40803,f341(f341(f146(x40801),x40804),x40806),f341(f341(f146(x40802),x40805),x40807))) % 19.23/19.03 [4097]E(f341(f82(x40971,x40972,x40973,x40974),f341(f82(x40975,x40971,x40973,x40976),x40977)),f341(f82(x40975,x40972,x40973,f341(f82(x40971,x40972,x40975,x40974),x40976)),x40977)) % 19.23/19.03 [4160]E(f341(f82(f861(x41601),f861(x41602),x41603,f341(f204(x41601,x41602),x41604)),f341(f341(f341(f81(x41603,f861(x41601)),x41605),x41606),f341(f235(x41601),x41607))),f341(f341(f341(f81(x41603,f861(x41602)),f341(f82(f861(x41601),f861(x41602),x41603,f341(f204(x41601,x41602),x41604)),x41605)),x41606),f341(f235(x41602),f341(x41604,x41607)))) % 19.23/19.03 [4280]E(f341(f261(x42801,x42802,x42803,x42803,x42804,f41(x42803)),f341(f261(x42801,x42801,x42805,x42803,f41(x42801),x42806),x42807)),f341(f341(f250(x42802,x42803),f341(x42804,f341(f249(x42801,x42805),x42807))),f341(x42806,f341(f259(x42801,x42805),x42807)))) % 19.23/19.03 [4281]E(f341(f261(x42811,x42811,x42812,x42813,f41(x42811),x42814),f341(f261(x42815,x42811,x42812,x42812,x42816,f41(x42812)),x42817)),f341(f341(f250(x42811,x42813),f341(x42816,f341(f249(x42815,x42812),x42817))),f341(x42814,f341(f259(x42815,x42812),x42817)))) % 19.23/19.03 [4294]E(f341(f261(x42941,x42942,x42943,x42943,x42944,f41(x42943)),f341(f261(x42945,x42941,x42943,x42943,x42946,f41(x42943)),x42947)),f341(f261(x42945,x42942,x42943,x42943,f341(f82(x42941,x42942,x42945,x42944),x42946),f41(x42943)),x42947)) % 19.23/19.03 [4295]E(f341(f261(x42951,x42951,x42952,x42953,f41(x42951),x42954),f341(f261(x42951,x42951,x42955,x42952,f41(x42951),x42956),x42957)),f341(f261(x42951,x42951,x42955,x42953,f41(x42951),f341(f82(x42952,x42953,x42955,x42954),x42956)),x42957)) % 19.23/19.03 [4304]E(f341(f261(x43041,x43042,x43043,x43043,x43044,f41(x43043)),f341(f261(x43041,x43041,x43045,x43043,f41(x43041),x43046),x43047)),f341(f261(x43042,x43042,x43045,x43043,f41(x43042),x43046),f341(f261(x43041,x43042,x43045,x43045,x43044,f41(x43045)),x43047))) % 19.23/19.03 [4000]E(f341(f341(f290(x40001,x40002,x40003),f341(f341(f290(x40001,x40004,x40002),x40005),x40006)),x40007),f341(f341(f290(x40001,x40004,x40003),x40005),f341(f341(f290(x40004,x40002,x40003),x40006),x40007))) % 19.23/19.03 [4072]E(f341(f341(f260(x40721,x40722,x40723),f341(f82(x40724,f864(x40722,x40723),x40721,x40725),x40726)),x40727),f341(f341(x40725,f341(x40726,f341(f249(x40721,x40722),x40727))),f341(f259(x40721,x40722),x40727))) % 19.23/19.03 [4122]E(f341(f82(x41221,x41222,x41223,x41224),f341(f341(f341(f81(x41223,x41221),x41225),x41226),x41227)),f341(f341(f341(f81(x41223,x41222),f341(f82(x41221,x41222,x41223,x41224),x41225)),x41226),f341(x41224,x41227))) % 19.23/19.03 [4156]E(f341(f138(x41561,x41562,f341(f9(x41562,x41561,x41561),x41563),x41564),f341(f148(x41562),f341(f341(f149(x41565,x41562),x41566),x41567))),f341(f138(x41561,x41565,f341(f9(x41565,x41561,x41561),f341(f82(x41562,f864(x41561,x41561),x41565,x41563),x41566)),x41564),f341(f148(x41565),x41567))) % 19.23/19.03 [4161]E(f328(x41611,f861(x41612),x41613,f341(f82(f861(x41614),f861(x41612),x41611,f341(f204(x41614,x41612),x41615)),x41616),f341(f82(f861(x41614),f861(x41612),x41613,f341(f204(x41614,x41612),x41615)),x41617)),f341(f82(f861(x41614),f861(x41612),f865(x41611,x41613),f341(f204(x41614,x41612),x41615)),f328(x41611,f861(x41614),x41613,x41616,x41617))) % 19.23/19.03 [4098]E(f341(f341(f54(x40981,f864(f863(x40982,x40983),a850)),x40984),f341(f341(f10(f864(f863(x40985,x40983),a850),f864(f863(x40982,x40983),a850),x40981),f341(f290(x40982,x40985,x40983),x40986)),x40987)),f341(f341(f290(x40982,x40985,x40983),x40986),f341(f341(f54(x40981,f864(f863(x40985,x40983),a850)),x40984),x40987))) % 19.23/19.03 [4243]E(f341(f341(f54(x42431,f864(f863(x42432,x42433),a850)),x42434),f341(f341(f9(x42431,f864(f863(x42435,x42433),a850),f864(f863(x42432,x42433),a850)),f341(f341(f10(f864(f863(x42432,x42435),a850),f864(f864(f863(x42435,x42433),a850),f864(f863(x42432,x42433),a850)),x42431),f290(x42432,x42435,x42433)),x42436)),x42437)),f341(f341(f290(x42432,x42435,x42433),f341(f341(f54(x42431,f864(f863(x42432,x42435),a850)),x42434),x42436)),x42437)) % 19.23/19.03 [4244]E(f341(f138(x42441,x42442,f341(f341(f9(x42441,f864(x42442,x42443),f864(x42442,x42441)),f341(f341(f10(f864(x42443,x42441),f864(f864(x42442,x42443),f864(x42442,x42441)),x42441),f10(x42443,x42441,x42442)),x42444)),x42445),x42446),x42447),f341(f138(x42441,x42443,x42444,x42446),f341(f341(f149(x42442,x42443),x42445),x42447))) % 19.23/19.03 [4305]E(f341(f341(f55(x43051,f864(x43052,a850)),x43053),f341(f341(f10(f864(x43054,f864(x43052,a850)),f864(x43052,a850),x43051),f341(f55(x43054,f864(x43052,a850)),x43055)),f341(f341(f9(x43051,f864(x43054,f864(x43052,a850)),f864(x43054,f864(x43052,a850))),f341(f341(f10(f864(f864(x43052,a850),f864(x43052,a850)),f864(f864(x43054,f864(x43052,a850)),f864(x43054,f864(x43052,a850))),x43051),f10(f864(x43052,a850),f864(x43052,a850),x43054)),f341(f341(f10(f864(x43052,a850),f864(f864(x43052,a850),f864(x43052,a850)),x43051),f110(f864(x43052,a850))),x43056))),x43057))),f341(f341(f110(f864(x43052,a850)),f341(f341(f55(x43051,f864(x43052,a850)),x43053),x43056)),f341(f341(f55(x43054,f864(x43052,a850)),x43055),x43057))) % 19.23/19.03 [4306]E(f341(f341(f54(x43061,f864(x43062,a850)),x43063),f341(f341(f10(f864(x43064,f864(x43062,a850)),f864(x43062,a850),x43061),f341(f54(x43064,f864(x43062,a850)),x43065)),f341(f341(f9(x43061,f864(x43064,f864(x43062,a850)),f864(x43064,f864(x43062,a850))),f341(f341(f10(f864(f864(x43062,a850),f864(x43062,a850)),f864(f864(x43064,f864(x43062,a850)),f864(x43064,f864(x43062,a850))),x43061),f10(f864(x43062,a850),f864(x43062,a850),x43064)),f341(f341(f10(f864(x43062,a850),f864(f864(x43062,a850),f864(x43062,a850)),x43061),f111(f864(x43062,a850))),x43066))),x43067))),f341(f341(f111(f864(x43062,a850)),f341(f341(f54(x43061,f864(x43062,a850)),x43063),x43066)),f341(f341(f54(x43064,f864(x43062,a850)),x43065),x43067))) % 19.23/19.03 [4299]E(f200(x42991,x42992,f341(f341(f341(x42993,x42994),x42995),x42996),f341(f341(f9(x42991,f863(a108,a108),f864(a108,f859(x42992))),f341(f341(f9(x42991,a108,f864(f863(a108,a108),f864(a108,f859(x42992)))),f341(f341(f9(x42991,a108,f864(a108,f864(f863(a108,a108),f864(a108,f859(x42992))))),x42997),x42994)),x42995)),x42996)),f341(f341(f341(f212(x42991,x42992,x42993,x42997),x42994),x42995),x42996)) % 19.23/19.03 [4312]E(f201(x43121,x43122,f341(f341(f341(x43123,x43124),x43125),x43126),f341(f341(f9(x43121,f863(a108,a108),f864(a108,f859(x43122))),f341(f341(f9(x43121,a108,f864(f863(a108,a108),f864(a108,f859(x43122)))),f341(f341(f9(x43121,a108,f864(a108,f864(f863(a108,a108),f864(a108,f859(x43122))))),x43127),x43124)),x43125)),x43126)),f214(x43121,x43122,x43123,x43127,x43124,x43125,x43126)) % 19.23/19.03 [4303]E(f198(x43031,x43032,f341(f341(f341(x43033,x43034),x43035),x43036),f341(f341(f9(x43031,f863(a108,a108),f864(a108,f859(f861(x43032)))),f341(f341(f9(x43031,a108,f864(f863(a108,a108),f864(a108,f859(f861(x43032))))),f341(f341(f9(x43031,a108,f864(a108,f864(f863(a108,a108),f864(a108,f859(f861(x43032)))))),x43037),x43034)),x43035)),x43036)),f341(f341(f341(f208(x43031,x43032,x43033,x43037),x43034),x43035),x43036)) % 19.23/19.03 [4314]E(f199(x43141,x43142,f341(f341(f341(x43143,x43144),x43145),x43146),f341(f341(f9(x43141,f863(a108,a108),f864(a108,f859(f861(x43142)))),f341(f341(f9(x43141,a108,f864(f863(a108,a108),f864(a108,f859(f861(x43142))))),f341(f341(f9(x43141,a108,f864(a108,f864(f863(a108,a108),f864(a108,f859(f861(x43142)))))),x43147),x43144)),x43145)),x43146)),f210(x43141,x43142,x43143,x43147,x43144,x43145,x43146)) % 19.23/19.03 [4217]E(f341(f261(x42171,x42172,x42173,x42174,x42175,x42176),f341(f341(f250(x42171,x42173),x42177),x42178)),f341(f341(f250(x42172,x42174),f341(x42175,x42177)),f341(x42176,x42178))) % 19.23/19.03 [4316]E(f341(f341(f149(f863(x43161,x43162),f863(x43163,x43164)),f341(f260(x43161,x43162,f863(x43163,x43164)),f341(f341(f9(x43161,f864(x43162,x43164),f864(x43162,f863(x43163,x43164))),f341(f341(f10(f864(x43164,f863(x43163,x43164)),f864(f864(x43162,x43164),f864(x43162,f863(x43163,x43164))),x43161),f10(x43164,f863(x43163,x43164),x43162)),f341(f341(f10(x43163,f864(x43164,f863(x43163,x43164)),x43161),f250(x43163,x43164)),x43165))),x43166))),f341(f341(f172(x43161,x43162),x43167),x43168)),f341(f341(f172(x43163,x43164),f341(f341(f149(x43161,x43163),x43165),x43167)),f341(f341(f149(x43162,x43164),x43166),x43168))) % 19.23/19.03 [4320]E(f341(f341(f149(f863(x43201,x43202),x43203),f341(f260(x43201,x43202,x43203),f341(f341(f10(f864(x43202,f863(x43201,x43204)),f864(x43202,x43203),x43201),f341(f10(f863(x43201,x43204),x43203,x43202),x43205)),f341(f341(f9(x43201,f864(x43202,x43204),f864(x43202,f863(x43201,x43204))),f341(f341(f10(f864(x43204,f863(x43201,x43204)),f864(f864(x43202,x43204),f864(x43202,f863(x43201,x43204))),x43201),f10(x43204,f863(x43201,x43204),x43202)),f250(x43201,x43204))),x43206)))),f341(f341(f172(x43201,x43202),x43207),x43208)),f341(f341(f149(f863(x43201,x43204),x43203),x43205),f341(f341(f172(x43201,x43204),x43207),f341(f341(f149(x43202,x43204),x43206),x43208)))) % 19.23/19.03 [4248]E(f341(f341(f149(f863(x42481,x42482),x42483),f341(f260(x42481,x42482,x42483),f341(f341(f10(f864(x42482,f863(x42484,x42482)),f864(x42482,x42483),x42481),f341(f10(f863(x42484,x42482),x42483,x42482),x42485)),f341(f341(f10(x42484,f864(x42482,f863(x42484,x42482)),x42481),f250(x42484,x42482)),x42486)))),f341(f341(f172(x42481,x42482),x42487),x42488)),f341(f341(f149(f863(x42484,x42482),x42483),x42485),f341(f341(f172(x42484,x42482),f341(f341(f149(x42481,x42484),x42486),x42487)),x42488))) % 19.23/19.03 [4208]E(f341(f341(f260(x42081,x42082,x42083),f341(f341(f10(f864(x42082,f863(x42084,x42085)),f864(x42082,x42083),x42081),f341(f10(f863(x42084,x42085),x42083,x42082),f341(f260(x42084,x42085,x42083),x42086))),x42087)),x42088),f341(f341(f260(x42084,x42085,x42083),x42086),f341(f341(f260(x42081,x42082,f863(x42084,x42085)),x42087),x42088))) % 19.23/19.03 [4321]E(f341(f341(f54(f863(x43211,x43212),f864(f863(x43213,x43214),a850)),f341(f341(f257(x43211,x43212),x43215),f341(f18(f864(x43212,a850),x43211),x43216))),f341(f260(x43211,x43212,f864(f863(x43213,x43214),a850)),f341(f341(f9(x43211,f864(x43212,f864(x43213,f864(x43214,a850))),f864(x43212,f864(f863(x43213,x43214),a850))),f341(f341(f10(f864(f864(x43213,f864(x43214,a850)),f864(f863(x43213,x43214),a850)),f864(f864(x43212,f864(x43213,f864(x43214,a850))),f864(x43212,f864(f863(x43213,x43214),a850))),x43211),f10(f864(x43213,f864(x43214,a850)),f864(f863(x43213,x43214),a850),x43212)),f341(f341(f10(f864(x43213,a850),f864(f864(x43213,f864(x43214,a850)),f864(f863(x43213,x43214),a850)),x43211),f257(x43213,x43214)),x43217))),f341(f341(f10(f864(x43214,a850),f864(x43213,f864(x43214,a850)),x43212),f18(f864(x43214,a850),x43213)),x43218)))),f341(f341(f257(x43213,x43214),f341(f341(f54(x43211,f864(x43213,a850)),x43215),x43217)),f341(f18(f864(x43214,a850),x43213),f341(f341(f54(x43212,f864(x43214,a850)),x43216),x43218)))) % 19.23/19.03 [4350]E(f39(x43501,x43502,x43503,x43504,x43505,x43506,x43507,x43508,x43509,a25),x43502) % 19.23/19.03 [4351]E(f40(x43511,x43512,x43513,x43514,x43515,x43516,x43517,x43518,x43519,a25),x43512) % 19.23/19.03 [4262]E(f341(f341(f262(x42621,x42622,x42623,x42624),f341(f341(f262(x42621,x42625,x42626,f863(x42622,x42623)),x42627),x42628)),x42629),f341(f341(f262(x42621,x42625,x42626,x42624),x42627),f341(f341(f9(x42625,f864(x42622,f864(x42623,x42624)),f864(x42626,x42624)),f341(f341(f10(f864(x42626,f863(x42622,x42623)),f864(f864(x42622,f864(x42623,x42624)),f864(x42626,x42624)),x42625),f262(x42626,x42622,x42623,x42624)),x42628)),x42629))) % 19.23/19.03 [4352]E(f39(x43521,x43522,x43523,x43524,x43525,x43526,x43527,x43528,x43529,f341(a29,x435210)),f341(x43528,x435210)) % 19.23/19.03 [4353]E(f40(x43531,x43532,x43533,x43534,x43535,x43536,x43537,x43538,x43539,f341(a29,x435310)),f341(x43538,x435310)) % 19.23/19.03 [4292]E(f341(f82(f863(x42921,x42922),f863(x42923,x42924),f863(x42925,x42926),f261(x42921,x42923,x42922,x42924,x42927,x42928)),f261(x42925,x42921,x42926,x42922,x42929,x429210)),f261(x42925,x42923,x42926,x42924,f341(f82(x42921,x42923,x42925,x42927),x42929),f341(f82(x42922,x42924,x42926,x42928),x429210))) % 19.23/19.03 [4354]E(f39(x43541,x43542,x43543,x43544,x43545,x43546,x43547,x43548,x43549,f30(x435410,x435411)),f341(f341(x43543,x435410),x435411)) % 19.23/19.03 [4355]E(f39(x43551,x43552,x43553,x43554,x43555,x43556,x43557,x43558,x43559,f38(x435510,x435511)),f341(f341(x43555,x435510),x435511)) % 19.23/19.03 [4356]E(f39(x43561,x43562,x43563,x43564,x43565,x43566,x43567,x43568,x43569,f37(x435610,x435611)),f341(f341(x43567,x435610),x435611)) % 19.23/19.03 [4357]E(f40(x43571,x43572,x43573,x43574,x43575,x43576,x43577,x43578,x43579,f30(x435710,x435711)),f341(f341(x43573,x435710),x435711)) % 19.23/19.03 [4363]E(f341(f341(f341(x43631,x43632),x43633),f40(x43634,x43635,x43636,x43637,x43638,x43639,x43631,x436310,x436311,x43633)),f40(x43634,x43635,x43636,x43637,x43638,x43639,x43631,x436310,x436311,f37(x43632,x43633))) % 19.23/19.03 [4367]E(f341(f341(f341(f341(x43671,x43672),x43673),f40(x43674,x43675,x43676,x43677,x43671,x43678,x43679,x436710,x436711,x43672)),f40(x43674,x43675,x43676,x43677,x43671,x43678,x43679,x436710,x436711,x43673)),f40(x43674,x43675,x43676,x43677,x43671,x43678,x43679,x436710,x436711,f38(x43672,x43673))) % 19.23/19.03 [4297]E(f341(f261(x42971,x42972,x42973,x42974,x42975,x42976),f341(f261(x42977,x42971,x42978,x42973,x42979,x429710),x429711)),f341(f261(x42977,x42972,x42978,x42974,f341(f82(x42971,x42972,x42977,x42975),x42979),f341(f82(x42973,x42974,x42978,x42976),x429710)),x429711)) % 19.23/19.03 [4364]E(f341(f341(f341(f341(x43641,x43642),x43643),x43644),f40(x43645,x43646,x43647,x43641,x43648,x43649,x436410,x436411,x436412,x43644)),f40(x43645,x43646,x43647,x43641,x43648,x43649,x436410,x436411,x436412,f34(x43642,x43643,x43644))) % 19.23/19.03 [4368]E(f341(f341(f341(f341(f341(x43681,x43682),x43683),x43684),f40(x43685,x43686,x43687,x43688,x43689,x43681,x436810,x436811,x436812,x43683)),f40(x43685,x43686,x43687,x43688,x43689,x43681,x436810,x436811,x436812,x43684)),f40(x43685,x43686,x43687,x43688,x43689,x43681,x436810,x436811,x436812,f35(x43682,x43683,x43684))) % 19.23/19.03 [4358]E(f39(x43581,x43582,x43583,x43584,x43585,x43586,x43587,x43588,x43589,f33(x435810,x435811,x435812)),f341(f341(f341(x43589,x435810),x435811),x435812)) % 19.23/19.03 [4359]E(f39(x43591,x43592,x43593,x43594,x43595,x43596,x43597,x43598,x43599,f35(x435910,x435911,x435912)),f341(f341(f341(x43596,x435910),x435911),x435912)) % 19.23/19.03 [4360]E(f39(x43601,x43602,x43603,x43604,x43605,x43606,x43607,x43608,x43609,f34(x436010,x436011,x436012)),f341(f341(f341(x43604,x436010),x436011),x436012)) % 19.23/19.03 [4361]E(f40(x43611,x43612,x43613,x43614,x43615,x43616,x43617,x43618,x43619,f33(x436110,x436111,x436112)),f341(f341(f341(x43619,x436110),x436111),x436112)) % 19.23/19.03 [6369]P10(a5000)+P85(f341(f341(f343(f863(a853,a851)),a712),f341(f163(f863(a853,a851)),a31))) % 19.23/19.03 [8403]P10(a5000)+~P85(f341(f341(f260(a853,a851,a850),f341(f18(f864(a851,a850),a853),a26)),a712)) % 19.23/19.03 [4502]~P58(x45021)+P58(f861(x45021)) % 19.23/19.03 [4505]~P140(x45051)+~E(f87(x45051),f2(x45051)) % 19.23/19.03 [4507]~E(x45071,f2(a108))+E(f341(a23,x45071),f2(a1)) % 19.23/19.03 [4508]~E(x45081,f2(a1))+E(f91(a1,x45081),f2(a1)) % 19.23/19.03 [4514]~P112(x45141)+P32(x45141,f2(x45141)) % 19.23/19.03 [4516]~P101(x45161)+P15(x45161,f122(x45161)) % 19.23/19.03 [4525]P85(x45251)+P85(f341(a337,x45251)) % 19.23/19.03 [4566]~P112(x45661)+~P32(x45661,f87(x45661)) % 19.23/19.03 [4610]~P85(x46101)+~P85(f341(a337,x46101)) % 19.23/19.03 [4634]E(f341(a114,x46341),f2(a857))+~P85(f341(a191,x46341)) % 19.23/19.03 [4694]~P92(x46941)+P16(x46941,x46941,f90(x46941)) % 19.23/19.03 [4695]~P101(x46951)+P16(x46951,x46951,f245(x46951)) % 19.23/19.03 [4696]~P101(x46961)+P16(x46961,x46961,f240(x46961)) % 19.23/19.03 [4697]~P98(x46971)+P16(x46971,x46971,f110(x46971)) % 19.23/19.03 [4698]~P99(x46981)+P16(x46981,x46981,f111(x46981)) % 19.23/19.03 [4699]~P65(x46991)+P17(x46991,x46991,f90(x46991)) % 19.23/19.03 [4512]E(x45121,f2(a857))+E(f341(a121,f606(x45121)),x45121) % 19.23/19.03 [4513]~E(x45131,f2(a857))+E(f341(f109(a1),x45131),f2(a1)) % 19.23/19.03 [4519]~P89(x45191)+E(f341(f113(x45191),a92),f2(x45191)) % 19.23/19.03 [4521]~E(f622(x45211),f2(a857))+E(f341(f160(a857),x45211),f2(a857)) % 19.23/19.03 [4522]~P103(x45221)+E(f243(x45221,f241(x45221)),f245(x45221)) % 19.23/19.03 [4523]~P103(x45231)+E(f244(x45231,f241(x45231)),f240(x45231)) % 19.23/19.03 [4524]~P82(x45241)+E(f91(x45241,f2(x45241)),f2(x45241)) % 19.23/19.03 [4531]~P112(x45311)+E(f341(f109(x45311),f2(a857)),f2(x45311)) % 19.23/19.03 [4532]~P112(x45321)+E(f341(f109(x45321),f87(a857)),f87(x45321)) % 19.23/19.03 [4533]~P136(x45331)+E(f341(f112(x45331),f2(a1)),f2(x45331)) % 19.23/19.03 [4534]~P136(x45341)+E(f341(f112(x45341),f87(a1)),f87(x45341)) % 19.23/19.03 [4535]E(x45351,f2(a857))+~E(f341(f109(a1),x45351),f2(a1)) % 19.23/19.03 [4560]~P70(x45601)+E(f341(f88(x45601),f2(x45601)),f2(x45601)) % 19.23/19.03 [4561]~P91(x45611)+E(f341(f88(x45611),f185(x45611)),f248(x45611)) % 19.23/19.03 [4562]~P91(x45621)+E(f341(f88(x45621),f248(x45621)),f185(x45621)) % 19.23/19.03 [4563]~P79(x45631)+E(f341(f84(x45631),f2(x45631)),f2(x45631)) % 19.23/19.03 [4564]~P113(x45641)+E(f341(f84(x45641),f87(x45641)),f87(x45641)) % 19.23/19.03 [4565]~P67(x45651)+E(f341(f160(x45651),f122(x45651)),f2(x45651)) % 19.23/19.03 [4586]~P34(x45861)+P37(f341(f163(a1),x45861)) % 19.23/19.03 [4615]~P89(x46151)+E(f341(f88(x46151),f87(x46151)),f341(f113(x46151),a106)) % 19.23/19.03 [4633]~P89(x46331)+P32(x46331,f341(f113(x46331),a92)) % 19.23/19.03 [4658]P34(x46581)+~P37(f341(f163(a1),x46581)) % 19.23/19.03 [4700]E(f341(f109(a1),f341(a114,x47001)),x47001)+P85(f341(a191,x47001)) % 19.23/19.03 [4766]~P106(x47661)+E(f252(x47661,f87(x47661),f90(x47661)),f251(x47661)) % 19.23/19.03 [4794]~P89(x47941)+~P32(x47941,f341(f113(x47941),a106)) % 19.23/19.03 [4804]E(f341(a32,x48041),f188(a851))+P85(f341(a26,f341(a29,x48041))) % 19.23/19.03 [4934]E(f341(f84(a1),x49341),x49341)+P85(f341(f341(f242(a1),x49341),f2(a1))) % 19.23/19.03 [4954]~E(f341(a114,x49541),f2(a857))+P85(f341(f341(f241(a1),x49541),f2(a1))) % 19.23/19.03 [4990]~E(f341(f84(a1),x49901),f87(a1))+P85(f341(f341(f288(a1),x49901),f87(a1))) % 19.23/19.03 [5020]~P85(f341(a191,x50201))+P85(f341(f341(f242(a1),x50201),f2(a1))) % 19.23/19.03 [5060]~P120(x50601)+P85(f341(f341(f242(x50601),f2(x50601)),f87(x50601))) % 19.23/19.03 [5061]~P120(x50611)+P85(f341(f341(f241(x50611),f2(x50611)),f87(x50611))) % 19.23/19.03 [5062]~P112(x50621)+P85(f341(f341(f343(x50621),f2(x50621)),f182(x50621))) % 19.23/19.03 [5063]~P136(x50631)+P85(f341(f341(f343(x50631),f2(x50631)),f119(x50631))) % 19.23/19.03 [5064]~P112(x50641)+P85(f341(f341(f343(x50641),f87(x50641)),f182(x50641))) % 19.23/19.03 [5065]~P136(x50651)+P85(f341(f341(f343(x50651),f87(x50651)),f119(x50651))) % 19.23/19.03 [5068]E(f341(f235(a851),f457(x50681)),f341(a32,x50681))+~P85(f341(a26,f341(a29,x50681))) % 19.23/19.03 [5069]E(f341(f235(a851),f553(x50691)),f341(a32,x50691))+~P85(f341(a26,f341(a29,x50691))) % 19.23/19.03 [5118]E(x51181,f2(a857))+~P85(f341(f341(f241(a857),x51181),f2(a857))) % 19.23/19.03 [5119]E(x51191,f87(a857))+~P85(f341(f341(f288(a857),x51191),f87(a857))) % 19.23/19.03 [5160]E(f341(a114,x51601),f2(a857))+~P85(f341(f341(f241(a1),x51601),f2(a1))) % 19.23/19.03 [5187]E(f341(f84(a1),x51871),f87(a1))+~P85(f341(f341(f288(a1),x51871),f87(a1))) % 19.23/19.03 [5214]P85(f341(a191,x52141))+~P85(f341(f341(f242(a1),x52141),f2(a1))) % 19.23/19.03 [5219]~P101(x52191)+P17(x52191,f858(x52191),f144(x52191,x52191,f7(x52191))) % 19.23/19.03 [5236]P37(x52361)+~P85(f341(f341(f241(a1),f2(a1)),f371(x52361))) % 19.23/19.03 [5242]E(f341(f84(a1),x52421),f341(f88(a1),x52421))+~P85(f341(f341(f242(a1),x52421),f2(a1))) % 19.23/19.03 [5412]~P120(x54121)+~P85(f341(f341(f242(x54121),f87(x54121)),f2(x54121))) % 19.23/19.03 [5413]~P120(x54131)+~P85(f341(f341(f241(x54131),f87(x54131)),f2(x54131))) % 19.23/19.03 [5425]~E(x54251,f2(a1))+P85(f341(f341(f242(a1),f341(f84(a1),x54251)),f87(a1))) % 19.23/19.03 [5426]~E(x54261,f2(a857))+P85(f341(f341(f241(a1),f341(f109(a1),x54261)),f2(a1))) % 19.23/19.03 [5540]~P67(x55401)+E(f138(x55401,x55401,f89(x55401),f2(x55401)),f160(x55401)) % 19.23/19.03 [5715]~P87(x57151)+P26(a857,x57151,f109(x57151),f248(f864(a857,a850))) % 19.23/19.03 [5913]E(x59131,f2(a857))+~P85(f341(f341(f241(a1),f341(f109(a1),x59131)),f2(a1))) % 19.23/19.03 [5914]E(x59141,f2(a1))+~P85(f341(f341(f242(a1),f341(f84(a1),x59141)),f87(a1))) % 19.23/19.03 [6739]~P85(f341(f341(f242(a1),x67391),f2(a1)))+P85(f341(f341(f242(a1),f341(f341(f89(a1),x67391),x67391)),f2(a1))) % 19.23/19.03 [7311]P85(f341(f341(f242(a1),x73111),f2(a1)))+~P85(f341(f341(f242(a1),f341(f341(f89(a1),x73111),x73111)),f2(a1))) % 19.23/19.03 [7875]E(x78751,f341(a5,f2(a857)))+P85(f341(f341(f242(a857),f341(f341(f3(a857),f341(a22,x78751)),f341(a121,f2(a857)))),f341(a22,x78751))) % 19.23/19.03 [8614]~P85(f341(f341(f242(a1),x86141),f2(a1)))+P85(f341(f341(f242(a1),f341(f341(f3(a1),f341(f341(f89(a1),x86141),x86141)),a106)),f2(a1))) % 19.23/19.03 [8698]~P85(f341(f341(f242(a1),x86981),f2(a1)))+P85(f341(f341(f242(a1),f341(f341(f89(a1),f341(f341(f89(a1),f87(a1)),x86981)),x86981)),f2(a1))) % 19.23/19.03 [8983]P85(f341(f341(f242(a1),x89831),f2(a1)))+~P85(f341(f341(f242(a1),f341(f341(f3(a1),f341(f341(f89(a1),x89831),x89831)),a106)),f2(a1))) % 19.23/19.03 [9049]P85(f341(f341(f242(a1),x90491),f2(a1)))+~P85(f341(f341(f242(a1),f341(f341(f89(a1),f341(f341(f89(a1),f87(a1)),x90491)),x90491)),f2(a1))) % 19.23/19.03 [4603]~E(a92,x46031)+E(f341(f341(f89(a1),x46031),x46031),a92) % 19.23/19.03 [4604]~E(x46041,a92)+E(f341(f341(f89(a1),x46041),x46041),a92) % 19.23/19.03 [4619]E(x46191,f2(a1))+E(f341(f341(f51(a1),x46191),x46191),f87(a1)) % 19.23/19.03 [4744]E(x47441,a92)+~E(f341(f341(f89(a1),x47441),x47441),a92) % 19.23/19.03 [4745]E(a92,x47451)+~E(f341(f341(f89(a1),x47451),x47451),a92) % 19.23/19.03 [4756]~P6(x47561)+E(f53(x47561,f185(f864(x47561,a850))),f248(x47561)) % 19.23/19.03 [4757]~P6(x47571)+E(f53(x47571,f248(f864(x47571,a850))),f185(x47571)) % 19.23/19.03 [4758]~P6(x47581)+E(f52(x47581,f185(f864(x47581,a850))),f185(x47581)) % 19.23/19.03 [4759]~P6(x47591)+E(f52(x47591,f248(f864(x47591,a850))),f248(x47591)) % 19.23/19.03 [4760]~P101(x47601)+E(f136(x47601,f185(f864(x47601,a850))),f122(x47601)) % 19.23/19.03 [4894]E(x48941,f2(a857))+P85(f341(f341(f242(a857),f2(a857)),x48941)) % 19.23/19.03 [4914]~P7(x49141)+P85(f341(f341(f241(a1),f2(a1)),x49141)) % 19.23/19.03 [4945]~E(f341(f113(a857),x49451),f2(a857))+P85(f341(f341(f241(a1),x49451),a92)) % 19.23/19.03 [4950]P37(x49501)+P85(f341(f341(f343(a1),f371(x49501)),x49501)) % 19.23/19.03 [4951]E(x49511,f341(a5,f2(a857)))+P85(f341(f341(f241(a108),f87(a108)),x49511)) % 19.23/19.03 [4995]P85(f341(a191,x49951))+P85(f341(f341(f241(a1),f2(a1)),x49951)) % 19.23/19.03 [5042]E(f341(f109(a1),f341(a114,x50421)),f2(a1))+P85(f341(f341(f241(a1),f2(a1)),x50421)) % 19.23/19.03 [5106]E(f341(f109(a1),f341(f113(a857),x51061)),f341(f113(a1),x51061))+P85(f341(a191,f341(f113(a1),x51061))) % 19.23/19.03 [5125]E(f341(f113(a857),x51251),f2(a857))+~P85(f341(a191,f341(f113(a1),x51251))) % 19.23/19.03 [5126]E(f341(f113(a857),x51261),f2(a857))+~P85(f341(f341(f241(a1),x51261),a92)) % 19.23/19.03 [5157]P7(x51571)+~P85(f341(f341(f241(a1),f2(a1)),x51571)) % 19.23/19.03 [5222]E(f341(a121,f624(x52221)),x52221)+~P85(f341(f341(f242(a857),f2(a857)),x52221)) % 19.23/19.03 [5223]E(f341(a121,f645(x52231)),x52231)+~P85(f341(f341(f242(a857),f2(a857)),x52231)) % 19.23/19.03 [5231]E(f341(a121,f341(f113(a857),x52311)),f87(a857))+~P85(f341(a191,f341(f113(a1),x52311))) % 19.23/19.03 [5238]E(f341(f109(a1),f739(x52381)),x52381)+~P85(f341(f341(f242(a1),f2(a1)),x52381)) % 19.23/19.03 [5245]~E(x52451,f341(a5,f2(a857)))+~P85(f341(f341(f241(a108),f87(a108)),x52451)) % 19.23/19.03 [5252]E(f341(f109(a1),f341(f113(a857),x52521)),f2(a1))+~P85(f341(a191,f341(f113(a1),x52521))) % 19.23/19.03 [5276]E(f341(f160(a857),x52761),f2(a857))+P85(f341(f341(f343(a857),f622(x52761)),f341(f163(a857),x52761))) % 19.23/19.03 [5296]E(f341(f109(a1),f341(a114,x52961)),x52961)+~P85(f341(f341(f241(a1),f2(a1)),x52961)) % 19.23/19.03 [5305]~P85(f341(a191,x53051))+~P85(f341(f341(f241(a1),f2(a1)),x53051)) % 19.23/19.03 [5405]E(f341(f341(f89(a857),f87(a857)),f341(f113(a857),x54051)),f87(a857))+~P85(f341(f341(f242(a1),x54051),a92)) % 19.23/19.03 [5462]E(x54621,f2(a857))+~P85(f341(f341(f242(a857),x54621),f341(a121,f2(a857)))) % 19.23/19.03 [5482]E(x54821,f341(a121,f2(a857)))+~P85(f341(f341(f288(a857),x54821),f341(a121,f2(a857)))) % 19.23/19.03 [5500]E(f341(f341(f89(a857),f341(f113(a857),x55001)),f87(a857)),f87(a857))+~P85(f341(f341(f242(a1),x55001),a92)) % 19.23/19.03 [5501]E(f341(f341(f3(a857),f341(f113(a857),x55011)),f87(a857)),f2(a857))+~P85(f341(f341(f241(a1),x55011),a92)) % 19.23/19.03 [5511]~P37(x55111)+E(f341(f50(a857),f341(f312(a1,a857,a114),x55111)),f341(f50(a1),x55111)) % 19.23/19.03 [5541]~P101(x55411)+E(f243(x55411,f341(f9(x55411,x55411,a850),f241(x55411))),f240(x55411)) % 19.23/19.03 [5542]~P101(x55421)+E(f244(x55421,f341(f9(x55421,x55421,a850),f241(x55421))),f245(x55421)) % 19.23/19.03 [5551]E(f60(a857,f341(a121,f2(a857)),f341(f113(a857),x55511)),f341(a121,f2(a857)))+~P85(f341(a191,f341(f113(a1),x55511))) % 19.23/19.03 [5559]P85(f341(f341(f242(a1),f2(a1)),x55591))+~P85(f341(f341(f241(a1),f87(a1)),x55591)) % 19.23/19.03 [5560]~P85(f341(f341(f242(a1),f2(a1)),x55601))+P85(f341(f341(f241(a1),f87(a1)),x55601)) % 19.23/19.03 [5570]E(f341(a121,f341(f341(f3(a857),x55701),f87(a857))),x55701)+~P85(f341(f341(f242(a857),f2(a857)),x55701)) % 19.23/19.03 [5628]P85(f341(f341(f242(a857),f2(a857)),f739(x56281)))+~P85(f341(f341(f242(a1),f2(a1)),x56281)) % 19.23/19.03 [5685]E(f60(a1,f341(f113(a1),a106),x56851),f341(f341(f3(a1),x56851),f87(a1)))+~P85(f341(f341(f242(a1),f2(a1)),x56851)) % 19.23/19.03 [5730]~P85(f341(f341(f242(a1),a92),x57301))+P85(f341(f341(f242(a857),f2(a857)),f341(f113(a857),x57301))) % 19.23/19.03 [5784]P85(f341(f341(f242(a857),f2(a857)),f341(a114,x57841)))+~P85(f341(f341(f242(a1),f2(a1)),x57841)) % 19.23/19.03 [5832]~P85(f341(f341(f242(a857),f2(a857)),x58321))+P85(f341(f341(f242(a1),f2(a1)),f341(f109(a1),x58321))) % 19.23/19.03 [5867]~P85(f341(f341(f242(a857),f2(a857)),f341(a114,x58671)))+P85(f341(f341(f242(a1),f2(a1)),x58671)) % 19.23/19.03 [5882]~P37(x58821)+E(f341(f312(a857,a1,f109(a1)),f341(f312(a1,a857,a114),x58821)),x58821) % 19.23/19.03 [5893]P85(f341(f341(f242(a1),a92),x58931))+~P85(f341(f341(f242(a857),f2(a857)),f341(f113(a857),x58931))) % 19.23/19.03 [5954]P85(f341(f341(f242(a857),f2(a857)),x59541))+~P85(f341(f341(f242(a1),f2(a1)),f341(f109(a1),x59541))) % 19.23/19.03 [6069]E(f341(f312(a857,a1,f109(a1)),f341(f266(a857),f341(a114,x60691))),f341(f303(a1,f2(a1)),x60691))+~P85(f341(f341(f241(a1),f2(a1)),x60691)) % 19.23/19.03 [6085]~P120(x60851)+P85(f341(f341(f242(x60851),f2(x60851)),f341(f341(f89(x60851),f87(x60851)),f87(x60851)))) % 19.23/19.03 [6136]P85(f341(f341(f242(a857),f341(a121,f2(a857))),f341(a114,x61361)))+~P85(f341(f341(f242(a1),f87(a1)),x61361)) % 19.23/19.03 [6232]E(x62321,f2(a1))+P85(f341(f64(f2(a1),x62321),f341(f341(f250(a1,a1),f2(a1)),f2(a1)))) % 19.23/19.03 [6412]~P85(f341(f341(f242(a857),f341(a121,f2(a857))),f341(a114,x64121)))+P85(f341(f341(f242(a1),f87(a1)),x64121)) % 19.23/19.03 [6860]~P108(x68601)+P35(x68601,f341(f265(f863(x68601,x68601)),f341(f260(x68601,x68601,a850),f242(x68601)))) % 19.23/19.03 [5452]E(f341(f113(a857),f341(f341(f3(a1),x54521),a106)),f341(a121,f341(f113(a857),x54521)))+P85(f341(a191,f341(f113(a1),x54521))) % 19.23/19.03 [5576]E(f341(f88(a1),f341(f109(a1),f341(a121,f756(x55761)))),x55761)+~P85(f341(f341(f242(a1),x55761),f2(a1))) % 19.23/19.03 [5586]E(f341(f341(f89(a857),f87(a857)),f341(f113(a857),x55861)),f341(f113(a857),f341(f341(f3(a1),x55861),a106)))+P85(f341(f341(f242(a1),x55861),a92)) % 19.23/19.03 [5630]E(f341(f341(f51(a1),f341(f113(a1),a106)),x56301),f341(f113(a1),a106))+~P85(f341(f341(f242(a1),f2(a1)),x56301)) % 19.23/19.03 [5726]E(f341(f341(f89(a857),f341(f113(a857),x57261)),f87(a857)),f341(f113(a857),f341(f341(f3(a1),x57261),a106)))+P85(f341(f341(f242(a1),x57261),a92)) % 19.23/19.03 [5727]E(f341(f341(f3(a857),f341(f113(a857),x57271)),f87(a857)),f341(f113(a857),f341(f341(f89(a1),x57271),a106)))+P85(f341(f341(f241(a1),x57271),a92)) % 19.23/19.03 [5770]E(f341(a114,f341(f341(f89(a1),f87(a1)),x57701)),f341(a121,f341(a114,x57701)))+~P85(f341(f341(f241(a1),f2(a1)),x57701)) % 19.23/19.03 [5808]E(f341(a121,f341(f341(f3(a857),x58081),f341(a121,f2(a857)))),x58081)+~P85(f341(f341(f242(a857),f2(a857)),x58081)) % 19.23/19.03 [6014]E(f60(a857,f341(a121,f2(a857)),f341(f113(a857),x60141)),f341(a114,f60(a1,f87(a1),f341(f113(a1),x60141))))+P85(f341(a191,f341(f113(a1),x60141))) % 19.23/19.03 [6060]~P85(f341(f341(f242(a1),a106),x60601))+P85(f341(f341(f242(a1),a106),f341(f341(f89(a1),x60601),x60601))) % 19.23/19.03 [6061]~P85(f341(f341(f242(a1),a92),x60611))+P85(f341(f341(f242(a1),a92),f341(f341(f89(a1),x60611),x60611))) % 19.23/19.03 [6062]~P85(f341(f341(f242(a1),a106),x60621))+P85(f341(f341(f241(a1),a106),f341(f341(f89(a1),x60621),x60621))) % 19.23/19.03 [6063]~P85(f341(f341(f241(a1),a92),x60631))+P85(f341(f341(f241(a1),a92),f341(f341(f89(a1),x60631),x60631))) % 19.23/19.03 [6246]~P85(f341(f71(x62461),f248(f864(x62461,a850))))+P85(f341(f71(f861(x62461)),f248(f864(f861(x62461),a850)))) % 19.23/19.03 [6337]~P85(f341(f341(f241(a1),f2(a1)),x63371))+P85(f341(f341(f242(a1),f2(a1)),f341(f341(f89(a1),f87(a1)),x63371))) % 19.23/19.03 [6343]E(f341(f249(a1,a1),f62(f87(a1),f341(f113(a1),x63431))),f341(f341(f51(a1),f87(a1)),f341(f113(a1),x63431)))+~P85(f341(f341(f241(a1),f2(a1)),f341(f113(a1),x63431))) % 19.23/19.03 [6368]E(f341(f259(a1,a1),f62(f87(a1),f341(f113(a1),x63681))),f60(a1,f87(a1),f341(f113(a1),x63681)))+~P85(f341(f341(f241(a1),f2(a1)),f341(f113(a1),x63681))) % 19.23/19.03 [6381]P85(f341(f71(x63811),f248(f864(x63811,a850))))+~P85(f341(f71(f861(x63811)),f248(f864(f861(x63811),a850)))) % 19.23/19.03 [6413]P85(f341(f341(f242(a1),a106),x64131))+~P85(f341(f341(f242(a1),a106),f341(f341(f89(a1),x64131),x64131))) % 19.23/19.03 [6414]P85(f341(f341(f242(a1),a106),x64141))+~P85(f341(f341(f241(a1),a106),f341(f341(f89(a1),x64141),x64141))) % 19.23/19.03 [6415]P85(f341(f341(f242(a1),a92),x64151))+~P85(f341(f341(f242(a1),a92),f341(f341(f89(a1),x64151),x64151))) % 19.23/19.03 [6416]P85(f341(f341(f241(a1),a92),x64161))+~P85(f341(f341(f241(a1),a92),f341(f341(f89(a1),x64161),x64161))) % 19.23/19.03 [6744]~P85(f341(f71(x67441),f248(f864(x67441,a850))))+P85(f341(f341(f242(a857),f2(a857)),f341(f50(x67441),f248(f864(x67441,a850))))) % 19.23/19.03 [7356]P85(f341(f71(a857),x73561))+~P85(f341(f71(a1),f341(f312(a857,a1,f109(a1)),x73561))) % 19.23/19.03 [5380]~E(a106,x53801)+E(f341(f341(f3(a1),f341(f341(f89(a1),x53801),x53801)),a106),a106) % 19.23/19.03 [5381]~E(x53811,a106)+E(f341(f341(f3(a1),f341(f341(f89(a1),x53811),x53811)),a106),a106) % 19.23/19.03 [5887]E(x58871,a106)+~E(f341(f341(f3(a1),f341(f341(f89(a1),x58871),x58871)),a106),a106) % 19.23/19.03 [5888]E(a106,x58881)+~E(f341(f341(f3(a1),f341(f341(f89(a1),x58881),x58881)),a106),a106) % 19.23/19.03 [6306]~E(f341(f113(a857),x63061),f2(a857))+P85(f341(a191,f341(f113(a1),f341(f341(f89(a1),x63061),a106)))) % 19.23/19.03 [6669]~P85(f341(a191,f341(f113(a1),x66691)))+P85(f341(a191,f341(f113(a1),f341(f341(f89(a1),x66691),x66691)))) % 19.23/19.03 [6670]~P85(f341(f341(f241(a1),x66701),a106))+P85(f341(f341(f242(a1),f341(f341(f89(a1),x66701),x66701)),a106)) % 19.23/19.03 [6671]~P85(f341(f341(f242(a1),x66711),a92))+P85(f341(f341(f242(a1),f341(f341(f89(a1),x66711),x66711)),a92)) % 19.23/19.03 [6672]~P85(f341(f341(f241(a1),x66721),a106))+P85(f341(f341(f241(a1),f341(f341(f89(a1),x66721),x66721)),a106)) % 19.23/19.03 [6673]~P85(f341(f341(f241(a1),x66731),a92))+P85(f341(f341(f241(a1),f341(f341(f89(a1),x66731),x66731)),a92)) % 19.23/19.03 [7001]E(f341(f113(a857),x70011),f2(a857))+~P85(f341(a191,f341(f113(a1),f341(f341(f89(a1),x70011),a106)))) % 19.23/19.03 [7259]~P85(f341(f341(f241(a1),f2(a1)),f341(f113(a1),x72591)))+P85(f341(f341(f241(a1),f2(a1)),f341(f113(a1),f341(f341(f89(a1),x72591),x72591)))) % 19.23/19.03 [7260]P85(f341(a191,f341(f113(a1),x72601)))+~P85(f341(a191,f341(f113(a1),f341(f341(f89(a1),x72601),x72601)))) % 19.23/19.03 [7261]P85(f341(f341(f242(a1),x72611),a92))+~P85(f341(f341(f242(a1),f341(f341(f89(a1),x72611),x72611)),a92)) % 19.23/19.03 [7262]P85(f341(f341(f241(a1),x72621),a106))+~P85(f341(f341(f242(a1),f341(f341(f89(a1),x72621),x72621)),a106)) % 19.23/19.03 [7263]P85(f341(f341(f241(a1),x72631),a106))+~P85(f341(f341(f241(a1),f341(f341(f89(a1),x72631),x72631)),a106)) % 19.23/19.03 [7264]P85(f341(f341(f241(a1),x72641),a92))+~P85(f341(f341(f241(a1),f341(f341(f89(a1),x72641),x72641)),a92)) % 19.23/19.03 [7642]E(f341(a117,f568(x76421)),x76421)+~P85(f341(f341(f343(f864(f863(a857,a857),a850)),x76421),a107)) % 19.23/19.03 [6220]~P89(x62201)+E(f341(f113(x62201),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f87(x62201)) % 19.23/19.03 [6723]~P85(f341(a191,f341(f113(a1),x67231)))+E(f341(f113(a857),f341(f341(f3(a1),f341(f341(f89(a1),x67231),x67231)),a106)),f2(a857)) % 19.23/19.03 [7821]~P85(f341(f341(f242(a1),f341(f113(a1),x78211)),f2(a1)))+E(f341(f249(a1,a1),f341(a66,f65(f341(f88(a1),f87(a1)),f341(f88(a1),f341(f113(a1),x78211))))),f341(f341(f51(a1),f87(a1)),f341(f113(a1),x78211))) % 19.23/19.03 [7834]~P85(f341(f341(f242(a1),f341(f113(a1),x78341)),f2(a1)))+E(f341(f259(a1,a1),f341(a66,f65(f341(f88(a1),f87(a1)),f341(f88(a1),f341(f113(a1),x78341))))),f60(a1,f87(a1),f341(f113(a1),x78341))) % 19.23/19.03 [7881]~P85(f341(f341(f242(a1),a106),x78811))+P85(f341(f341(f242(a1),a106),f341(f341(f3(a1),f341(f341(f89(a1),x78811),x78811)),a106))) % 19.23/19.03 [7882]~P85(f341(f341(f241(a1),a92),x78821))+P85(f341(f341(f242(a1),a92),f341(f341(f3(a1),f341(f341(f89(a1),x78821),x78821)),a106))) % 19.23/19.03 [7883]~P85(f341(f341(f241(a1),a106),x78831))+P85(f341(f341(f241(a1),a106),f341(f341(f3(a1),f341(f341(f89(a1),x78831),x78831)),a106))) % 19.23/19.03 [7884]~P85(f341(f341(f241(a1),a92),x78841))+P85(f341(f341(f241(a1),a92),f341(f341(f3(a1),f341(f341(f89(a1),x78841),x78841)),a106))) % 19.23/19.03 [8178]~P89(x81781)+~P32(x81781,f341(f113(x81781),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106))) % 19.23/19.03 [8359]P85(f341(f341(f242(a1),a106),x83591))+~P85(f341(f341(f242(a1),a106),f341(f341(f3(a1),f341(f341(f89(a1),x83591),x83591)),a106))) % 19.23/19.03 [8360]P85(f341(f341(f241(a1),a106),x83601))+~P85(f341(f341(f241(a1),a106),f341(f341(f3(a1),f341(f341(f89(a1),x83601),x83601)),a106))) % 19.23/19.03 [8361]P85(f341(f341(f241(a1),a92),x83611))+~P85(f341(f341(f242(a1),a92),f341(f341(f3(a1),f341(f341(f89(a1),x83611),x83611)),a106))) % 19.23/19.03 [8362]P85(f341(f341(f241(a1),a92),x83621))+~P85(f341(f341(f241(a1),a92),f341(f341(f3(a1),f341(f341(f89(a1),x83621),x83621)),a106))) % 19.23/19.03 [8657]E(f341(f113(a857),f341(f341(f3(a1),f341(f341(f89(a1),x86571),x86571)),a106)),f341(f341(f95(a857,a857),f341(f113(a857),x86571)),f341(f341(f10(a857,a857,a857),a121),f341(f341(f20(a857,a857,a857),f89(a857)),f7(a857)))))+P85(f341(a191,f341(f113(a1),x86571))) % 19.23/19.03 [9430]E(x94301,f185(f864(f863(a857,a857),a850)))+P85(f341(f341(f343(f863(f864(f863(a857,a857),a850),f864(f863(a857,a857),a850))),f341(f341(f250(f864(f863(a857,a857),a850),f864(f863(a857,a857),a850)),x94301),f185(f864(f863(a857,a857),a850)))),a48)) % 19.23/19.03 [8591]~P85(f341(a191,f341(f113(a1),x85911)))+P85(f341(a191,f341(f113(a1),f341(f341(f3(a1),f341(f341(f89(a1),x85911),x85911)),a106)))) % 19.23/19.03 [8592]~P85(f341(f341(f242(a1),x85921),a106))+P85(f341(f341(f242(a1),f341(f341(f3(a1),f341(f341(f89(a1),x85921),x85921)),a106)),a106)) % 19.23/19.03 [8593]~P85(f341(f341(f242(a1),x85931),a92))+P85(f341(f341(f242(a1),f341(f341(f3(a1),f341(f341(f89(a1),x85931),x85931)),a106)),a92)) % 19.23/19.03 [8594]~P85(f341(f341(f241(a1),x85941),a106))+P85(f341(f341(f241(a1),f341(f341(f3(a1),f341(f341(f89(a1),x85941),x85941)),a106)),a106)) % 19.23/19.03 [8595]~P85(f341(f341(f242(a1),x85951),a92))+P85(f341(f341(f241(a1),f341(f341(f3(a1),f341(f341(f89(a1),x85951),x85951)),a106)),a92)) % 19.23/19.03 [8691]~P85(f341(f341(f241(a1),f2(a1)),f341(f113(a1),x86911)))+P85(f341(f341(f241(a1),f2(a1)),f341(f113(a1),f341(f341(f3(a1),f341(f341(f89(a1),x86911),x86911)),a106)))) % 19.23/19.03 [8824]~P89(x88241)+E(f341(f341(f89(x88241),f87(x88241)),f87(x88241)),f341(f113(x88241),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))) % 19.23/19.03 [8969]P85(f341(a191,f341(f113(a1),x89691)))+~P85(f341(a191,f341(f113(a1),f341(f341(f3(a1),f341(f341(f89(a1),x89691),x89691)),a106)))) % 19.23/19.03 [8970]P85(f341(f341(f242(a1),x89701),a106))+~P85(f341(f341(f242(a1),f341(f341(f3(a1),f341(f341(f89(a1),x89701),x89701)),a106)),a106)) % 19.23/19.03 [8971]P85(f341(f341(f242(a1),x89711),a92))+~P85(f341(f341(f242(a1),f341(f341(f3(a1),f341(f341(f89(a1),x89711),x89711)),a106)),a92)) % 19.23/19.03 [8972]P85(f341(f341(f242(a1),x89721),a92))+~P85(f341(f341(f241(a1),f341(f341(f3(a1),f341(f341(f89(a1),x89721),x89721)),a106)),a92)) % 19.23/19.03 [8973]P85(f341(f341(f241(a1),x89731),a106))+~P85(f341(f341(f241(a1),f341(f341(f3(a1),f341(f341(f89(a1),x89731),x89731)),a106)),a106)) % 19.23/19.03 [9480]~P85(f341(f71(f863(a857,a857)),x94801))+P85(f341(f341(f343(f863(f864(f863(a857,a857),a850),f864(f863(a857,a857),a850))),f341(f341(f250(f864(f863(a857,a857),a850),f864(f863(a857,a857),a850)),f185(f864(f863(a857,a857),a850))),x94801)),a78)) % 19.23/19.03 [9265]~P112(x92651)+E(f341(f341(f251(x92651),f2(x92651)),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),f2(x92651)) % 19.23/19.03 [9266]~P112(x92661)+E(f341(f341(f251(x92661),f87(x92661)),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),f87(x92661)) % 19.23/19.03 [9685]~P85(f341(f341(f242(a857),f87(a857)),x96851))+P85(f341(f341(f242(a857),f2(a857)),f341(f341(f51(a857),x96851),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))))) % 19.23/19.03 [9691]~P85(f341(f341(f242(a857),f2(a857)),x96911))+P85(f341(f341(f242(a857),f2(a857)),f341(f341(f51(a857),f341(f341(f89(a857),x96911),f87(a857))),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))))) % 19.23/19.03 [9730]~E(f60(a857,x97301,f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),f87(a857))+P85(f341(f341(f242(a857),f2(a857)),f60(a857,x97301,f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))))) % 19.23/19.03 [9765]E(f60(a857,x97651,f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),f87(a857))+~P85(f341(f341(f242(a857),f2(a857)),f60(a857,x97651,f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))))) % 19.23/19.03 [4539]~P35(x45391,x45392)+P55(x45391,x45392) % 19.23/19.03 [4540]~P41(x45401,x45402)+P55(x45401,x45402) % 19.23/19.03 [4500]E(x45001,x45002)+~E(f42(x45001),f42(x45002)) % 19.23/19.03 [4501]E(x45011,x45012)+~E(f43(x45011),f43(x45012)) % 19.23/19.03 [4503]~E(x45031,x45032)+E(f275(x45031,x45032),f87(a108)) % 19.23/19.03 [4506]E(f219(x45061,x45062),x45061)+~E(x45062,f2(a857)) % 19.23/19.03 [4511]P36(x45111,x45112)+~E(x45112,f188(x45111)) % 19.23/19.03 [4517]~P36(x45172,x45171)+E(x45171,f188(x45172)) % 19.23/19.03 [4544]~P100(x45442)+P100(f864(x45441,x45442)) % 19.23/19.03 [4545]~P104(x45452)+P104(f864(x45451,x45452)) % 19.23/19.03 [4546]~P103(x45462)+P103(f864(x45461,x45462)) % 19.23/19.03 [4547]~P91(x45472)+P91(f864(x45471,x45472)) % 19.23/19.03 [4548]~P84(x45482)+P84(f864(x45481,x45482)) % 19.23/19.03 [4549]~P72(x45492)+P72(f864(x45491,x45492)) % 19.23/19.03 [4550]~P102(x45502)+P102(f864(x45501,x45502)) % 19.23/19.03 [4551]~P94(x45512)+P93(f864(x45511,x45512)) % 19.23/19.03 [4552]~P95(x45522)+P95(f864(x45521,x45522)) % 19.23/19.03 [4553]~P95(x45532)+P98(f864(x45531,x45532)) % 19.23/19.03 [4554]~P95(x45542)+P99(f864(x45541,x45542)) % 19.23/19.03 [4555]~P96(x45552)+P96(f864(x45551,x45552)) % 19.23/19.03 [4556]~P6(x45562)+P6(f864(x45561,x45562)) % 19.23/19.03 [4557]~P107(x45572)+P107(f864(x45571,x45572)) % 19.23/19.03 [4558]~P94(x45582)+P97(f864(x45581,x45582)) % 19.23/19.03 [4559]~P94(x45592)+P94(f864(x45591,x45592)) % 19.23/19.03 [4571]E(x45711,x45712)+~E(f341(a29,x45711),f341(a29,x45712)) % 19.23/19.03 [4573]E(x45731,x45732)+~E(f341(a121,x45731),f341(a121,x45732)) % 19.23/19.03 [4574]E(x45741,x45742)+~E(f341(a5,x45741),f341(a5,x45742)) % 19.23/19.03 [4576]E(x45761,x45762)+~E(f341(a22,x45761),f341(a22,x45762)) % 19.23/19.03 [4577]E(x45771,x45772)+~E(f341(a117,x45771),f341(a117,x45772)) % 19.23/19.03 [4674]~P4(x46741)+E(f60(x46741,x46742,x46742),f2(x46741)) % 19.23/19.03 [4707]~P35(x47071,x47072)+P35(f858(x47071),f142(x47071,x47072)) % 19.23/19.03 [4708]~P35(x47081,x47082)+P35(f858(x47081),f141(x47081,x47082)) % 19.23/19.03 [4799]~P35(x47991,x47992)+P35(f864(x47991,a850),f333(x47991,x47992)) % 19.23/19.03 [4800]~P35(x48001,x48002)+P35(f864(x48001,a850),f334(x48001,x48002)) % 19.23/19.03 [4919]~P7(x49191)+P37(f304(a1,x49191,x49192)) % 19.23/19.03 [5023]~P35(x50231,x50232)+P57(x50231,f77(x50231,x50231,x50232)) % 19.23/19.03 [5505]~P77(x55051)+P26(x55051,x55051,f88(x55051),x55052) % 19.23/19.03 [4527]~E(x45272,f122(x45271))+E(f341(f147(x45271),x45272),f122(x45271)) % 19.23/19.03 [4528]~E(x45282,f122(x45281))+E(f341(f148(x45281),x45282),f122(x45281)) % 19.23/19.03 [4581]E(x45811,f341(a114,x45812))+~E(f341(f109(a1),x45811),x45812) % 19.23/19.03 [4584]E(x45841,f122(x45842))+~E(f341(f147(x45842),x45841),f122(x45842)) % 19.23/19.03 [4585]E(x45851,f122(x45852))+~E(f341(f148(x45852),x45851),f122(x45852)) % 19.23/19.03 [4600]~P89(x46001)+E(f341(f113(x46001),x46002),f341(f112(x46001),x46002)) % 19.23/19.03 [4607]~E(x46072,f188(x46071))+E(f234(x46071,x46072),f185(f864(x46071,a850))) % 19.23/19.03 [4609]~P58(x46091)+P85(f341(f71(x46091),x46092)) % 19.23/19.03 [4616]E(x46161,f188(x46162))+E(f341(f235(x46162),f552(x46162,x46161)),x46161) % 19.23/19.03 [4617]E(x46171,f188(x46172))+E(f341(f235(x46172),f566(x46172,x46171)),x46171) % 19.23/19.03 [4618]E(x46181,f188(x46182))+E(f341(f235(x46182),f607(x46182,x46181)),x46181) % 19.23/19.03 [4620]~E(f731(x46202,x46201),f122(x46201))+E(f169(x46201,x46202),f122(f858(x46201))) % 19.23/19.03 [4629]~E(x46292,f122(x46291))+E(f341(f163(x46291),x46292),f185(f864(x46291,a850))) % 19.23/19.03 [4630]~E(x46302,f122(x46301))+E(f185(f864(x46301,a850)),f341(f163(x46301),x46302)) % 19.23/19.03 [4632]E(x46321,x46322)+~E(f341(f109(a1),x46321),f341(f109(a1),x46322)) % 19.23/19.03 [4635]E(f217(x46351,x46352),f2(a857))+P85(f341(f71(x46351),x46352)) % 19.23/19.03 [4653]~P113(x46531)+E(f91(x46531,f91(x46531,x46532)),f91(x46531,x46532)) % 19.23/19.03 [4665]~P86(x46651)+E(f341(f341(f251(x46651),x46652),f87(a857)),x46652) % 19.23/19.03 [4666]~P75(x46661)+E(f341(f341(f251(x46661),x46662),f87(a857)),x46662) % 19.23/19.03 [4668]E(x46681,x46682)+E(f275(x46681,x46682),f341(f341(f89(a108),x46682),f87(a108))) % 19.23/19.03 [4671]E(f341(f50(x46711),x46712),f2(a857))+P85(f341(f71(x46711),x46712)) % 19.23/19.03 [4677]~P67(x46771)+E(f341(f341(f89(x46771),x46772),f2(x46771)),x46772) % 19.23/19.03 [4678]~P68(x46781)+E(f341(f341(f89(x46781),x46782),f2(x46781)),x46782) % 19.23/19.03 [4679]~P86(x46791)+E(f341(f341(f89(x46791),x46792),f2(x46791)),x46792) % 19.23/19.03 [4680]~P86(x46801)+E(f341(f341(f90(x46801),x46802),f87(x46801)),x46802) % 19.23/19.03 [4681]~P75(x46811)+E(f341(f341(f90(x46811),x46812),f87(x46811)),x46812) % 19.23/19.03 [4682]~P71(x46821)+E(f341(f341(f90(x46821),x46822),f87(x46821)),x46822) % 19.23/19.03 [4683]~P4(x46831)+E(f341(f341(f51(x46831),x46832),f87(x46831)),x46832) % 19.23/19.03 [4684]~P70(x46841)+E(f341(f341(f3(x46841),x46842),f2(x46841)),x46842) % 19.23/19.03 [4685]~P116(x46851)+E(f341(f341(f292(x46851),x46852),f87(x46851)),x46852) % 19.23/19.03 [4686]~P93(x46861)+E(f341(f341(f110(x46861),x46862),f185(x46861)),x46862) % 19.23/19.03 [4687]~P97(x46871)+E(f341(f341(f111(x46871),x46872),f248(x46871)),x46872) % 19.23/19.03 [4688]~P86(x46881)+E(f341(f341(f251(x46881),x46882),f2(a857)),f87(x46881)) % 19.23/19.03 [4689]~P106(x46891)+E(f341(f341(f251(x46891),x46892),f2(a857)),f87(x46891)) % 19.23/19.03 [4690]~E(x46902,f185(f864(x46901,a850)))+E(f341(f50(x46901),x46902),f2(a857)) % 19.23/19.03 [4701]~P4(x47011)+E(f60(x47011,x47012,f2(x47011)),x47012) % 19.23/19.03 [4709]~P86(x47091)+E(f341(f341(f90(x47091),x47092),f2(x47091)),f2(x47091)) % 19.23/19.03 [4710]~P124(x47101)+E(f341(f341(f90(x47101),x47102),f2(x47101)),f2(x47101)) % 19.23/19.03 [4711]~P4(x47111)+E(f341(f341(f51(x47111),x47112),f2(x47111)),f2(x47111)) % 19.23/19.03 [4712]~P117(x47121)+E(f341(f341(f292(x47121),x47122),f2(x47121)),f2(x47121)) % 19.23/19.03 [4713]~P97(x47131)+E(f341(f341(f110(x47131),x47132),f248(x47131)),f248(x47131)) % 19.23/19.03 [4714]~P93(x47141)+E(f341(f341(f111(x47141),x47142),f185(x47141)),f185(x47141)) % 19.23/19.03 [4715]E(x47151,f188(x47152))+~E(f234(x47152,x47151),f185(f864(x47152,a850))) % 19.23/19.03 [4716]~P4(x47161)+E(f60(x47161,x47162,f87(x47161)),f2(x47161)) % 19.23/19.03 [4717]~P4(x47171)+E(f60(x47171,f2(x47171),x47172),f2(x47171)) % 19.23/19.03 [4768]P35(x47681,x47682)+~E(f623(x47682,x47681),f185(f864(x47681,a850))) % 19.23/19.03 [4769]E(x47691,f122(x47692))+~E(f341(f163(x47692),x47691),f185(f864(x47692,a850))) % 19.23/19.03 [4770]E(x47701,f122(x47702))+~E(f185(f864(x47702,a850)),f341(f163(x47702),x47701)) % 19.23/19.03 [4773]~E(x47731,x47732)+P85(f341(f341(a338,x47731),x47732)) % 19.23/19.03 [4783]P85(x47831)+P85(f341(f341(a344,x47831),x47832)) % 19.23/19.03 [4784]E(x47841,f122(x47842))+E(f341(f341(f158(x47842),x47841),f2(a857)),f341(f137(x47842),x47841)) % 19.23/19.03 [4790]~P85(x47902)+P85(f341(f341(a344,x47901),x47902)) % 19.23/19.03 [4791]~P85(x47912)+P85(f341(f341(a340,x47911),x47912)) % 19.23/19.03 [4792]~P85(x47921)+P85(f341(f341(a340,x47921),x47922)) % 19.23/19.03 [4802]~E(f732(x48022,x48021),f737(x48022,x48021))+P85(f341(f134(x48021),x48022)) % 19.23/19.03 [4810]E(f341(f265(x48101),x48102),f185(f864(x48101,a850)))+P85(f341(x48102,f578(x48102))) % 19.23/19.03 [4811]E(f185(f864(x48111,a850)),f341(f265(x48111),x48112))+P85(f341(x48112,f567(x48112))) % 19.23/19.03 [4875]~P113(x48751)+E(f341(f341(f90(x48751),x48752),f91(x48751,x48752)),f341(f84(x48751),x48752)) % 19.23/19.03 [4887]~E(x48871,f2(a1))+E(f61(x48871,x48872),f341(f341(f250(a1,a1),f2(a1)),f2(a1))) % 19.23/19.03 [4918]~P55(x49181,x49182)+P55(x49181,f341(f287(x49181,x49181),x49182)) % 19.23/19.03 [4935]~E(f341(a32,x49351),f341(f235(a851),x49352))+P85(f341(a26,f341(a29,x49351))) % 19.23/19.03 [4939]E(x49391,x49392)+~P85(f341(f341(a338,x49391),x49392)) % 19.23/19.03 [4943]~P85(f341(a26,x49432))+P85(f341(a26,f37(x49431,x49432))) % 19.23/19.03 [4952]P85(x49521)+~P85(f341(f341(a339,x49522),x49521)) % 19.23/19.03 [4953]P85(x49531)+~P85(f341(f341(a339,x49531),x49532)) % 19.23/19.03 [4957]~P107(x49571)+P85(f341(f341(f241(x49571),x49572),f248(x49571))) % 19.23/19.03 [4958]~P86(x49581)+P85(f341(f341(f288(x49581),x49582),f2(x49581))) % 19.23/19.03 [4963]E(x49631,x49632)+~E(f341(x49631,f373(x49632,x49631)),f341(x49632,f373(x49632,x49631))) % 19.23/19.03 [4997]E(x49971,f2(a857))+E(f219(x49971,f60(a857,x49972,x49971)),f219(x49972,x49971)) % 19.23/19.03 [5002]~P101(x50021)+P15(x50021,f341(f341(f146(x50021),x50022),f122(x50021))) % 19.23/19.03 [5004]E(x50041,f2(a1))+P85(f341(f64(x50042,x50041),f61(x50042,x50041))) % 19.23/19.03 [5021]~E(x50211,x50212)+P85(f341(f341(f242(a857),x50211),f341(a121,x50212))) % 19.23/19.03 [5031]~E(x50311,f2(a857))+P85(f341(f341(f242(a857),x50311),f341(a121,x50312))) % 19.23/19.03 [5041]P85(f341(x50411,x50412))+P85(f341(f341(f241(a1),f2(a1)),f799(x50411))) % 19.23/19.03 [5077]P85(f341(a26,x50771))+~P85(f341(a26,f37(x50772,x50771))) % 19.23/19.03 [5079]P85(f341(a26,x50791))+~P85(f341(a26,f38(x50792,x50791))) % 19.23/19.03 [5081]P85(f341(a26,x50811))+~P85(f341(a26,f38(x50811,x50812))) % 19.23/19.03 [5109]P55(x51091,x51092)+~P55(x51091,f341(f287(x51091,x51091),x51092)) % 19.23/19.03 [5111]~E(f60(a857,x51112,x51111),f2(a857))+E(f341(f341(f90(a857),x51111),f805(x51111,x51112)),x51112) % 19.23/19.03 [5112]~E(f60(a1,x51122,x51121),f2(a1))+E(f341(f341(f90(a1),x51121),f806(x51121,x51122)),x51122) % 19.23/19.03 [5138]~P85(f341(x51381,x51382))+P85(f341(f341(f241(a1),f2(a1)),f771(x51381))) % 19.23/19.03 [5149]E(f341(f341(f3(a857),f341(a114,x51491)),f341(a114,x51492)),f341(a114,x51491))+~P85(f341(a191,x51492)) % 19.23/19.03 [5177]E(f276(x51771,x51772),f87(a108))+~P85(f341(f341(f241(a108),x51771),f87(a108))) % 19.23/19.03 [5264]E(f341(f341(f158(x52641),x52642),f732(x52642,x52641)),f341(f341(f158(x52641),x52642),f737(x52642,x52641)))+P85(f341(f134(x52641),x52642)) % 19.23/19.03 [5306]~P85(f341(x53061,f99(x53062,x53061)))+P85(f341(x53061,f625(x53062,x53061))) % 19.23/19.03 [5370]P57(x53701,x53702)+~P85(f341(f330(x53701,x53702),f579(x53702,x53701))) % 19.23/19.03 [5512]~E(f341(a121,f60(a857,x55121,x55122)),x55122)+E(f60(a857,f341(a121,x55121),x55122),f2(a857)) % 19.23/19.03 [5566]P35(x55661,x55662)+P85(f341(f341(f343(x55661),f701(x55662,x55661)),f702(x55662,x55661))) % 19.23/19.03 [5572]~P112(x55721)+P85(f341(f341(f343(x55721),f341(f109(x55721),x55722)),f182(x55721))) % 19.23/19.03 [5573]~P136(x55731)+P85(f341(f341(f343(x55731),f341(f109(x55731),x55732)),f119(x55731))) % 19.23/19.03 [5574]~P136(x55741)+P85(f341(f341(f343(x55741),f341(f112(x55741),x55742)),f119(x55741))) % 19.23/19.03 [5575]~P89(x55751)+P85(f341(f341(f343(x55751),f341(f113(x55751),x55752)),f119(x55751))) % 19.23/19.03 [5729]E(f341(a121,f60(a857,x57291,x57292)),x57292)+E(f60(a857,f341(a121,x57291),x57292),f341(a121,f60(a857,x57291,x57292))) % 19.23/19.03 [6149]P35(x61491,x61492)+~P85(f341(f341(f343(x61491),f580(x61492,x61491)),f331(x61491,x61492))) % 19.23/19.03 [6183]~P120(x61831)+~P85(f341(f341(f242(x61831),f341(f109(x61831),x61832)),f2(x61831))) % 19.23/19.03 [6184]~P79(x61841)+~P85(f341(f341(f242(x61841),f341(f84(x61841),x61842)),f2(x61841))) % 19.23/19.03 [6275]P85(f341(f341(f242(a1),x62751),f60(a1,x62752,x62751)))+~P85(f341(f341(f242(a1),x62751),f2(a1))) % 19.23/19.03 [6383]E(f341(f341(f311(a857),f341(a121,x63831)),f304(a857,x63832,x63831)),f304(a857,x63832,f341(a121,x63831)))+~P85(f341(f341(f241(a857),x63832),f341(a121,x63831))) % 19.23/19.03 [6608]E(f341(f147(x66081),x66082),x66082)+~P85(f341(f341(f241(a857),f341(f186(f858(x66081)),x66082)),f87(a857))) % 19.23/19.03 [6631]~P79(x66311)+P85(f341(f341(f241(x66311),f341(f88(x66311),f341(f84(x66311),x66312))),f2(x66311))) % 19.23/19.03 [6666]~P35(x66661,x66662)+P35(x66661,f341(f341(f290(x66661,x66661,x66661),x66662),f309(x66661,x66662))) % 19.23/19.03 [6897]~P85(f341(f341(f242(a1),x68972),f2(a1)))+P85(f341(f341(f241(a1),f60(a1,x68971,x68972)),f2(a1))) % 19.23/19.03 [7306]~P112(x73061)+E(f187(x73061,f341(f341(f9(x73061,x73061,x73061),f89(x73061)),f87(x73061)),x73062,f2(x73061)),f341(f109(x73061),x73062)) % 19.23/19.03 [7339]~P121(x73391)+~P85(f341(f341(f242(x73391),f341(f341(f90(x73391),x73392),x73392)),f2(x73391))) % 19.23/19.03 [9864]~P113(x98641)+~P85(f341(f341(f242(x98641),f341(f341(f251(x98641),x98642),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106))))),f2(x98641))) % 19.23/19.03 [4582]~E(x45822,f122(x45821))+E(f341(f186(f858(x45821)),x45822),f2(a857)) % 19.23/19.03 [4621]~E(x46211,f2(a857))+E(f341(f341(f89(a857),x46211),x46212),x46212) % 19.23/19.03 [4622]~E(x46222,f2(a857))+E(f341(f341(f90(a857),x46221),x46222),f2(a857)) % 19.23/19.03 [4624]~E(x46241,f2(a857))+E(f341(f341(f90(a857),x46241),x46242),f2(a857)) % 19.23/19.03 [4625]~E(x46252,f2(a1))+E(f341(f341(f51(a1),x46251),x46252),f2(a1)) % 19.23/19.03 [4626]~E(x46262,f2(a857))+E(f341(f341(f251(a857),x46261),x46262),f87(a857)) % 19.23/19.03 [4636]E(x46361,f122(x46362))+~E(f341(f186(f858(x46362)),x46361),f2(a857)) % 19.23/19.03 [4638]~P92(x46381)+E(f341(f341(f90(x46381),x46382),x46382),x46382) % 19.23/19.03 [4640]~P101(x46401)+E(f341(f341(f245(x46401),x46402),x46402),x46402) % 19.23/19.03 [4642]~P101(x46421)+E(f341(f341(f240(x46421),x46422),x46422),x46422) % 19.23/19.03 [4643]~P95(x46431)+E(f341(f341(f110(x46431),x46432),x46432),x46432) % 19.23/19.03 [4645]~P98(x46451)+E(f341(f341(f110(x46451),x46452),x46452),x46452) % 19.23/19.03 [4646]~P95(x46461)+E(f341(f341(f111(x46461),x46462),x46462),x46462) % 19.23/19.03 [4648]~P99(x46481)+E(f341(f341(f111(x46481),x46482),x46482),x46482) % 19.23/19.03 [4664]~P70(x46641)+E(f341(f341(f3(x46641),x46642),x46642),f2(x46641)) % 19.23/19.03 [4675]~P70(x46751)+E(f341(f88(x46751),f341(f88(x46751),x46752)),x46752) % 19.23/19.03 [4676]~P91(x46761)+E(f341(f88(x46761),f341(f88(x46761),x46762)),x46762) % 19.23/19.03 [4693]~E(x46932,f2(a857))+E(f341(f341(f251(a857),x46931),x46932),f341(a121,f2(a857))) % 19.23/19.03 [4725]~P67(x47251)+E(f341(f341(f89(x47251),f2(x47251)),x47252),x47252) % 19.23/19.03 [4726]~P68(x47261)+E(f341(f341(f89(x47261),f2(x47261)),x47262),x47262) % 19.23/19.03 [4727]~P86(x47271)+E(f341(f341(f89(x47271),f2(x47271)),x47272),x47272) % 19.23/19.03 [4728]~P86(x47281)+E(f341(f341(f90(x47281),f87(x47281)),x47282),x47282) % 19.23/19.03 [4729]~P75(x47291)+E(f341(f341(f90(x47291),f87(x47291)),x47292),x47292) % 19.23/19.03 [4730]~P71(x47301)+E(f341(f341(f90(x47301),f87(x47301)),x47302),x47302) % 19.23/19.03 [4731]~P93(x47311)+E(f341(f341(f110(x47311),f185(x47311)),x47312),x47312) % 19.23/19.03 [4732]~P97(x47321)+E(f341(f341(f111(x47321),f248(x47321)),x47322),x47322) % 19.23/19.03 [4749]~P86(x47491)+E(f341(f341(f90(x47491),f2(x47491)),x47492),f2(x47491)) % 19.23/19.03 [4750]~P124(x47501)+E(f341(f341(f90(x47501),f2(x47501)),x47502),f2(x47501)) % 19.23/19.03 [4751]~P4(x47511)+E(f341(f341(f51(x47511),f2(x47511)),x47512),f2(x47511)) % 19.23/19.03 [4752]~P75(x47521)+E(f341(f341(f251(x47521),f87(x47521)),x47522),f87(x47521)) % 19.23/19.03 [4753]~P116(x47531)+E(f341(f341(f292(x47531),f2(x47531)),x47532),f2(x47531)) % 19.23/19.03 [4754]~P97(x47541)+E(f341(f341(f110(x47541),f248(x47541)),x47542),f248(x47541)) % 19.23/19.03 [4755]~P93(x47551)+E(f341(f341(f111(x47551),f185(x47551)),x47552),f185(x47551)) % 19.23/19.03 [4763]E(x47631,f122(x47632))+E(f140(x47632,f341(f148(x47632),x47631)),f341(f137(x47632),x47631)) % 19.23/19.03 [4764]E(x47641,f122(x47642))+E(f341(f137(x47642),f341(f148(x47642),x47641)),f140(x47642,x47641)) % 19.23/19.03 [4765]E(x47651,f2(a857))+~E(f341(f341(f89(a857),x47652),x47651),x47652) % 19.23/19.03 [4771]~P136(x47711)+E(f341(f112(x47711),f341(f109(a1),x47712)),f341(f109(x47711),x47712)) % 19.23/19.03 [4772]~P89(x47721)+E(f341(f112(x47721),f341(f113(a1),x47722)),f341(f113(x47721),x47722)) % 19.23/19.03 [4779]E(x47791,f2(a857))+~E(f341(f341(f89(a857),x47792),x47791),f2(a857)) % 19.23/19.03 [4780]E(x47801,f2(a857))+~E(f341(f341(f89(a857),x47801),x47802),f2(a857)) % 19.23/19.03 [4781]E(x47811,f87(a857))+~E(f341(f341(f90(a857),x47812),x47811),f87(a857)) % 19.23/19.03 [4782]E(x47821,f87(a857))+~E(f341(f341(f90(a857),x47821),x47822),f87(a857)) % 19.23/19.03 [4795]~P113(x47951)+E(f341(f84(x47951),f341(f109(x47951),x47952)),f341(f109(x47951),x47952)) % 19.23/19.03 [4796]~P79(x47961)+E(f341(f84(x47961),f341(f88(x47961),x47962)),f341(f84(x47961),x47962)) % 19.23/19.03 [4797]~P79(x47971)+E(f341(f84(x47971),f341(f84(x47971),x47972)),f341(f84(x47971),x47972)) % 19.23/19.03 [4798]~P68(x47981)+E(f341(f160(x47981),f341(f148(x47981),x47982)),f341(f160(x47981),x47982)) % 19.23/19.03 [4803]~E(x48031,f341(a121,f2(a857)))+E(f341(f341(f251(a857),x48031),x48032),f341(a121,f2(a857))) % 19.23/19.03 [4813]~P70(x48131)+E(f341(f341(f3(x48131),f2(x48131)),x48132),f341(f88(x48131),x48132)) % 19.23/19.03 [4814]~E(x48142,f2(a857))+E(f136(a857,f341(f303(a857,x48141),x48142)),f122(a857)) % 19.23/19.03 [4823]~P89(x48231)+E(f341(f341(f89(x48231),x48232),f341(f113(x48231),a92)),x48232) % 19.23/19.03 [4824]E(x48241,f2(a1))+E(f62(f341(f84(a1),x48242),f341(f84(a1),x48241)),f68(x48242,x48241)) % 19.23/19.03 [4836]~E(x48361,x48362)+P85(f341(f341(f241(a857),x48361),x48362)) % 19.23/19.03 [4840]~E(x48401,x48402)+P85(f341(f341(f288(a857),x48401),x48402)) % 19.23/19.03 [4847]~E(x48471,f2(a108))+E(f341(f341(f89(a857),f341(a22,x48471)),x48472),x48472) % 19.23/19.03 [4848]~E(f341(f113(a1),x48482),f341(f109(a1),x48481))+E(x48481,f341(a114,f341(f113(a1),x48482))) % 19.23/19.03 [4857]~P7(x48571)+P7(f341(f341(f251(a1),x48571),x48572)) % 19.23/19.03 [4858]~P70(x48581)+E(f341(f341(f89(x48581),x48582),f341(f88(x48581),x48582)),f2(x48581)) % 19.23/19.03 [4859]~P91(x48591)+E(f341(f341(f110(x48591),x48592),f341(f88(x48591),x48592)),f248(x48591)) % 19.23/19.03 [4860]~P91(x48601)+E(f341(f341(f111(x48601),x48602),f341(f88(x48601),x48602)),f185(x48601)) % 19.23/19.03 [4884]E(x48841,f2(a857))+~E(f341(f88(a1),f341(f109(a1),x48842)),f341(f109(a1),x48841)) % 19.23/19.03 [4885]E(x48851,f2(a857))+~E(f341(f88(a1),f341(f109(a1),x48851)),f341(f109(a1),x48852)) % 19.23/19.03 [4895]E(f193(x48951,x48952),f2(a1))+P85(f341(f341(f241(a1),x48952),x48951)) % 19.23/19.03 [4896]E(f247(x48961,x48962),f2(a108))+P85(f341(f341(f242(a108),x48961),x48962)) % 19.23/19.03 [4897]E(f168(x48971,x48972),f122(a1))+P85(f341(f341(f241(a1),x48971),x48972)) % 19.23/19.03 [4910]E(x49101,f341(a121,f2(a857)))+~E(f341(f341(f90(a857),x49102),x49101),f341(a121,f2(a857))) % 19.23/19.03 [4911]E(x49111,f341(a121,f2(a857)))+~E(f341(f341(f90(a857),x49111),x49112),f341(a121,f2(a857))) % 19.23/19.03 [4912]~P104(x49121)+P85(f341(f341(f241(x49121),x49122),x49122)) % 19.23/19.03 [4913]~P86(x49131)+P85(f341(f341(f288(x49131),x49132),x49132)) % 19.23/19.03 [4916]~P89(x49161)+E(f341(f341(f90(x49161),x49162),f341(f113(x49161),a106)),f341(f88(x49161),x49162)) % 19.23/19.03 [4932]~P136(x49321)+E(f341(f88(x49321),f341(f112(x49321),x49322)),f341(f112(x49321),f341(f88(a1),x49322))) % 19.23/19.03 [4933]~P89(x49331)+E(f341(f88(x49331),f341(f113(x49331),x49332)),f341(f113(x49331),f341(f88(a1),x49332))) % 19.23/19.03 [4968]~E(x49681,f341(a121,x49682))+P85(f341(f341(f242(a857),f2(a857)),x49681)) % 19.23/19.03 [4985]~P101(x49851)+E(f341(f88(f864(x49851,a850)),f341(f302(x49851),x49852)),f341(f305(x49851),x49852)) % 19.23/19.03 [4986]~P101(x49861)+E(f341(f88(f864(x49861,a850)),f341(f266(x49861),x49862)),f341(f267(x49861),x49862)) % 19.23/19.03 [4987]~P101(x49871)+E(f341(f88(f864(x49871,a850)),f341(f267(x49871),x49872)),f341(f266(x49871),x49872)) % 19.23/19.03 [4988]~P101(x49881)+E(f341(f88(f864(x49881,a850)),f341(f305(x49881),x49882)),f341(f302(x49881),x49882)) % 19.23/19.03 [4996]~E(f341(f109(a1),x49962),x49961)+P85(f341(f341(f241(a1),f2(a1)),x49961)) % 19.23/19.03 [5003]~E(x50032,f2(a1))+E(f68(x50031,x50032),f341(f341(f250(a1,a1),f2(a1)),f341(f84(a1),x50031))) % 19.23/19.03 [5005]~P102(x50051)+P85(f341(f341(f241(x50051),f185(x50051)),x50052)) % 19.23/19.03 [5006]~P86(x50061)+P85(f341(f341(f288(x50061),f87(x50061)),x50062)) % 19.23/19.03 [5036]E(x50361,x50362)+~E(f341(f341(f89(a1),x50361),x50361),f341(f341(f89(a1),x50362),x50362)) % 19.23/19.03 [5040]~P85(f341(x50401,x50402))+P85(f341(x50401,f341(a114,f771(x50401)))) % 19.23/19.03 [5066]~P113(x50661)+E(f341(f341(f90(x50661),f91(x50661,x50662)),f341(f84(x50661),x50662)),x50662) % 19.23/19.03 [5067]E(x50671,x50672)+~P85(f341(f341(f192(a25),x50671),x50672)) % 19.23/19.03 [5075]~E(x50752,f2(a857))+E(f94(f863(a857,a857),f63(x50751,x50752)),f341(f341(f250(a857,a857),f2(a857)),x50751)) % 19.23/19.03 [5086]~E(x50861,x50862)+~P85(f341(f341(f242(a857),x50861),x50862)) % 19.23/19.03 [5087]~E(x50871,x50872)+~P85(f341(f341(f242(a1),x50871),x50872)) % 19.23/19.03 [5090]~P112(x50901)+E(f341(f341(f89(x50901),f87(x50901)),f341(f109(x50901),x50902)),f341(f109(x50901),f341(a121,x50902))) % 19.23/19.03 [5094]~E(x50941,f2(a857))+~P85(f341(f341(f242(a857),x50942),x50941)) % 19.23/19.03 [5107]E(f341(f50(x51071),f341(f163(x51071),x51072)),f341(f186(f858(x51071)),x51072))+~P85(f341(f134(x51071),x51072)) % 19.23/19.03 [5116]~P85(f341(x51161,f772(x51161)))+P85(f341(x51161,f341(f109(a1),x51162))) % 19.23/19.03 [5127]E(f247(x51271,x51272),x51272)+~P85(f341(f341(f242(a108),x51271),x51272)) % 19.23/19.03 [5129]E(f276(x51291,x51292),f87(a108))+~P85(f341(f341(f242(a108),x51292),x51291)) % 19.23/19.03 [5130]E(f168(x51301,x51302),f122(a1))+~P85(f341(f341(f242(a1),x51302),x51301)) % 19.23/19.03 [5133]~P100(x51331)+E(f304(x51331,x51332,x51332),f341(f341(f311(x51331),x51332),f185(f864(x51331,a850)))) % 19.23/19.03 [5152]~E(f341(f341(f3(a857),x51521),x51522),f2(a857))+P85(f341(f341(f241(a857),x51521),x51522)) % 19.23/19.03 [5178]~P104(x51781)+~P85(f341(f341(f242(x51781),x51782),x51782)) % 19.23/19.03 [5181]~E(f60(a1,x51811,x51812),f2(a1))+E(f60(a1,x51811,f341(f88(a1),x51812)),f2(a1)) % 19.23/19.03 [5183]~E(f60(a1,x51831,x51832),f2(a1))+E(f60(a1,f341(f88(a1),x51831),x51832),f2(a1)) % 19.23/19.03 [5189]E(f341(f303(a857,x51891),f341(a121,x51892)),f185(f864(a857,a850)))+P85(f341(f341(f241(a857),x51891),x51892)) % 19.23/19.03 [5206]E(f136(a857,f341(f303(a857,x52061),x52062)),f122(a857))+P85(f341(f341(f242(a857),x52061),x52062)) % 19.23/19.03 [5211]~E(f341(f50(x52111),f341(f163(x52111),x52112)),f341(f186(f858(x52111)),x52112))+P85(f341(f134(x52111),x52112)) % 19.23/19.03 [5215]~P85(f341(f134(x52151),x52152))+P85(f341(f134(x52151),f341(f147(x52151),x52152))) % 19.23/19.03 [5216]~P85(f341(f134(x52161),x52162))+P85(f341(f134(x52161),f341(f162(x52161),x52162))) % 19.23/19.03 [5217]~P85(f341(f134(x52171),x52172))+P85(f341(f134(x52171),f341(f148(x52171),x52172))) % 19.23/19.03 [5225]P85(f341(x52251,x52252))+~P85(f341(x52251,f341(a114,f799(x52251)))) % 19.23/19.03 [5226]P85(f341(f341(f241(a857),x52262),x52261))+P85(f341(f341(f241(a857),x52261),x52262)) % 19.23/19.03 [5227]P85(f341(f341(f241(a1),x52272),x52271))+P85(f341(f341(f241(a1),x52271),x52272)) % 19.23/19.03 [5229]~P79(x52291)+P85(f341(f341(f241(x52291),x52292),f341(f84(x52291),x52292))) % 19.23/19.03 [5232]P85(f341(x52321,f773(x52321)))+~P85(f341(x52321,f341(f109(a1),x52322))) % 19.23/19.03 [5255]E(f341(f341(f51(a857),x52551),x52552),f2(a857))+~P85(f341(f341(f242(a857),x52551),x52552)) % 19.23/19.03 [5257]E(f341(f341(f3(a857),x52571),x52572),f2(a857))+~P85(f341(f341(f241(a857),x52571),x52572)) % 19.23/19.03 [5274]E(f60(a857,x52741,x52742),x52741)+~P85(f341(f341(f242(a857),x52741),x52742)) % 19.23/19.03 [5281]E(f60(a1,x52811,f341(f88(a1),x52812)),f293(x52811,x52812))+P85(f341(f341(f241(a1),f2(a1)),x52812)) % 19.23/19.03 [5294]E(f341(f341(f3(a1),x52941),x52942),f193(x52941,x52942))+~P85(f341(f341(f241(a1),x52942),x52941)) % 19.23/19.03 [5312]P85(f341(f341(f241(a1),f2(a1)),f772(x53121)))+P85(f341(x53121,f341(f109(a1),x53122))) % 19.23/19.03 [5326]~P120(x53261)+P85(f341(f341(f241(x53261),f2(x53261)),f341(f109(x53261),x53262))) % 19.23/19.03 [5327]~P79(x53271)+P85(f341(f341(f241(x53271),f2(x53271)),f341(f84(x53271),x53272))) % 19.23/19.03 [5355]E(f341(f341(f89(a857),x53551),f774(x53552,x53551)),x53552)+~P85(f341(f341(f241(a857),x53551),x53552)) % 19.23/19.03 [5356]E(f341(f341(f89(a857),x53561),f646(x53562,x53561)),x53562)+~P85(f341(f341(f242(a857),x53561),x53562)) % 19.23/19.03 [5368]~E(f341(f113(a1),x53681),f341(f109(a1),x53682))+P85(f341(f341(f241(a1),f2(a1)),f341(f113(a1),x53681))) % 19.23/19.03 [5371]E(f304(a1,x53711,x53712),f185(f864(a1,a850)))+~P85(f341(f341(f242(a1),x53712),x53711)) % 19.23/19.03 [5374]~P113(x53741)+E(f341(f341(f90(x53741),f341(f84(x53741),x53742)),f341(f84(x53741),x53742)),f341(f341(f90(x53741),x53742),x53742)) % 19.23/19.03 [5379]E(f136(a857,f341(f303(a857,x53791),f341(a121,x53792))),f122(a857))+P85(f341(f341(f241(a857),x53791),x53792)) % 19.23/19.03 [5383]E(f341(f341(f51(a1),x53831),x53832),f294(x53831,x53832))+~P85(f341(f341(f241(a1),f2(a1)),x53832)) % 19.23/19.03 [5403]P85(f341(f134(x54031),x54032))+~P85(f341(f134(x54031),f341(f147(x54031),x54032))) % 19.23/19.03 [5404]P85(f341(f134(x54041),x54042))+~P85(f341(f134(x54041),f341(f148(x54041),x54042))) % 19.23/19.03 [5427]P85(f341(f71(a857),x54271))+P85(f341(f341(f343(a857),f375(x54271,x54272)),x54271)) % 19.23/19.03 [5428]P85(f341(f71(a857),x54281))+P85(f341(f341(f343(a857),f378(x54281,x54282)),x54281)) % 19.23/19.03 [5429]P85(f341(f341(f242(a857),x54292),f341(a121,x54291)))+P85(f341(f341(f242(a857),x54291),x54292)) % 19.23/19.03 [5430]E(f60(a1,x54301,x54302),f293(x54301,x54302))+~P85(f341(f341(f241(a1),f2(a1)),x54302)) % 19.23/19.03 [5433]E(f136(a857,f341(f303(a857,x54331),x54332)),f122(a857))+~P85(f341(f341(f241(a857),x54332),x54331)) % 19.23/19.03 [5434]~P77(x54341)+E(f341(f312(x54341,x54341,f88(x54341)),f341(f302(x54341),x54342)),f341(f267(x54341),f341(f88(x54341),x54342))) % 19.23/19.03 [5435]~P77(x54351)+E(f341(f312(x54351,x54351,f88(x54351)),f341(f266(x54351),x54352)),f341(f305(x54351),f341(f88(x54351),x54352))) % 19.23/19.03 [5436]~P77(x54361)+E(f341(f312(x54361,x54361,f88(x54361)),f341(f267(x54361),x54362)),f341(f302(x54361),f341(f88(x54361),x54362))) % 19.23/19.03 [5437]~P77(x54371)+E(f341(f312(x54371,x54371,f88(x54371)),f341(f305(x54371),x54372)),f341(f266(x54371),f341(f88(x54371),x54372))) % 19.23/19.03 [5448]E(x54481,f185(f864(x54482,a850)))+P85(f341(f341(f343(x54482),f347(x54481,x54482)),x54481)) % 19.23/19.03 [5449]E(x54491,f185(f864(x54492,a850)))+P85(f341(f341(f343(x54492),f348(x54491,x54492)),x54491)) % 19.23/19.03 [5460]~P85(f341(f341(f242(a857),x54601),x54602))+P85(f341(f341(f241(a857),x54601),x54602)) % 19.23/19.03 [5461]~P85(f341(f341(f242(a1),x54611),x54612))+P85(f341(f341(f241(a1),x54611),x54612)) % 19.23/19.03 [5473]E(f62(x54731,x54732),f341(f341(f250(a1,a1),f2(a1)),x54731))+~P85(f341(f341(f242(a1),x54731),x54732)) % 19.23/19.03 [5474]E(f218(f341(f88(a1),x54741),f341(f88(a1),x54742)),f218(x54741,x54742))+~P85(f341(f341(f242(a1),x54742),f2(a1))) % 19.23/19.03 [5486]E(x54861,x54862)+~E(f341(a5,f341(a121,f341(a22,x54861))),f341(a5,f341(a121,f341(a22,x54862)))) % 19.23/19.03 [5491]E(f62(x54911,x54912),f341(f341(f250(a1,a1),f2(a1)),x54911))+~P85(f341(f341(f241(a1),x54912),f2(a1))) % 19.23/19.03 [5518]E(f60(a857,f341(f113(a857),x55181),f341(f113(a857),x55182)),f2(a857))+~P85(f341(a191,f341(f113(a1),x55181))) % 19.23/19.03 [5533]P85(f341(f341(f241(a1),f2(a1)),f773(x55331)))+~P85(f341(x55331,f341(f109(a1),x55332))) % 19.23/19.03 [5564]P37(f304(a1,x55641,x55642))+~P85(f341(f341(f241(a1),f2(a1)),x55641)) % 19.23/19.03 [5568]~P85(f341(f71(x55681),x55682))+P85(f341(f71(f864(x55681,a850)),f341(f310(x55681),x55682))) % 19.23/19.03 [5581]E(f341(f341(f89(a1),x55811),f341(f109(a1),f802(x55812,x55811))),x55812)+~P85(f341(f341(f241(a1),x55811),x55812)) % 19.23/19.03 [5589]P85(f341(f341(f241(a857),x55891),x55892))+P85(f341(f341(f241(a857),f341(a121,x55892)),x55891)) % 19.23/19.03 [5634]E(f341(f341(f51(a857),f341(f113(a857),x56341)),f341(f113(a857),x56342)),f2(a857))+~P85(f341(a191,f341(f113(a1),x56341))) % 19.23/19.03 [5635]E(f341(f341(f90(a857),f341(f113(a857),x56351)),f341(f113(a857),x56352)),f2(a857))+~P85(f341(f341(f242(a1),x56351),a92)) % 19.23/19.03 [5637]P85(f341(f341(f242(a857),x56371),f341(a121,x56372)))+~P85(f341(f341(f242(a857),x56371),x56372)) % 19.23/19.03 [5639]P85(f341(f341(f242(a857),x56391),f341(a121,x56392)))+~P85(f341(f341(f241(a857),x56391),x56392)) % 19.23/19.03 [5641]P85(f341(f341(f241(a857),x56411),f341(a121,x56412)))+~P85(f341(f341(f241(a857),x56411),x56412)) % 19.23/19.03 [5642]~E(x56421,x56422)+P85(f341(f341(f242(a1),x56421),f341(f341(f89(a1),x56422),f87(a1)))) % 19.23/19.03 [5645]E(f60(a1,x56451,x56452),f2(a1))+E(f341(f341(f3(a1),x56452),f60(a1,x56451,x56452)),f60(a1,f341(f88(a1),x56451),x56452)) % 19.23/19.03 [5653]E(x56531,f122(x56532))+P85(f341(f341(f343(x56532),f140(x56532,x56531)),f341(f163(x56532),x56531))) % 19.23/19.03 [5665]E(f94(f863(a857,a857),f63(x56651,x56652)),f341(f341(f250(a857,a857),f2(a857)),x56651))+~P85(f341(f341(f242(a857),x56651),x56652)) % 19.23/19.03 [5705]E(f341(f341(f89(a857),f341(f113(a857),x57051)),f341(f113(a857),x57052)),f341(f113(a857),x57052))+~P85(f341(f341(f242(a1),x57051),a92)) % 19.23/19.03 [5706]E(f341(f341(f3(a857),f341(f113(a857),x57061)),f341(f113(a857),x57062)),f341(f113(a857),x57061))+~P85(f341(f341(f242(a1),x57062),a92)) % 19.23/19.03 [5711]E(f341(a121,f341(f341(f89(a857),x57111),f660(x57112,x57111))),x57112)+~P85(f341(f341(f242(a857),x57111),x57112)) % 19.23/19.03 [5712]E(f341(a121,f341(f341(f89(a857),x57121),f669(x57122,x57121))),x57122)+~P85(f341(f341(f242(a857),x57121),x57122)) % 19.23/19.03 [5719]~P85(f341(f341(f288(a1),x57191),x57192))+P85(f341(f341(f288(a1),x57191),f341(f88(a1),x57192))) % 19.23/19.03 [5720]P85(f341(f341(f242(a857),f2(a857)),f646(x57201,x57202)))+~P85(f341(f341(f242(a857),x57202),x57201)) % 19.23/19.03 [5739]P85(f341(x57391,x57392))+~P85(f341(x57391,f341(a98,f595(x57392,x57391)))) % 19.23/19.03 [5747]~P85(f341(f341(f242(a857),x57471),f341(a121,x57472)))+P85(f341(f341(f241(a857),x57471),x57472)) % 19.23/19.03 [5796]E(f341(f341(f311(a857),x57961),f341(f303(a857,x57962),x57961)),f341(f303(a857,x57962),f341(a121,x57961)))+~P85(f341(f341(f241(a857),x57962),x57961)) % 19.23/19.03 [5801]E(x58011,f122(x58012))+E(f341(f341(f132(x58012),f123(x58012,x58011)),f341(f341(f146(x58012),f140(x58012,x58011)),f122(x58012))),x58011) % 19.23/19.03 [5812]P85(f341(f71(x58121),x58122))+~P85(f341(f341(f242(a857),f2(a857)),f341(f50(x58121),x58122))) % 19.23/19.03 [5816]~E(x58161,f185(f864(x58162,a850)))+~P85(f341(f341(f242(a857),f2(a857)),f341(f50(x58162),x58161))) % 19.23/19.03 [5826]~P85(f341(f341(f242(a857),x58261),x58262))+P85(f341(f341(f241(a857),f341(a121,x58261)),x58262)) % 19.23/19.03 [5835]E(x58351,f122(x58352))+P85(f341(f341(f343(x58352),f341(f137(x58352),x58351)),f341(f163(x58352),x58351))) % 19.23/19.03 [5841]~P120(x58411)+P85(f341(f341(f242(x58411),x58412),f341(f341(f89(x58411),x58412),f87(x58411)))) % 19.23/19.03 [5843]~P79(x58431)+P85(f341(f341(f241(x58431),f341(f88(x58431),x58432)),f341(f84(x58431),x58432))) % 19.23/19.03 [5855]P85(f341(f341(f288(a1),x58551),x58552))+~P85(f341(f341(f288(a1),x58551),f341(f88(a1),x58552))) % 19.23/19.03 [5856]~E(x58561,x58562)+E(f291(a857,f288(a857),x58561,x58562),f341(f341(f311(a857),x58561),f185(f864(a857,a850)))) % 19.23/19.03 [5874]P85(f341(f71(a857),x58741))+~P85(f341(f341(f242(a857),f378(x58741,x58742)),x58742)) % 19.23/19.03 [5875]P85(f341(f71(a857),x58751))+~P85(f341(f341(f241(a857),f375(x58751,x58752)),x58752)) % 19.23/19.03 [5879]~P85(f341(f71(f863(x58791,x58791)),x58792))+P85(f341(f71(x58791),f341(f285(x58791),x58792))) % 19.23/19.03 [5929]E(f291(a857,f288(a857),x59291,x59292),f185(f864(a857,a850)))+P85(f341(f341(f288(a857),x59291),x59292)) % 19.23/19.03 [5935]~P85(f341(f341(f242(a857),x59352),f341(a121,x59351)))+~P85(f341(f341(f242(a857),x59351),x59352)) % 19.23/19.03 [5936]~P100(x59361)+E(f341(f341(f111(f864(x59361,a850)),f341(f302(x59361),x59362)),f341(f267(x59361),x59362)),f341(f341(f311(x59361),x59362),f185(f864(x59361,a850)))) % 19.23/19.03 [5949]P85(f341(f71(x59491),x59492))+~P85(f341(f71(f864(x59491,a850)),f341(f310(x59491),x59492))) % 19.23/19.03 [5972]P85(f341(f341(f242(a857),f341(a121,x59721)),f341(a121,x59722)))+~P85(f341(f341(f242(a857),x59721),x59722)) % 19.23/19.03 [5973]P85(f341(f341(f242(a857),f341(a22,x59731)),f341(a22,x59732)))+~P85(f341(f341(f242(a108),x59731),x59732)) % 19.23/19.03 [5974]P85(f341(f341(f242(a108),f341(a5,x59741)),f341(a5,x59742)))+~P85(f341(f341(f242(a857),x59741),x59742)) % 19.23/19.03 [5975]P85(f341(f341(f241(a857),f341(a121,x59751)),f341(a121,x59752)))+~P85(f341(f341(f241(a857),x59751),x59752)) % 19.23/19.03 [5976]P85(f341(f341(f241(a857),f341(a22,x59761)),f341(a22,x59762)))+~P85(f341(f341(f241(a108),x59761),x59762)) % 19.23/19.03 [5977]P85(f341(f341(f241(a108),f341(a5,x59771)),f341(a5,x59772)))+~P85(f341(f341(f241(a857),x59771),x59772)) % 19.23/19.03 [5980]E(x59801,x59802)+~E(f341(f312(a857,a1,f109(a1)),x59801),f341(f312(a857,a1,f109(a1)),x59802)) % 19.23/19.03 [5996]P85(f341(f341(f242(a857),x59961),x59962))+~P85(f341(f341(f242(a857),f341(a121,x59961)),x59962)) % 19.23/19.03 [5999]P85(f341(f341(f242(a857),x59991),x59992))+~P85(f341(f341(f241(a857),f341(a121,x59991)),x59992)) % 19.23/19.03 [6000]P85(f341(f341(f241(a857),x60001),x60002))+~P85(f341(f341(f241(a857),f341(a121,x60001)),x60002)) % 19.23/19.03 [6017]E(f60(a1,x60171,x60172),f2(a1))+E(f341(f341(f3(a1),f60(a1,x60171,x60172)),x60172),f60(a1,x60171,f341(f88(a1),x60172))) % 19.23/19.03 [6088]E(f341(f50(f864(x60881,a850)),f341(f310(x60881),x60882)),f341(f341(f251(a857),f341(a121,f341(a121,f2(a857)))),f341(f50(x60881),x60882)))+~P85(f341(f71(x60881),x60882)) % 19.23/19.03 [6091]E(x60911,f122(x60912))+E(f341(f341(f158(x60912),x60911),f341(f341(f3(a857),f341(f186(f858(x60912)),x60911)),f87(a857))),f140(x60912,x60911)) % 19.23/19.03 [6115]E(x61151,f122(x61152))+E(f341(f341(f132(x61152),f341(f162(x61152),x61151)),f341(f341(f146(x61152),f341(f137(x61152),x61151)),f122(x61152))),f341(f147(x61152),x61151)) % 19.23/19.03 [6146]~P85(f341(f71(x61461),f52(f864(x61461,a850),x61462)))+P85(f341(f71(f864(x61461,a850)),x61462)) % 19.23/19.03 [6167]P85(f341(f341(f241(a857),f341(f113(a857),x61671)),f341(f113(a857),x61672)))+~P85(f341(f341(f241(a1),x61671),a92)) % 19.23/19.03 [6187]~P85(f341(f341(f242(a1),x61871),x61872))+P85(f341(f341(f242(a1),x61871),f341(f341(f89(a1),x61872),f87(a1)))) % 19.23/19.03 [6188]~P85(f341(f341(f241(a1),x61881),x61882))+P85(f341(f341(f242(a1),x61881),f341(f341(f89(a1),x61882),f87(a1)))) % 19.23/19.03 [6189]~P85(f341(f341(f242(a1),x61891),x61892))+P85(f341(f341(f241(a1),x61891),f341(f341(f3(a1),x61892),f87(a1)))) % 19.23/19.03 [6192]~P85(f341(f341(f242(a857),x61921),x61922))+P85(f341(f341(f242(a1),f341(f109(a1),x61921)),f341(f109(a1),x61922))) % 19.23/19.03 [6193]~P85(f341(f341(f242(a1),x61931),x61932))+P85(f341(f341(f242(a1),f341(f113(a1),x61931)),f341(f113(a1),x61932))) % 19.23/19.03 [6194]~P85(f341(f341(f241(a1),x61941),x61942))+P85(f341(f341(f241(a857),f341(f113(a857),x61941)),f341(f113(a857),x61942))) % 19.23/19.03 [6196]~P85(f341(f341(f241(a857),x61961),x61962))+P85(f341(f341(f241(a1),f341(f109(a1),x61961)),f341(f109(a1),x61962))) % 19.23/19.03 [6197]~P85(f341(f341(f241(a1),x61971),x61972))+P85(f341(f341(f241(a1),f341(f113(a1),x61971)),f341(f113(a1),x61972))) % 19.23/19.03 [6199]~P85(f341(f341(f288(a857),x61991),x61992))+P85(f341(f341(f288(a1),f341(f109(a1),x61991)),f341(f109(a1),x61992))) % 19.23/19.03 [6215]~P85(f341(f341(f241(a857),x62151),x62152))+~P85(f341(f341(f241(a857),f341(a121,x62152)),x62151)) % 19.23/19.03 [6262]~P85(f341(f341(f242(a857),f341(a121,x62621)),f341(a121,x62622)))+P85(f341(f341(f242(a857),x62621),x62622)) % 19.23/19.03 [6263]~P85(f341(f341(f242(a108),f341(a5,x62631)),f341(a5,x62632)))+P85(f341(f341(f242(a857),x62631),x62632)) % 19.23/19.03 [6264]~P85(f341(f341(f242(a857),f341(a114,x62641)),f341(a114,x62642)))+P85(f341(f341(f242(a1),x62641),x62642)) % 19.23/19.03 [6265]~P85(f341(f341(f242(a857),f341(a22,x62651)),f341(a22,x62652)))+P85(f341(f341(f242(a108),x62651),x62652)) % 19.23/19.03 [6266]~P85(f341(f341(f241(a857),f341(a121,x62661)),f341(a121,x62662)))+P85(f341(f341(f241(a857),x62661),x62662)) % 19.23/19.03 [6267]~P85(f341(f341(f241(a108),f341(a5,x62671)),f341(a5,x62672)))+P85(f341(f341(f241(a857),x62671),x62672)) % 19.23/19.03 [6268]~P85(f341(f341(f241(a857),f341(a22,x62681)),f341(a22,x62682)))+P85(f341(f341(f241(a108),x62681),x62682)) % 19.23/19.03 [6312]~P85(f341(f341(f242(a857),f341(a114,x63122)),f341(a114,x63121)))+P85(f341(f341(f242(a1),f2(a1)),x63121)) % 19.23/19.03 [6323]~E(f60(a1,f341(f113(a1),x63232),f341(f113(a1),x63231)),f2(a1))+P85(f341(f341(f288(a1),f341(f113(a1),x63231)),f341(f113(a1),x63232))) % 19.23/19.03 [6342]P85(f341(f341(f241(a1),f2(a1)),f60(a1,x63421,x63422)))+~P85(f341(f341(f242(a1),f2(a1)),x63422)) % 19.23/19.03 [6510]P35(x65101,x65102)+~E(f341(f341(f290(x65101,x65101,x65101),x65102),x65102),f185(f864(f863(x65101,x65101),a850))) % 19.23/19.03 [6526]~P35(x65261,x65262)+P35(x65261,f341(f341(f290(x65261,x65261,x65261),x65262),x65262)) % 19.23/19.03 [6538]P85(f341(f341(f242(a1),x65381),x65382))+~P85(f341(f341(f241(a1),x65381),f341(f341(f3(a1),x65382),f87(a1)))) % 19.23/19.03 [6539]P85(f341(f341(f241(a1),x65391),x65392))+~P85(f341(f341(f242(a1),x65391),f341(f341(f89(a1),x65392),f87(a1)))) % 19.23/19.03 [6542]P85(f341(f341(f242(a857),x65421),x65422))+~P85(f341(f341(f242(a1),f341(f109(a1),x65421)),f341(f109(a1),x65422))) % 19.23/19.03 [6543]P85(f341(f341(f242(a1),x65431),x65432))+~P85(f341(f341(f242(a857),f341(f113(a857),x65431)),f341(f113(a857),x65432))) % 19.23/19.03 [6544]P85(f341(f341(f242(a1),x65441),x65442))+~P85(f341(f341(f242(a1),f341(f113(a1),x65441)),f341(f113(a1),x65442))) % 19.23/19.03 [6546]P85(f341(f341(f241(a857),x65461),x65462))+~P85(f341(f341(f241(a1),f341(f109(a1),x65461)),f341(f109(a1),x65462))) % 19.23/19.03 [6547]P85(f341(f341(f241(a1),x65471),x65472))+~P85(f341(f341(f241(a1),f341(f113(a1),x65471)),f341(f113(a1),x65472))) % 19.23/19.03 [6549]P85(f341(f341(f288(a857),x65491),x65492))+~P85(f341(f341(f288(a1),f341(f109(a1),x65491)),f341(f109(a1),x65492))) % 19.23/19.03 [6604]E(f60(a1,f341(f113(a1),x66041),f341(f113(a1),x66042)),f2(a1))+~P85(f341(f341(f288(a1),f341(f113(a1),x66042)),f341(f113(a1),x66041))) % 19.23/19.03 [6619]~E(f291(a857,f288(a857),x66191,x66192),f185(f864(a857,a850)))+~P85(f341(f341(f288(a857),x66191),x66192)) % 19.23/19.03 [6647]~E(f783(x66472,x66471),f122(x66471))+E(f341(f138(f858(x66471),f858(x66471),f132(x66471),f122(x66471)),x66472),f122(x66471)) % 19.23/19.03 [6648]~E(f784(x66482,x66481),f122(x66481))+E(f341(f138(f858(x66481),f858(x66481),f132(x66481),f122(x66481)),x66482),f122(x66481)) % 19.23/19.03 [6654]~P6(x66541)+E(f341(f138(x66541,x66541,f111(x66541),f248(x66541)),x66542),f53(x66541,f341(f163(x66541),x66542))) % 19.23/19.03 [6655]~P6(x66551)+E(f341(f138(x66551,x66551,f110(x66551),f185(x66551)),x66552),f52(x66551,f341(f163(x66551),x66552))) % 19.23/19.03 [6667]E(x66671,f2(a108))+E(f341(f341(f89(a857),f341(a22,f341(f341(f3(a108),x66671),f87(a108)))),f341(a121,x66672)),f341(f341(f89(a857),f341(a22,x66671)),x66672)) % 19.23/19.03 [6719]P85(f341(f341(f242(a1),f341(f341(f3(a1),x67191),x67192)),f2(a1)))+~P85(f341(f341(f242(a1),x67191),x67192)) % 19.23/19.03 [6746]~P101(x67461)+E(f341(f341(f110(f864(x67461,a850)),f341(f341(f311(x67461),x67462),f185(f864(x67461,a850)))),f341(f305(x67461),x67462)),f341(f267(x67461),x67462)) % 19.23/19.03 [6828]~P57(x68281,x68282)+P35(x68281,f341(f265(f863(x68281,x68281)),f341(f260(x68281,x68281,a850),x68282))) % 19.23/19.03 [6829]~P57(x68291,x68292)+P55(x68291,f341(f265(f863(x68291,x68291)),f341(f260(x68291,x68291,a850),x68292))) % 19.23/19.03 [6830]E(x68301,f185(f864(x68302,a850)))+~P85(f341(f341(f241(f864(x68302,a850)),x68301),f185(f864(x68302,a850)))) % 19.23/19.03 [6915]~P85(f341(f341(f242(a857),f2(a857)),x69152))+P85(f341(f341(f242(a857),f60(a857,x69151,x69152)),x69152)) % 19.23/19.03 [6917]~P85(f341(f341(f242(a1),f2(a1)),x69172))+P85(f341(f341(f242(a1),f60(a1,x69171,x69172)),x69172)) % 19.23/19.03 [6918]~P85(f341(f341(f242(a857),f2(a857)),x69182))+P85(f341(f341(f241(a857),f60(a857,x69181,x69182)),x69182)) % 19.23/19.03 [6919]~P85(f341(f341(f241(a1),f2(a1)),x69191))+P85(f341(f341(f241(a1),f60(a1,x69191,x69192)),x69191)) % 19.23/19.03 [6990]~P100(x69901)+E(f341(f341(f3(f864(x69901,a850)),f341(f341(f311(x69901),x69902),f185(f864(x69901,a850)))),f341(f266(x69901),x69902)),f341(f341(f311(x69901),x69902),f185(f864(x69901,a850)))) % 19.23/19.03 [7068]~P48(x70681,x70682)+P46(x70681,f248(f864(x70681,a850)),f341(f265(f863(x70681,x70681)),f341(f260(x70681,x70681,a850),x70682))) % 19.23/19.03 [7069]P85(f341(x70691,x70692))+P85(f341(f341(f343(f864(f863(a857,a857),a850)),f595(x70692,x70691)),a107)) % 19.23/19.03 [7111]E(f341(f341(f132(a857),f136(a857,f341(f303(a857,x71111),x71112))),f341(f341(f146(a857),x71112),f122(a857))),f136(a857,f341(f303(a857,x71111),f341(a121,x71112))))+~P85(f341(f341(f241(a857),x71111),x71112)) % 19.23/19.03 [7268]E(x72681,f2(a857))+~E(f341(f138(a857,a857,f89(a857),x72681),x72682),f2(a857)) % 19.23/19.03 [7297]~P85(f341(f341(f242(a1),f341(f341(f3(a1),x72971),x72972)),f2(a1)))+P85(f341(f341(f242(a1),x72971),x72972)) % 19.23/19.03 [7327]P35(x73271,x73272)+~P35(x73271,f341(f341(f290(x73271,x73271,x73271),x73272),x73272)) % 19.23/19.03 [7359]~P85(f341(f341(f241(a857),f341(a121,x73591)),x73592))+P85(f181(a850,a184,f341(f241(a857),x73591),x73592)) % 19.23/19.03 [7518]P26(a857,a857,f341(f341(f9(a857,a857,a857),f3(a857)),x75181),x75182)+P85(f341(f341(f343(a857),f613(x75181,x75182)),x75182)) % 19.23/19.03 [7577]E(f341(f341(f341(f75(a857,x75771,f89(a857)),f341(f18(a857,x75771),f87(a857))),f2(a857)),x75772),f341(f50(x75771),x75772))+~P85(f341(f71(x75771),x75772)) % 19.23/19.03 [7620]P26(a857,a857,f341(f341(f9(a857,a857,a857),f3(a857)),x76201),x76202)+~P85(f341(f341(f241(a857),x76201),f613(x76201,x76202))) % 19.23/19.03 [7677]P35(x76771,x76772)+P85(f341(f341(f241(f864(x76771,a850)),f623(x76772,x76771)),f341(f286(x76771,x76771,x76772),f623(x76772,x76771)))) % 19.23/19.03 [7681]P57(x76811,x76812)+~P35(x76811,f341(f265(f863(x76811,x76811)),f341(f260(x76811,x76811,a850),x76812))) % 19.23/19.03 [7753]P85(f341(f341(f241(a857),f341(a121,x77531)),x77532))+~P85(f181(a850,a184,f341(f241(a857),x77531),x77532)) % 19.23/19.03 [7809]P85(f341(f341(f343(f863(a857,a857)),f341(f341(f250(a857,a857),x78091),x78092)),f309(a857,a332)))+~P85(f341(f341(f241(a857),x78091),x78092)) % 19.23/19.03 [7903]P48(x79031,x79032)+~P46(x79031,f248(f864(x79031,a850)),f341(f265(f863(x79031,x79031)),f341(f260(x79031,x79031,a850),x79032))) % 19.23/19.03 [8156]~P35(x81561,f341(f287(x81561,x81561),x81562))+P35(x81561,f341(f287(x81561,x81561),f341(f341(f290(x81561,x81561,x81561),x81562),f309(x81561,x81562)))) % 19.23/19.03 [8274]P85(f341(f71(f863(x82741,x82741)),f341(f341(f290(x82741,x82741,x82741),x82742),f309(x82741,x82742))))+~P85(f341(f71(f863(x82741,x82741)),x82742)) % 19.23/19.03 [8304]E(x83041,f2(a1))+P85(f341(f64(x83042,x83041),f341(f341(f250(a1,a1),f341(f341(f51(a1),x83042),x83041)),f60(a1,x83042,x83041)))) % 19.23/19.03 [8318]~P85(f341(f341(f343(f863(a857,a857)),f341(f341(f250(a857,a857),x83181),x83182)),f309(a857,a332)))+P85(f341(f341(f241(a857),x83181),x83182)) % 19.23/19.03 [8339]~P67(x83391)+E(f341(f138(x83391,x83391,f341(f9(x83391,x83391,x83391),f89(x83391)),f2(x83391)),f341(f148(x83391),x83392)),f341(f138(x83391,x83391,f89(x83391),f2(x83391)),x83392)) % 19.23/19.03 [8613]P85(f341(f341(f343(f863(a857,a857)),f341(f341(f250(a857,a857),x86131),x86132)),f341(f341(f290(a857,a857,a857),a332),f309(a857,a332))))+~P85(f341(f341(f242(a857),x86131),x86132)) % 19.23/19.03 [8655]~P85(f341(f71(f863(x86551,x86551)),f341(f341(f290(x86551,x86551,x86551),x86552),f309(x86551,x86552))))+P85(f341(f71(f863(x86551,x86551)),x86552)) % 19.23/19.03 [8877]P55(x88771,x88772)+P85(f341(f341(f343(f863(x88771,x88771)),f341(f341(f250(x88771,x88771),f639(x88772,x88771)),f639(x88772,x88771))),f341(f341(f290(x88771,x88771,x88771),x88772),f309(x88771,x88772)))) % 19.23/19.03 [8878]P55(x88781,x88782)+P85(f341(f341(f343(f863(x88781,x88781)),f341(f341(f250(x88781,x88781),f652(x88782,x88781)),f652(x88782,x88781))),f341(f341(f290(x88781,x88781,x88781),x88782),f309(x88781,x88782)))) % 19.23/19.03 [8986]~P85(f341(f341(f343(f863(a857,a857)),f341(f341(f250(a857,a857),x89861),x89862)),f341(f341(f290(a857,a857,a857),a332),f309(a857,a332))))+P85(f341(f341(f242(a857),x89861),x89862)) % 19.23/19.03 [4981]~P89(x49811)+E(f341(f341(f89(x49811),f341(f113(x49811),a92)),x49812),x49812) % 19.23/19.03 [5011]~P70(x50111)+E(f341(f341(f89(x50111),f341(f88(x50111),x50112)),x50112),f2(x50111)) % 19.23/19.03 [5012]~P3(x50121)+E(f341(f341(f89(x50121),f341(f88(x50121),x50122)),x50122),f2(x50121)) % 19.23/19.03 [5013]~P91(x50131)+E(f341(f341(f110(x50131),f341(f88(x50131),x50132)),x50132),f248(x50131)) % 19.23/19.03 [5014]~P91(x50141)+E(f341(f341(f111(x50141),f341(f88(x50141),x50142)),x50142),f185(x50141)) % 19.23/19.03 [5044]~P89(x50441)+E(f341(f341(f90(x50441),f341(f113(x50441),a106)),x50442),f341(f88(x50441),x50442)) % 19.23/19.03 [5200]~P105(x52001)+E(f341(f341(f90(x52001),f341(f88(x52001),f87(x52001))),x52002),f341(f88(x52001),x52002)) % 19.23/19.03 [5241]E(f341(f84(a1),x52411),f87(a1))+~E(f341(f84(a1),f341(f341(f90(a1),x52411),x52412)),f87(a1)) % 19.23/19.03 [5329]~P89(x53291)+E(f341(f341(f89(x53291),f87(x53291)),f341(f113(x53291),x53292)),f341(f113(x53291),f341(f341(f3(a1),x53292),a106))) % 19.23/19.03 [5384]~P95(x53841)+E(f15(x53841,f341(f341(f311(x53841),x53842),f185(f864(x53841,a850)))),x53842) % 19.23/19.03 [5385]~P95(x53851)+E(f12(x53851,f341(f341(f311(x53851),x53852),f185(f864(x53851,a850)))),x53852) % 19.23/19.03 [5386]~P101(x53861)+E(f16(x53861,f341(f341(f311(x53861),x53862),f185(f864(x53861,a850)))),x53862) % 19.23/19.03 [5387]~P101(x53871)+E(f17(x53871,f341(f341(f311(x53871),x53872),f185(f864(x53871,a850)))),x53872) % 19.23/19.03 [5388]~P6(x53881)+E(f53(x53881,f341(f341(f311(x53881),x53882),f185(f864(x53881,a850)))),x53882) % 19.23/19.03 [5389]~P6(x53891)+E(f52(x53891,f341(f341(f311(x53891),x53892),f185(f864(x53891,a850)))),x53892) % 19.23/19.03 [5411]E(f341(f341(f89(a857),x54111),f341(f341(f3(a857),x54112),x54111)),x54112)+P85(f341(f341(f242(a857),x54112),x54111)) % 19.23/19.03 [5443]E(x54431,f122(x54432))+P85(f341(f341(f242(a857),f2(a857)),f341(f186(f858(x54432)),x54431))) % 19.23/19.03 [5561]~P101(x55611)+E(f13(x55611,f240(x55611),f341(f341(f311(x55611),x55612),f185(f864(x55611,a850)))),x55612) % 19.23/19.03 [5562]~P101(x55621)+E(f14(x55621,f245(x55621),f341(f341(f311(x55621),x55622),f185(f864(x55621,a850)))),x55622) % 19.23/19.03 [5623]E(f341(f341(f89(a857),x56231),f341(f341(f3(a857),x56232),x56231)),x56232)+~P85(f341(f341(f241(a857),x56231),x56232)) % 19.23/19.03 [5624]E(f341(f341(f90(a1),x56241),f341(f341(f51(a1),x56242),x56241)),x56242)+~P85(f341(f341(f288(a1),x56241),x56242)) % 19.23/19.03 [5625]E(f341(f341(f3(a857),x56251),f341(f341(f3(a857),x56251),x56252)),x56252)+~P85(f341(f341(f241(a857),x56252),x56251)) % 19.23/19.03 [5644]E(f60(a857,f341(f341(f3(a857),x56441),x56442),x56442),f60(a857,x56441,x56442))+P85(f341(f341(f242(a857),x56441),x56442)) % 19.23/19.03 [5654]E(f341(f88(a1),f341(f341(f51(a1),x56541),f341(f88(a1),x56542))),f294(x56541,x56542))+P85(f341(f341(f241(a1),f2(a1)),x56542)) % 19.23/19.03 [5656]~E(x56562,f2(a857))+P85(f341(f341(f242(a857),f2(a857)),f341(f341(f251(a857),x56561),x56562))) % 19.23/19.03 [5716]~P89(x57161)+E(f341(f341(f89(x57161),f341(f88(x57161),f87(x57161))),f341(f113(x57161),x57162)),f341(f113(x57161),f341(f341(f89(a1),x57162),a106))) % 19.23/19.03 [5717]E(f341(f341(f251(a857),f341(f113(a857),x57171)),x57172),f341(f341(f251(a857),f2(a857)),x57172))+~P85(f341(a191,f341(f113(a1),x57171))) % 19.23/19.03 [5818]E(f341(f137(a857),f136(a857,f341(f303(a857,x58181),x58182))),x58181)+~P85(f341(f341(f242(a857),x58181),x58182)) % 19.23/19.03 [5836]E(f341(f341(f90(a857),f341(f113(a857),x58361)),f341(f113(a857),x58362)),f341(f113(a857),f341(f341(f90(a1),x58361),x58362)))+P85(f341(f341(f242(a1),x58361),a92)) % 19.23/19.03 [5842]~P121(x58421)+P85(f341(f341(f241(x58421),f2(x58421)),f341(f341(f90(x58421),x58422),x58422))) % 19.23/19.03 [5854]E(f341(f341(f3(a857),f341(a121,x58541)),x58542),f341(a121,f341(f341(f3(a857),x58541),x58542)))+~P85(f341(f341(f241(a857),x58542),x58541)) % 19.23/19.03 [5857]E(f60(a857,f341(f341(f3(a857),x58571),x58572),x58572),f60(a857,x58571,x58572))+~P85(f341(f341(f241(a857),x58572),x58571)) % 19.23/19.03 [5909]E(f341(f341(f251(a857),f341(a114,x59091)),x59092),f341(a114,f341(f341(f251(a1),x59091),x59092)))+~P85(f341(f341(f241(a1),f2(a1)),x59091)) % 19.23/19.03 [5924]P85(f341(f134(x59241),x59242))+P85(f341(f341(f242(a857),f732(x59242,x59241)),f341(f186(f858(x59241)),x59242))) % 19.23/19.03 [5925]P85(f341(f134(x59251),x59252))+P85(f341(f341(f242(a857),f737(x59252,x59251)),f341(f186(f858(x59251)),x59252))) % 19.23/19.03 [5940]~P85(f341(f341(f288(a1),x59401),x59402))+P85(f341(f341(f288(a1),f341(f88(a1),x59401)),x59402)) % 19.23/19.03 [5943]~E(x59431,f122(x59432))+~P85(f341(f341(f242(a857),f2(a857)),f341(f186(f858(x59432)),x59431))) % 19.23/19.03 [5956]E(f140(a857,f136(a857,f341(f303(a857,x59561),x59562))),f341(f341(f3(a857),x59562),f87(a857)))+~P85(f341(f341(f242(a857),x59561),x59562)) % 19.23/19.03 [5959]E(f341(f341(f89(a1),x59591),f341(f109(a1),f341(a121,f704(x59592,x59591)))),x59592)+~P85(f341(f341(f242(a1),x59591),x59592)) % 19.23/19.03 [5965]E(x59651,f2(a857))+E(f341(f341(f90(a857),x59652),f341(f341(f251(a857),x59652),f341(f341(f3(a857),x59651),f87(a857)))),f341(f341(f251(a857),x59652),x59651)) % 19.23/19.03 [5990]E(f341(f341(f90(a857),f341(a114,x59901)),f341(a114,x59902)),f341(a114,f341(f341(f90(a1),x59901),x59902)))+~P85(f341(f341(f241(a1),f2(a1)),x59901)) % 19.23/19.03 [5991]E(f341(f341(f51(a857),f341(a114,x59911)),f341(a114,x59912)),f341(a114,f341(f341(f51(a1),x59911),x59912)))+~P85(f341(f341(f241(a1),f2(a1)),x59911)) % 19.23/19.03 [6005]~P86(x60051)+E(f341(f341(f89(x60051),x60052),x60052),f341(f341(f90(x60051),f341(f341(f89(x60051),f87(x60051)),f87(x60051))),x60052)) % 19.23/19.03 [6024]E(f341(f341(f51(a1),f341(f84(a1),x60241)),f341(f84(a1),x60242)),f341(f84(a1),f341(f341(f51(a1),x60241),x60242)))+~P85(f341(f341(f288(a1),x60242),x60241)) % 19.23/19.03 [6025]E(f341(f341(f3(a1),f341(f109(a1),x60251)),f341(f109(a1),x60252)),f341(f109(a1),f341(f341(f3(a857),x60251),x60252)))+~P85(f341(f341(f241(a857),x60252),x60251)) % 19.23/19.03 [6027]E(f341(f341(f250(a1,a1),f341(f113(a1),a106)),f341(f341(f89(a1),x60271),x60272)),f65(x60271,x60272))+~P85(f341(f341(f241(a1),x60272),f2(a1))) % 19.23/19.03 [6066]E(f169(x60661,x60662),f122(f858(x60661)))+P85(f341(f341(f343(f858(x60661)),f731(x60662,x60661)),f341(f163(f858(x60661)),x60662))) % 19.23/19.03 [6130]~P85(f341(f341(f288(a857),x61301),x61302))+P85(f341(f341(f288(a857),x61301),f341(f341(f89(a857),x61302),x61301))) % 19.23/19.03 [6152]E(f341(f341(f146(a1),x61521),f168(f341(f341(f89(a1),x61521),f87(a1)),x61522)),f168(x61521,x61522))+~P85(f341(f341(f241(a1),x61521),x61522)) % 19.23/19.03 [6190]~P85(f341(f341(f242(a857),x61902),x61901))+P85(f341(f341(f242(a857),f2(a857)),f341(f341(f3(a857),x61901),x61902))) % 19.23/19.03 [6222]~P85(f341(f341(f242(a857),x62221),f341(a114,x62222)))+P85(f341(f341(f242(a1),f341(f109(a1),x62221)),x62222)) % 19.23/19.03 [6223]P85(f341(f341(f288(a1),x62231),x62232))+~P85(f341(f341(f288(a1),f341(f88(a1),x62231)),x62232)) % 19.23/19.03 [6252]~P101(x62521)+E(f341(f341(f110(f864(x62521,a850)),f341(f266(x62521),x62522)),f341(f341(f311(x62521),x62522),f185(f864(x62521,a850)))),f341(f302(x62521),x62522)) % 19.23/19.03 [6255]~P85(f341(f341(f242(a857),f2(a857)),x62551))+P85(f341(f341(f242(a857),f2(a857)),f341(f341(f251(a857),x62551),x62552))) % 19.23/19.03 [6256]~P85(f341(f341(f241(a1),f2(a1)),x62561))+P85(f341(f341(f241(a1),f2(a1)),f341(f341(f251(a1),x62561),x62562))) % 19.23/19.03 [6284]~E(f341(x62841,f2(a857)),f2(a857))+E(f341(f341(f8(a857,a857),x62841),f304(a857,f341(a121,f2(a857)),x62842)),f341(f341(f8(a857,a857),x62841),f304(a857,f2(a857),x62842))) % 19.23/19.03 [6350]~P89(x63501)+E(f341(f341(f90(x63501),f341(f341(f89(x63501),f87(x63501)),f87(x63501))),f341(f113(x63501),x63502)),f341(f113(x63501),f341(f341(f89(a1),x63502),x63502))) % 19.23/19.03 [6372]E(f341(f341(f311(a1),x63721),f304(a1,f341(f341(f89(a1),x63721),f87(a1)),x63722)),f304(a1,x63721,x63722))+P85(f341(f341(f242(a1),x63722),x63721)) % 19.23/19.03 [6373]P85(f341(f341(f242(a857),x63731),f341(a114,x63732)))+~P85(f341(f341(f242(a1),f341(f109(a1),x63731)),x63732)) % 19.23/19.03 [6475]P85(f341(f341(f288(a857),x64751),x64752))+~P85(f341(f341(f288(a857),x64751),f341(f341(f89(a857),x64752),x64751))) % 19.23/19.03 [6481]E(f341(a114,f341(f341(f51(a1),f341(f113(a1),x64811)),f341(f113(a1),x64812))),f341(f341(f51(a857),f341(f113(a857),x64811)),f341(f113(a857),x64812)))+P85(f341(a191,f341(f113(a1),x64811))) % 19.23/19.03 [6540]P85(f341(f341(f242(a857),x65401),x65402))+~P85(f341(f341(f242(a857),f2(a857)),f341(f341(f3(a857),x65402),x65401))) % 19.23/19.03 [6583]P85(f341(f341(f242(a857),f2(a857)),x65831))+~P85(f341(f341(f242(a857),f2(a857)),f341(f341(f90(a857),x65832),x65831))) % 19.23/19.03 [6584]P85(f341(f341(f242(a857),f2(a857)),x65841))+~P85(f341(f341(f242(a857),f2(a857)),f341(f341(f90(a857),x65841),x65842))) % 19.23/19.03 [6600]~P85(f341(f341(f241(a1),x66001),f2(a1)))+E(f341(f341(f90(a857),f341(a114,f341(f88(a1),x66001))),f341(a114,f341(f88(a1),x66002))),f341(a114,f341(f341(f90(a1),x66001),x66002))) % 19.23/19.03 [6665]~E(x66652,f185(f864(x66651,a850)))+P85(f341(f341(f241(f864(x66651,a850)),x66652),f341(f88(f864(x66651,a850)),x66652))) % 19.23/19.03 [6728]~P89(x67281)+E(f341(f341(f89(x67281),f341(f341(f89(x67281),f2(x67281)),f341(f113(x67281),x67282))),f341(f113(x67281),x67282)),f341(f113(x67281),f341(f341(f89(a1),x67282),x67282))) % 19.23/19.03 [6737]~P85(f341(f341(f288(a1),f341(f109(a1),x67371)),x67372))+P85(f341(f341(f288(a857),x67371),f341(a114,f341(f84(a1),x67372)))) % 19.23/19.03 [6788]~P85(f341(f341(f242(a1),x67881),x67882))+P85(f341(f341(f241(a1),f341(f341(f89(a1),x67881),f87(a1))),x67882)) % 19.23/19.03 [6827]P85(f341(f341(f288(a1),f341(f109(a1),x68271)),x68272))+~P85(f341(f341(f288(a857),x68271),f341(a114,f341(f84(a1),x68272)))) % 19.23/19.03 [6861]E(x68611,f2(a857))+~P85(f341(f341(f241(a1),f341(f109(a1),x68612)),f341(f88(a1),f341(f109(a1),x68611)))) % 19.23/19.03 [6862]E(x68621,f2(a857))+~P85(f341(f341(f241(a1),f341(f109(a1),x68621)),f341(f88(a1),f341(f109(a1),x68622)))) % 19.23/19.03 [6966]E(f341(f341(f250(a1,a1),f341(f113(a1),a106)),f341(f341(f89(a1),x69661),x69662)),f65(x69661,x69662))+~P85(f341(f341(f241(a1),f2(a1)),f341(f341(f89(a1),x69661),x69662))) % 19.23/19.03 [7003]~P27(x70031,x70032)+P35(x70031,f341(f249(f864(f863(x70031,x70031),a850),f864(f863(x70031,x70031),a850)),x70032)) % 19.23/19.03 [7024]~P85(f341(f341(f241(a857),f341(a121,f2(a857))),x70241))+P85(f341(f341(f241(a857),f341(a121,f2(a857))),f341(f341(f251(a857),x70241),x70242))) % 19.23/19.03 [7193]~P85(f341(f341(f242(a1),x71931),x71932))+P85(f341(f341(f242(a1),f341(f341(f89(a1),x71931),x71931)),f341(f341(f89(a1),x71932),x71932))) % 19.23/19.03 [7205]~P85(f341(f341(f241(a1),x72051),x72052))+P85(f341(f341(f241(a1),f341(f341(f89(a1),x72051),x72051)),f341(f341(f89(a1),x72052),x72052))) % 19.23/19.03 [7272]~P85(f341(f341(f242(a857),f2(a857)),x72721))+P85(f341(f341(f242(a857),f341(f341(f3(a857),x72721),f341(a121,x72722))),x72721)) % 19.23/19.03 [7309]P85(f341(f341(f241(a857),f341(a121,f2(a857))),x73091))+~P85(f341(f341(f241(a857),f341(a121,f2(a857))),f341(f341(f90(a857),x73092),x73091))) % 19.23/19.03 [7310]P85(f341(f341(f241(a857),f341(a121,f2(a857))),x73101))+~P85(f341(f341(f241(a857),f341(a121,f2(a857))),f341(f341(f90(a857),x73101),x73102))) % 19.23/19.03 [7314]P85(f341(f341(f241(a857),f341(f341(f158(a857),x73141),x73142)),f341(f160(a857),x73141)))+~P85(f341(f341(f242(a857),x73142),f341(f186(f858(a857)),x73141))) % 19.23/19.03 [7358]P85(f341(f341(f242(a1),x73581),x73582))+~P85(f341(f341(f241(a1),f341(f341(f89(a1),x73581),f87(a1))),x73582)) % 19.23/19.03 [7404]P85(f341(f71(x74041),f248(f864(x74041,a850))))+~P85(f341(f71(f864(x74042,x74041)),f248(f864(f864(x74042,x74041),a850)))) % 19.23/19.03 [7405]P85(f341(f71(x74051),f248(f864(x74051,a850))))+~P85(f341(f71(f865(x74052,x74051)),f248(f864(f865(x74052,x74051),a850)))) % 19.23/19.03 [7406]P85(f341(f71(x74061),f248(f864(x74061,a850))))+~P85(f341(f71(f865(x74061,x74062)),f248(f864(f865(x74061,x74062),a850)))) % 19.23/19.03 [7444]E(x74441,f185(f864(x74442,a850)))+~P85(f341(f341(f241(f864(x74442,a850)),x74441),f341(f88(f864(x74442,a850)),x74441))) % 19.23/19.03 [7587]E(f341(f138(f858(x75871),f858(x75871),f132(x75871),f122(x75871)),x75872),f122(x75871))+P85(f341(f341(f343(f858(x75871)),f783(x75872,x75871)),f341(f163(f858(x75871)),x75872))) % 19.23/19.03 [7588]E(f341(f138(f858(x75881),f858(x75881),f132(x75881),f122(x75881)),x75882),f122(x75881))+P85(f341(f341(f343(f858(x75881)),f784(x75882,x75881)),f341(f163(f858(x75881)),x75882))) % 19.23/19.03 [7829]P85(f341(f341(f242(a1),x78291),x78292))+~P85(f341(f341(f242(a1),f341(f341(f89(a1),x78291),x78291)),f341(f341(f89(a1),x78292),x78292))) % 19.23/19.03 [7832]P85(f341(f341(f241(a1),x78321),x78322))+~P85(f341(f341(f241(a1),f341(f341(f89(a1),x78321),x78321)),f341(f341(f89(a1),x78322),x78322))) % 19.23/19.03 [7924]~P86(x79241)+E(f341(f341(f90(x79241),f341(f341(f89(x79241),f87(x79241)),f87(x79241))),f341(f341(f8(a857,x79241),f109(x79241)),f304(a857,f87(a857),x79242))),f341(f341(f90(x79241),f341(f109(x79241),x79242)),f341(f341(f89(x79241),f341(f109(x79241),x79242)),f87(x79241)))) % 19.23/19.03 [7980]P85(f341(f341(f343(a857),x79801),x79802))+~P85(f341(f341(f343(a1),f341(f109(a1),x79801)),f341(f312(a857,a1,f109(a1)),x79802))) % 19.23/19.03 [8128]~P85(f341(f71(x81281),x81282))+E(f341(f312(a857,x81281,f581(x81282,x81281)),f341(f265(a857),f341(f341(f9(a857,a857,a850),f242(a857)),f582(x81282,x81281)))),x81282) % 19.23/19.03 [8412]P47(x84121,x84122)+P85(f341(f341(f343(f863(x84121,x84121)),f341(f341(f250(x84121,x84121),f369(x84122,x84121)),f369(x84122,x84121))),x84122)) % 19.23/19.03 [8546]~P89(x85461)+E(f341(f341(f3(x85461),f87(x85461)),f341(f113(x85461),x85462)),f341(f113(x85461),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f88(a1),x85462)))) % 19.23/19.03 [8651]~P85(f341(f341(f242(f864(a857,a850)),x86511),x86512))+P85(f341(f341(f242(f864(a1,a850)),f341(f312(a857,a1,f109(a1)),x86511)),f341(f312(a857,a1,f109(a1)),x86512))) % 19.23/19.03 [8678]~P85(f341(f341(f242(a1),x86781),x86782))+P85(f341(f341(f242(a1),f341(f341(f3(a1),f341(f341(f89(a1),x86781),x86781)),a106)),f341(f341(f89(a1),x86782),x86782))) % 19.23/19.03 [8680]~P85(f341(f341(f242(a1),x86801),x86802))+P85(f341(f341(f241(a1),f341(f341(f3(a1),f341(f341(f89(a1),x86801),x86801)),a106)),f341(f341(f89(a1),x86802),x86802))) % 19.23/19.03 [8747]~P85(f341(f341(f343(a857),x87471),f341(f163(a857),x87472)))+P85(f341(f341(f241(a857),x87471),f341(f138(a857,a857,f89(a857),f2(a857)),x87472))) % 19.23/19.03 [8822]P43(x88221,x88222)+~P85(f341(f341(f343(f863(x88221,x88221)),f341(f341(f250(x88221,x88221),f356(x88222,x88221)),f356(x88222,x88221))),x88222)) % 19.23/19.03 [8953]~P85(f341(f341(f242(f864(a1,a850)),f341(f312(a857,a1,f109(a1)),x89531)),f341(f312(a857,a1,f109(a1)),x89532)))+P85(f341(f341(f242(f864(a857,a850)),x89531),x89532)) % 19.23/19.03 [8954]~P85(f341(f341(f241(f864(a1,a850)),f341(f312(a857,a1,f109(a1)),x89541)),f341(f312(a857,a1,f109(a1)),x89542)))+P85(f341(f341(f241(f864(a857,a850)),x89541),x89542)) % 19.23/19.03 [9037]P85(f341(f341(f242(a1),x90371),x90372))+~P85(f341(f341(f242(a1),f341(f341(f3(a1),f341(f341(f89(a1),x90371),x90371)),a106)),f341(f341(f89(a1),x90372),x90372))) % 19.23/19.03 [9039]P85(f341(f341(f242(a1),x90391),x90392))+~P85(f341(f341(f241(a1),f341(f341(f3(a1),f341(f341(f89(a1),x90391),x90391)),a106)),f341(f341(f89(a1),x90392),x90392))) % 19.23/19.03 [9902]~P85(f341(f71(x99021),x99022))+E(f341(f186(f858(x99021)),f99(f858(x99021),f341(f341(f20(f858(x99021),a850,a850),f341(f341(f10(a850,f864(a850,a850),f858(x99021)),a339),f341(f341(f9(f858(x99021),f864(x99021,a850),a850),f341(f341(f10(f864(x99021,a850),f864(f864(x99021,a850),a850),f858(x99021)),a338),f163(x99021))),x99022))),f134(x99021)))),f217(x99021,x99022)) % 19.23/19.03 [5955]E(f341(f341(f89(a857),f341(f341(f3(a857),x59551),x59552)),x59552),x59551)+~P85(f341(f341(f241(a857),x59552),x59551)) % 19.23/19.03 [6020]E(f341(f341(f51(a857),f341(f341(f90(a857),x60201),x60202)),x60202),x60201)+~P85(f341(f341(f242(a857),f2(a857)),x60202)) % 19.23/19.03 [6021]E(f341(f341(f51(a857),f341(f341(f90(a857),x60211),x60212)),x60211),x60212)+~P85(f341(f341(f242(a857),f2(a857)),x60211)) % 19.23/19.03 [6026]~P68(x60261)+E(f341(f341(f8(a857,x60261),f341(f158(x60261),x60262)),f341(f303(a857,f2(a857)),f341(f186(f858(x60261)),x60262))),f341(f160(x60261),x60262)) % 19.23/19.03 [6144]E(f60(a857,f341(a121,f341(f341(f90(a857),x61441),x61442)),x61441),f87(a857))+~P85(f341(f341(f242(a857),f87(a857)),x61441)) % 19.23/19.03 [6150]E(f341(a121,f341(f341(f89(a857),f341(f113(a857),x61501)),x61502)),f341(f341(f89(a857),f87(a857)),x61502))+~P85(f341(a191,f341(f113(a1),x61501))) % 19.23/19.03 [6176]E(f341(a114,f341(f341(f251(a1),f341(f113(a1),x61761)),x61762)),f341(f341(f251(a857),f341(f113(a857),x61761)),x61762))+P85(f341(a191,f341(f113(a1),x61761))) % 19.23/19.03 [6428]E(f341(f341(f3(a857),x64281),f341(f113(a857),f341(f341(f89(a1),x64282),a106))),f341(f341(f3(a857),f341(a121,x64281)),f341(f113(a857),x64282)))+~P85(f341(f341(f242(a1),a92),x64282)) % 19.23/19.03 [6509]E(x65091,f2(a857))+E(f341(a121,f341(f341(f89(a857),f341(f341(f3(a857),x65091),f87(a857))),x65092)),f341(f341(f89(a857),x65091),x65092)) % 19.23/19.03 [6554]E(x65541,f2(a1))+P85(f341(f341(f242(a1),f2(a1)),f341(f341(f251(a1),f341(f84(a1),x65541)),x65542))) % 19.23/19.03 [6569]~E(x65692,f2(a857))+P85(f341(f341(f242(a1),f2(a1)),f341(f341(f251(a1),f341(f84(a1),x65691)),x65692))) % 19.23/19.03 [6605]E(x66051,f2(a857))+E(f341(f341(f89(a857),x66052),f341(f341(f90(a857),f341(f341(f3(a857),x66051),f87(a857))),x66052)),f341(f341(f90(a857),x66051),x66052)) % 19.23/19.03 [6659]~P85(f341(f341(f241(a1),x66591),x66592))+P85(f341(f341(f242(a1),f341(f341(f89(a1),x66591),a106)),x66592)) % 19.23/19.03 [6792]E(f341(f341(f146(a857),x67921),f136(a857,f341(f303(a857,f341(a121,x67921)),x67922))),f136(a857,f341(f303(a857,x67921),x67922)))+~P85(f341(f341(f242(a857),x67921),x67922)) % 19.23/19.03 [6960]~P85(f341(f341(f288(a1),x69601),f341(f109(a1),x69602)))+P85(f341(f341(f288(a857),f341(a114,f341(f84(a1),x69601))),x69602)) % 19.23/19.03 [6994]E(x69941,x69942)+~E(f341(f341(f3(a1),f341(f341(f89(a1),x69941),x69941)),a106),f341(f341(f3(a1),f341(f341(f89(a1),x69942),x69942)),a106)) % 19.23/19.03 [6997]E(x69971,f122(x69972))+E(f272(x69972,f341(f341(f149(x69972,f863(a108,x69972)),f341(f250(a108,x69972),f87(a108))),x69971)),f279(x69972,x69971)) % 19.23/19.03 [7235]P85(f341(f341(f241(a1),x72351),x72352))+~P85(f341(f341(f242(a1),f341(f341(f89(a1),x72351),a106)),x72352)) % 19.23/19.03 [7377]P85(f341(f341(f288(a1),x73771),f341(f109(a1),x73772)))+~P85(f341(f341(f288(a857),f341(a114,f341(f84(a1),x73771))),x73772)) % 19.23/19.03 [7726]~P85(f341(f341(f242(a857),x77261),x77262))+P85(f341(f341(f343(f863(a857,a857)),f341(f341(f250(a857,a857),x77261),x77262)),a246)) % 19.23/19.03 [7954]~P85(f341(f341(f242(a108),f2(a108)),x79541))+P85(f341(f341(f242(a108),f341(f249(a108,f863(a108,a108)),f341(f273(x79541),x79542))),x79541)) % 19.23/19.03 [8253]~P79(x82531)+P85(f341(f341(f241(x82531),f341(f84(x82531),f341(f160(x82531),x82532))),f341(f160(x82531),f341(f341(f149(x82531,x82531),f84(x82531)),x82532)))) % 19.23/19.03 [8276]P85(f341(f341(f242(a857),x82761),x82762))+~P85(f341(f341(f343(f863(a857,a857)),f341(f341(f250(a857,a857),x82761),x82762)),a246)) % 19.23/19.03 [8435]E(f341(f341(f250(x84351,x84351),f661(x84352,x84351)),f661(x84352,x84351)),x84352)+~P85(f341(f341(f343(f863(x84351,x84351)),x84352),f309(x84351,f185(f864(f863(x84351,x84351),a850))))) % 19.23/19.03 [8479]E(f341(f303(a857,x84791),f341(f341(f89(a857),x84791),f341(f50(a857),x84792))),x84792)+~P85(f341(f341(f241(f864(a857,a850)),x84792),f341(f303(a857,x84791),f341(f341(f89(a857),x84791),f341(f50(a857),x84792))))) % 19.23/19.03 [8780]E(f341(f341(f51(a1),f341(f113(a1),f341(f341(f3(a1),f341(f341(f89(a1),x87801),x87801)),a106))),f341(f113(a1),f341(f341(f89(a1),x87802),x87802))),f341(f341(f51(a1),f341(f113(a1),x87801)),f341(f113(a1),x87802)))+~P85(f341(f341(f241(a1),f2(a1)),f341(f113(a1),x87802))) % 19.23/19.03 [8887]E(f167(f858(x88871),f341(f341(f10(a850,a850,f858(x88871)),a337),f341(f341(f9(f858(x88871),f858(x88871),a850),a338),f122(x88871))),x88872),f169(x88871,f169(x88871,x88872)))+~P15(a857,f341(f148(a857),f341(f341(f149(f858(x88871),a857),f186(f858(x88871))),x88872))) % 19.23/19.03 [8890]E(f341(f341(f51(a1),f341(f113(a1),f341(f341(f3(a1),f341(f341(f89(a1),x88901),x88901)),a106))),f341(f113(a1),f341(f341(f89(a1),x88902),x88902))),f341(f341(f51(a1),f341(f341(f89(a1),f341(f113(a1),x88901)),f87(a1))),f341(f113(a1),x88902)))+P85(f341(f341(f241(a1),f2(a1)),f341(f113(a1),x88902))) % 19.23/19.03 [9670]P85(f341(a191,x96702))+E(f341(f341(f95(a1,a857),f341(f341(f3(a1),x96701),x96702)),f341(f341(f20(a1,a857,a857),f341(f341(f9(a1,a857,f864(a857,a857)),f341(f341(f10(a850,f864(a857,f864(a857,a857)),a1),f105(a857)),a191)),f2(a857))),a114)),f341(f341(f3(a857),f341(a114,x96701)),f341(a114,x96702))) % 19.23/19.03 [9674]E(f341(f341(f95(a1,a857),f341(f113(a1),f341(f341(f89(a1),x96741),f341(f88(a1),x96742)))),f341(f341(f20(a1,a857,a857),f341(f341(f9(a1,a857,f864(a857,a857)),f341(f341(f10(a850,f864(a857,f864(a857,a857)),a1),f105(a857)),a191)),f2(a857))),a114)),f341(f341(f3(a857),f341(f113(a857),x96741)),f341(f113(a857),x96742)))+P85(f341(f341(f242(a1),x96742),a92)) % 19.23/19.03 [9675]~P27(x96751,x96752)+P85(f341(f341(f241(f864(f863(x96751,x96751),a850)),f341(f341(f290(x96751,x96751,x96751),f341(f249(f864(f863(x96751,x96751),a850),f864(f863(x96751,x96751),a850)),x96752)),f341(f259(f864(f863(x96751,x96751),a850),f864(f863(x96751,x96751),a850)),x96752))),f341(f249(f864(f863(x96751,x96751),a850),f864(f863(x96751,x96751),a850)),x96752))) % 19.23/19.03 [9731]~E(f341(f50(a857),f341(f265(a857),f341(f341(f20(a857,a850,a850),f341(f341(f10(a850,f864(a850,a850),a857),a339),f341(f341(f9(a857,f864(a857,a850),a850),f343(a857)),x97311))),f341(f341(f9(a857,a857,a850),f242(a857)),f341(a121,x97312))))),f2(a857))+~P85(f341(f341(f343(a857),f2(a857)),x97311)) % 19.23/19.03 [9744]E(f300(a857,f341(f341(f20(a857,f864(a857,a850),f864(a857,a850)),f341(f341(f10(f864(a857,f864(a850,a850)),f864(f864(a857,a850),f864(a857,a850)),a857),f20(a857,a850,a850)),f341(f341(f10(f864(a857,a850),f864(a857,f864(a850,a850)),a857),f341(f10(a850,f864(a850,a850),a857),a339)),f288(a857)))),f341(f341(f10(f864(a857,a850),f864(a857,a850),a857),f341(f10(a850,a850,a857),a337)),f341(f9(a857,a857,a850),f288(a857)))),x97441,x97442),f185(f864(a857,a850)))+~P85(f341(f341(f288(a857),x97442),x97441)) % 19.23/19.03 [9752]E(f301(a857,f288(a857),f341(f341(f20(a857,f864(a857,a850),f864(a857,a850)),f341(f341(f10(f864(a857,f864(a850,a850)),f864(f864(a857,a850),f864(a857,a850)),a857),f20(a857,a850,a850)),f341(f341(f10(f864(a857,a850),f864(a857,f864(a850,a850)),a857),f341(f10(a850,f864(a850,a850),a857),a339)),f288(a857)))),f341(f341(f10(f864(a857,a850),f864(a857,a850),a857),f341(f10(a850,a850,a857),a337)),f341(f9(a857,a857,a850),f288(a857)))),x97521,x97522),f185(f864(a857,a850)))+P85(f341(f341(f288(a857),x97521),x97522)) % 19.23/19.03 [9753]E(f298(a857,f288(a857),f341(f341(f20(a857,f864(a857,a850),f864(a857,a850)),f341(f341(f10(f864(a857,f864(a850,a850)),f864(f864(a857,a850),f864(a857,a850)),a857),f20(a857,a850,a850)),f341(f341(f10(f864(a857,a850),f864(a857,f864(a850,a850)),a857),f341(f10(a850,f864(a850,a850),a857),a339)),f288(a857)))),f341(f341(f10(f864(a857,a850),f864(a857,a850),a857),f341(f10(a850,a850,a857),a337)),f341(f9(a857,a857,a850),f288(a857)))),x97531,x97532),f185(f864(a857,a850)))+P85(f341(f341(f288(a857),x97531),x97532)) % 19.23/19.03 [9757]E(f301(a857,f288(a857),f341(f341(f20(a857,f864(a857,a850),f864(a857,a850)),f341(f341(f10(f864(a857,f864(a850,a850)),f864(f864(a857,a850),f864(a857,a850)),a857),f20(a857,a850,a850)),f341(f341(f10(f864(a857,a850),f864(a857,f864(a850,a850)),a857),f341(f10(a850,f864(a850,a850),a857),a339)),f288(a857)))),f341(f341(f10(f864(a857,a850),f864(a857,a850),a857),f341(f10(a850,a850,a857),a337)),f341(f9(a857,a857,a850),f288(a857)))),x97571,x97572),f185(f864(a857,a850)))+~P85(f341(f341(f288(a857),x97572),x97571)) % 19.23/19.03 [9759]E(f298(a857,f288(a857),f341(f341(f20(a857,f864(a857,a850),f864(a857,a850)),f341(f341(f10(f864(a857,f864(a850,a850)),f864(f864(a857,a850),f864(a857,a850)),a857),f20(a857,a850,a850)),f341(f341(f10(f864(a857,a850),f864(a857,f864(a850,a850)),a857),f341(f10(a850,f864(a850,a850),a857),a339)),f288(a857)))),f341(f341(f10(f864(a857,a850),f864(a857,a850),a857),f341(f10(a850,a850,a857),a337)),f341(f9(a857,a857,a850),f288(a857)))),x97591,x97592),f185(f864(a857,a850)))+~P85(f341(f341(f288(a857),x97592),x97591)) % 19.23/19.03 [9802]E(f60(a1,f341(f113(a1),f341(f341(f3(a1),f341(f341(f89(a1),x98021),x98021)),a106)),f341(f113(a1),f341(f341(f89(a1),x98022),x98022))),f341(f341(f89(a1),f341(f341(f90(a1),f341(f113(a1),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),f60(a1,f341(f113(a1),x98021),f341(f113(a1),x98022)))),f87(a1)))+~P85(f341(f341(f241(a1),f2(a1)),f341(f113(a1),x98022))) % 19.23/19.03 [9811]E(f60(a1,f341(f113(a1),f341(f341(f3(a1),f341(f341(f89(a1),x98111),x98111)),a106)),f341(f113(a1),f341(f341(f89(a1),x98112),x98112))),f341(f341(f3(a1),f341(f341(f90(a1),f341(f113(a1),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),f60(a1,f341(f341(f89(a1),f341(f113(a1),x98111)),f87(a1)),f341(f113(a1),x98112)))),f87(a1)))+P85(f341(f341(f241(a1),f2(a1)),f341(f113(a1),x98112))) % 19.23/19.03 [9873]~P6(x98731)+E(f52(x98731,f341(f265(x98731),f341(f341(f10(f864(x98731,a850),a850,x98731),f97(x98731)),f341(f341(f10(f864(x98731,a850),f864(x98731,a850),x98731),f341(f20(x98731,a850,a850),f341(f341(f10(a850,f864(a850,a850),x98731),a344),f341(f341(f9(x98731,f864(x98731,a850),a850),f343(x98731)),x98732)))),f241(x98731))))),f53(x98731,x98732)) % 19.23/19.03 [9895]~P35(x98951,x98952)+P57(x98951,f341(f341(f9(x98951,f864(f863(x98951,x98951),a850),f864(x98951,a850)),f341(f341(f10(f864(x98951,f864(f864(f863(x98951,x98951),a850),a850)),f864(f864(f863(x98951,x98951),a850),f864(x98951,a850)),x98951),f9(x98951,f864(f863(x98951,x98951),a850),a850)),f341(f341(f10(f864(x98951,f863(x98951,x98951)),f864(x98951,f864(f864(f863(x98951,x98951),a850),a850)),x98951),f341(f10(f863(x98951,x98951),f864(f864(f863(x98951,x98951),a850),a850),x98951),f343(f863(x98951,x98951)))),f250(x98951,x98951)))),x98952)) % 19.23/19.03 [9896]~P9(x98961,f248(f864(x98961,a850)),x98962)+P8(x98961,f341(f341(f9(x98961,f864(f863(x98961,x98961),a850),f864(x98961,a850)),f341(f341(f10(f864(x98961,f864(f864(f863(x98961,x98961),a850),a850)),f864(f864(f863(x98961,x98961),a850),f864(x98961,a850)),x98961),f9(x98961,f864(f863(x98961,x98961),a850),a850)),f341(f341(f10(f864(x98961,f863(x98961,x98961)),f864(x98961,f864(f864(f863(x98961,x98961),a850),a850)),x98961),f341(f10(f863(x98961,x98961),f864(f864(f863(x98961,x98961),a850),a850),x98961),f343(f863(x98961,x98961)))),f250(x98961,x98961)))),x98962)) % 19.23/19.03 [9931]P35(x99311,x99312)+~P57(x99311,f341(f341(f9(x99311,f864(f863(x99311,x99311),a850),f864(x99311,a850)),f341(f341(f10(f864(x99311,f864(f864(f863(x99311,x99311),a850),a850)),f864(f864(f863(x99311,x99311),a850),f864(x99311,a850)),x99311),f9(x99311,f864(f863(x99311,x99311),a850),a850)),f341(f341(f10(f864(x99311,f863(x99311,x99311)),f864(x99311,f864(f864(f863(x99311,x99311),a850),a850)),x99311),f341(f10(f863(x99311,x99311),f864(f864(f863(x99311,x99311),a850),a850),x99311),f343(f863(x99311,x99311)))),f250(x99311,x99311)))),x99312)) % 19.23/19.03 [9932]P9(x99321,f248(f864(x99321,a850)),x99322)+~P8(x99321,f341(f341(f9(x99321,f864(f863(x99321,x99321),a850),f864(x99321,a850)),f341(f341(f10(f864(x99321,f864(f864(f863(x99321,x99321),a850),a850)),f864(f864(f863(x99321,x99321),a850),f864(x99321,a850)),x99321),f9(x99321,f864(f863(x99321,x99321),a850),a850)),f341(f341(f10(f864(x99321,f863(x99321,x99321)),f864(x99321,f864(f864(f863(x99321,x99321),a850),a850)),x99321),f341(f10(f863(x99321,x99321),f864(f864(f863(x99321,x99321),a850),a850),x99321),f343(f863(x99321,x99321)))),f250(x99321,x99321)))),x99322)) % 19.23/19.03 [7181]E(f341(f341(f89(a857),f341(f113(a857),f341(f341(f3(a1),x71811),a106))),x71812),f341(a121,f341(f341(f89(a857),f341(f113(a857),x71811)),x71812)))+P85(f341(a191,f341(f113(a1),x71811))) % 19.23/19.03 [7645]~P89(x76451)+E(f341(f341(f89(x76451),f341(f341(f89(x76451),f87(x76451)),f341(f113(x76451),x76452))),f341(f113(x76451),x76452)),f341(f113(x76451),f341(f341(f3(a1),f341(f341(f89(a1),x76452),x76452)),a106))) % 19.23/19.03 [8278]~P85(f341(f341(f241(a1),x82781),x82782))+P85(f341(f341(f242(a1),f341(f341(f89(a1),x82781),x82781)),f341(f341(f3(a1),f341(f341(f89(a1),x82782),x82782)),a106))) % 19.23/19.03 [8280]~P85(f341(f341(f241(a1),x82801),x82802))+P85(f341(f341(f241(a1),f341(f341(f89(a1),x82801),x82801)),f341(f341(f3(a1),f341(f341(f89(a1),x82802),x82802)),a106))) % 19.23/19.03 [8682]P85(f341(f341(f241(a1),x86821),x86822))+~P85(f341(f341(f242(a1),f341(f341(f89(a1),x86821),x86821)),f341(f341(f3(a1),f341(f341(f89(a1),x86822),x86822)),a106))) % 19.23/19.03 [8684]P85(f341(f341(f241(a1),x86841),x86842))+~P85(f341(f341(f241(a1),f341(f341(f89(a1),x86841),x86841)),f341(f341(f3(a1),f341(f341(f89(a1),x86842),x86842)),a106))) % 19.23/19.03 [8945]~P85(f341(f341(f242(a1),x89451),x89452))+P85(f341(f341(f242(a1),f341(f341(f3(a1),f341(f341(f89(a1),x89451),x89451)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),x89452),x89452)),a106))) % 19.23/19.03 [8947]~P85(f341(f341(f241(a1),x89471),x89472))+P85(f341(f341(f241(a1),f341(f341(f3(a1),f341(f341(f89(a1),x89471),x89471)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),x89472),x89472)),a106))) % 19.23/19.03 [9182]P85(f341(f341(f242(a1),x91821),x91822))+~P85(f341(f341(f242(a1),f341(f341(f3(a1),f341(f341(f89(a1),x91821),x91821)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),x91822),x91822)),a106))) % 19.23/19.03 [9184]P85(f341(f341(f241(a1),x91841),x91842))+~P85(f341(f341(f241(a1),f341(f341(f3(a1),f341(f341(f89(a1),x91841),x91841)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),x91842),x91842)),a106))) % 19.23/19.03 [9214]~P85(f341(f71(x92141),x92142))+P85(f341(f71(f864(x92141,a850)),f341(f265(f864(x92141,a850)),f341(f341(f9(f864(x92141,a850),f864(x92141,a850),a850),f241(f864(x92141,a850))),x92142)))) % 19.23/19.03 [9260]~E(f341(f286(f863(a857,a857),f863(a857,a857),a118),f341(f341(f311(f863(a857,a857)),x92601),f185(f864(f863(a857,a857),a850)))),f341(f286(f863(a857,a857),f863(a857,a857),a118),f341(f341(f311(f863(a857,a857)),x92602),f185(f864(f863(a857,a857),a850)))))+P85(f341(f341(f343(f863(f863(a857,a857),f863(a857,a857))),f341(f341(f250(f863(a857,a857),f863(a857,a857)),x92601),x92602)),a118)) % 19.23/19.03 [9347]E(f341(f286(f863(a857,a857),f863(a857,a857),a118),f341(f341(f311(f863(a857,a857)),x93471),f185(f864(f863(a857,a857),a850)))),f341(f286(f863(a857,a857),f863(a857,a857),a118),f341(f341(f311(f863(a857,a857)),x93472),f185(f864(f863(a857,a857),a850)))))+~P85(f341(f341(f343(f863(f863(a857,a857),f863(a857,a857))),f341(f341(f250(f863(a857,a857),f863(a857,a857)),x93471),x93472)),a118)) % 19.23/19.03 [9380]P85(f341(f341(f241(a1),f2(a1)),f707(x93801,x93802)))+E(f341(f265(a1),f341(f341(f20(a1,a850,a850),f341(f341(f10(a850,f864(a850,a850),a1),a339),f341(f241(a1),f2(a1)))),x93801)),f341(f265(a1),f341(f341(f20(a1,a850,a850),f341(f341(f10(a850,f864(a850,a850),a1),a339),f341(f241(a1),f2(a1)))),x93802))) % 19.23/19.03 [9881]~P6(x98811)+E(f53(x98811,f341(f265(x98811),f341(f341(f10(f864(x98811,a850),a850,x98811),f97(x98811)),f341(f341(f10(f864(x98811,a850),f864(x98811,a850),x98811),f341(f20(x98811,a850,a850),f341(f341(f10(a850,f864(a850,a850),x98811),a344),f341(f341(f9(x98811,f864(x98811,a850),a850),f343(x98811)),x98812)))),f341(f9(x98811,x98811,a850),f241(x98811)))))),f52(x98811,x98812)) % 19.23/19.03 [9901]P85(f341(f341(f343(a857),f2(a857)),x99011))+E(f341(f50(a857),f341(f265(a857),f341(f341(f20(a857,a850,a850),f341(f341(f10(a850,f864(a850,a850),a857),a339),f341(f341(f9(a857,f864(a857,a850),a850),f341(f341(f10(a857,f864(f864(a857,a850),a850),a857),f343(a857)),a121)),x99011))),f341(f341(f9(a857,a857,a850),f242(a857)),x99012)))),f341(f50(a857),f341(f265(a857),f341(f341(f20(a857,a850,a850),f341(f341(f10(a850,f864(a850,a850),a857),a339),f341(f341(f9(a857,f864(a857,a850),a850),f343(a857)),x99011))),f341(f341(f9(a857,a857,a850),f242(a857)),f341(a121,x99012)))))) % 19.23/19.03 [9946]P85(f341(f341(f288(a857),x99461),x99462))+~P85(f341(f341(f343(a857),x99462),f296(a857,f341(f341(f20(a857,f864(a857,a850),f864(a857,a850)),f341(f341(f10(f864(a857,f864(a850,a850)),f864(f864(a857,a850),f864(a857,a850)),a857),f20(a857,a850,a850)),f341(f341(f10(f864(a857,a850),f864(a857,f864(a850,a850)),a857),f341(f10(a850,f864(a850,a850),a857),a339)),f288(a857)))),f341(f341(f10(f864(a857,a850),f864(a857,a850),a857),f341(f10(a850,a850,a857),a337)),f341(f9(a857,a857,a850),f288(a857)))),x99461))) % 19.23/19.03 [9947]P85(f341(f341(f288(a857),x99471),x99472))+~P85(f341(f341(f343(a857),x99471),f299(a857,f341(f341(f20(a857,f864(a857,a850),f864(a857,a850)),f341(f341(f10(f864(a857,f864(a850,a850)),f864(f864(a857,a850),f864(a857,a850)),a857),f20(a857,a850,a850)),f341(f341(f10(f864(a857,a850),f864(a857,f864(a850,a850)),a857),f341(f10(a850,f864(a850,a850),a857),a339)),f288(a857)))),f341(f341(f10(f864(a857,a850),f864(a857,a850),a857),f341(f10(a850,a850,a857),a337)),f341(f9(a857,a857,a850),f288(a857)))),x99472))) % 19.23/19.03 [9948]~P85(f341(f341(f288(a857),x99481),x99482))+~P85(f341(f341(f343(a857),x99482),f299(a857,f341(f341(f20(a857,f864(a857,a850),f864(a857,a850)),f341(f341(f10(f864(a857,f864(a850,a850)),f864(f864(a857,a850),f864(a857,a850)),a857),f20(a857,a850,a850)),f341(f341(f10(f864(a857,a850),f864(a857,f864(a850,a850)),a857),f341(f10(a850,f864(a850,a850),a857),a339)),f288(a857)))),f341(f341(f10(f864(a857,a850),f864(a857,a850),a857),f341(f10(a850,a850,a857),a337)),f341(f9(a857,a857,a850),f288(a857)))),x99481))) % 19.23/19.03 [9949]~P85(f341(f341(f288(a857),x99491),x99492))+~P85(f341(f341(f343(a857),x99491),f296(a857,f341(f341(f20(a857,f864(a857,a850),f864(a857,a850)),f341(f341(f10(f864(a857,f864(a850,a850)),f864(f864(a857,a850),f864(a857,a850)),a857),f20(a857,a850,a850)),f341(f341(f10(f864(a857,a850),f864(a857,f864(a850,a850)),a857),f341(f10(a850,f864(a850,a850),a857),a339)),f288(a857)))),f341(f341(f10(f864(a857,a850),f864(a857,a850),a857),f341(f10(a850,a850,a857),a337)),f341(f9(a857,a857,a850),f288(a857)))),x99492))) % 19.23/19.03 [7512]~P89(x75121)+E(f341(f341(f90(x75121),x75122),f341(f113(x75121),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106))),x75122) % 19.23/19.03 [7779]~P89(x77791)+E(f341(f341(f89(x77791),f341(f113(x77791),x77792)),f87(x77791)),f341(f113(x77791),f341(f341(f89(a1),x77792),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))) % 19.23/19.03 [7923]P85(f341(f341(f241(a1),f2(a1)),f341(f113(a1),x79232)))+E(f341(f341(f251(a1),x79231),f341(f113(a857),f341(f341(f3(a1),f341(f341(f89(a1),x79232),x79232)),a106))),f87(a1)) % 19.23/19.03 [9238]~P85(f341(f341(f241(a1),f2(a1)),f341(f113(a1),x92382)))+E(f341(f341(f251(a1),x92381),f341(f113(a857),f341(f341(f3(a1),f341(f341(f89(a1),x92382),x92382)),a106))),f341(f341(f95(a1,a1),f341(f341(f251(a1),x92381),f341(f113(a857),x92382))),f341(f341(f20(a1,a1,a1),f341(f341(f10(a1,f864(a1,a1),a1),f90(a1)),f341(f90(a1),x92381))),f7(a1)))) % 19.23/19.03 [9721]~P85(f341(f341(f242(a857),f341(f113(a857),x97211)),f341(a121,x97212)))+P85(f341(f341(f95(a1,a850),f341(f113(a1),f341(f341(f89(a1),x97211),a106))),f341(f341(f20(a1,a850,a850),f341(f341(f10(a850,f864(a850,a850),a1),a344),f341(f341(f10(a850,a850,a1),a337),a191))),f341(f341(f9(a1,a857,a850),f341(f341(f10(a857,f864(a857,a850),a1),f242(a857)),a114)),x97212)))) % 19.23/19.03 [9722]~P85(f341(f341(f241(a857),f341(f113(a857),x97221)),f341(a121,x97222)))+P85(f341(f341(f95(a1,a850),f341(f113(a1),f341(f341(f89(a1),x97221),a106))),f341(f341(f20(a1,a850,a850),f341(f341(f10(a850,f864(a850,a850),a1),a344),f341(f341(f10(a850,a850,a1),a337),a191))),f341(f341(f9(a1,a857,a850),f341(f341(f10(a857,f864(a857,a850),a1),f241(a857)),a114)),x97222)))) % 19.23/19.03 [9786]P85(f341(f341(f242(a857),f341(f113(a857),x97861)),f341(a121,x97862)))+~P85(f341(f341(f95(a1,a850),f341(f113(a1),f341(f341(f89(a1),x97861),a106))),f341(f341(f20(a1,a850,a850),f341(f341(f10(a850,f864(a850,a850),a1),a344),f341(f341(f10(a850,a850,a1),a337),a191))),f341(f341(f9(a1,a857,a850),f341(f341(f10(a857,f864(a857,a850),a1),f242(a857)),a114)),x97862)))) % 19.23/19.03 [9787]P85(f341(f341(f241(a857),f341(f113(a857),x97871)),f341(a121,x97872)))+~P85(f341(f341(f95(a1,a850),f341(f113(a1),f341(f341(f89(a1),x97871),a106))),f341(f341(f20(a1,a850,a850),f341(f341(f10(a850,f864(a850,a850),a1),a344),f341(f341(f10(a850,a850,a1),a337),a191))),f341(f341(f9(a1,a857,a850),f341(f341(f10(a857,f864(a857,a850),a1),f241(a857)),a114)),x97872)))) % 19.23/19.03 [9817]~P85(f341(f341(f242(a857),f341(a121,x98172)),f341(f113(a857),x98171)))+P85(f341(f341(f95(a1,a850),f341(f113(a1),f341(f341(f89(a1),x98171),a106))),f341(f341(f20(a1,a850,a850),f341(f341(f10(a850,f864(a850,a850),a1),a339),f341(f341(f10(a850,a850,a1),a337),a191))),f341(f341(f20(a1,a850,a850),f341(f341(f10(a850,f864(a850,a850),a1),a344),f341(f341(f10(a850,a850,a1),a337),a191))),f341(f341(f10(a857,a850,a1),f341(f242(a857),x98172)),a114))))) % 19.23/19.03 [9818]~P85(f341(f341(f241(a857),f341(a121,x98182)),f341(f113(a857),x98181)))+P85(f341(f341(f95(a1,a850),f341(f113(a1),f341(f341(f89(a1),x98181),a106))),f341(f341(f20(a1,a850,a850),f341(f341(f10(a850,f864(a850,a850),a1),a339),f341(f341(f10(a850,a850,a1),a337),a191))),f341(f341(f20(a1,a850,a850),f341(f341(f10(a850,f864(a850,a850),a1),a344),f341(f341(f10(a850,a850,a1),a337),a191))),f341(f341(f10(a857,a850,a1),f341(f241(a857),x98182)),a114))))) % 19.23/19.03 [9871]P85(f341(f341(f242(a857),f341(a121,x98711)),f341(f113(a857),x98712)))+~P85(f341(f341(f95(a1,a850),f341(f113(a1),f341(f341(f89(a1),x98712),a106))),f341(f341(f20(a1,a850,a850),f341(f341(f10(a850,f864(a850,a850),a1),a339),f341(f341(f10(a850,a850,a1),a337),a191))),f341(f341(f20(a1,a850,a850),f341(f341(f10(a850,f864(a850,a850),a1),a344),f341(f341(f10(a850,a850,a1),a337),a191))),f341(f341(f10(a857,a850,a1),f341(f242(a857),x98711)),a114))))) % 19.23/19.03 [9872]P85(f341(f341(f241(a857),f341(a121,x98721)),f341(f113(a857),x98722)))+~P85(f341(f341(f95(a1,a850),f341(f113(a1),f341(f341(f89(a1),x98722),a106))),f341(f341(f20(a1,a850,a850),f341(f341(f10(a850,f864(a850,a850),a1),a339),f341(f341(f10(a850,a850,a1),a337),a191))),f341(f341(f20(a1,a850,a850),f341(f341(f10(a850,f864(a850,a850),a1),a344),f341(f341(f10(a850,a850,a1),a337),a191))),f341(f341(f10(a857,a850,a1),f341(f241(a857),x98721)),a114))))) % 19.23/19.03 [9939]~P85(f341(f341(f343(a857),f2(a857)),x99391))+E(f341(a121,f341(f50(a857),f341(f265(a857),f341(f341(f20(a857,a850,a850),f341(f341(f10(a850,f864(a850,a850),a857),a339),f341(f341(f9(a857,f864(a857,a850),a850),f341(f341(f10(a857,f864(f864(a857,a850),a850),a857),f343(a857)),a121)),x99391))),f341(f341(f9(a857,a857,a850),f242(a857)),x99392))))),f341(f50(a857),f341(f265(a857),f341(f341(f20(a857,a850,a850),f341(f341(f10(a850,f864(a850,a850),a857),a339),f341(f341(f9(a857,f864(a857,a850),a850),f343(a857)),x99391))),f341(f341(f9(a857,a857,a850),f242(a857)),f341(a121,x99392)))))) % 19.23/19.03 [8461]~P89(x84611)+E(f341(f341(f90(x84611),f341(f113(x84611),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106))),x84612),x84612) % 19.23/19.03 [8520]~P89(x85201)+E(f341(f341(f89(x85201),f87(x85201)),f341(f113(x85201),x85202)),f341(f113(x85201),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),x85202))) % 19.23/19.03 [8566]~P89(x85661)+E(f341(f341(f3(x85661),f341(f113(x85661),x85662)),f87(x85661)),f341(f113(x85661),f341(f341(f89(a1),x85662),f341(f88(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106))))) % 19.23/19.03 [8700]~P85(f341(f341(f242(a857),f341(f113(a857),a92)),x87002))+E(f341(f341(f3(a857),x87001),f341(f341(f3(a857),x87002),f341(f113(a857),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),f341(f341(f3(a857),f341(a121,x87001)),x87002)) % 19.23/19.03 [9277]~P86(x92771)+E(f341(f341(f90(x92771),x92772),x92772),f341(f341(f251(x92771),x92772),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106))))) % 19.23/19.03 [9278]~P75(x92781)+E(f341(f341(f251(x92781),x92782),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),f341(f341(f90(x92781),x92782),x92782)) % 19.23/19.03 [9280]~P89(x92801)+E(f341(f341(f90(x92801),x92802),f341(f113(x92801),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),f341(f341(f89(x92801),x92802),x92802)) % 19.23/19.03 [9514]~P136(x95141)+E(f341(f341(f251(x95141),f341(f88(x95141),x95142)),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),f341(f341(f251(x95141),x95142),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106))))) % 19.23/19.03 [9515]~P113(x95151)+E(f341(f341(f251(x95151),f341(f84(x95151),x95152)),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),f341(f341(f251(x95151),x95152),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106))))) % 19.23/19.03 [9511]~P89(x95111)+E(f341(f341(f90(x95111),f341(f113(x95111),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),x95112),f341(f341(f89(x95111),x95112),x95112)) % 19.23/19.03 [9634]~P113(x96341)+E(f341(f84(x96341),f341(f341(f251(x96341),x96342),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106))))),f341(f341(f251(x96341),x96342),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106))))) % 19.23/19.03 [9682]~P113(x96821)+P85(f341(f341(f241(x96821),f2(x96821)),f341(f341(f251(x96821),x96822),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))))) % 19.23/19.03 [9862]~E(f341(a121,x98622),f341(f113(a857),x98621))+P85(f341(f341(f95(a1,a850),f341(f113(a1),f341(f341(f89(a1),x98621),a106))),f341(f341(f20(a1,a850,a850),f341(f341(f10(a850,f864(a850,a850),a1),a339),f341(f341(f10(a850,a850,a1),a337),a191))),f341(f341(f20(a1,a850,a850),f341(f341(f10(a850,f864(a850,a850),a1),a344),f341(f341(f10(a850,a850,a1),a337),a191))),f341(f341(f9(a1,a857,a850),f341(f341(f10(a857,f864(a857,a850),a1),a338),a114)),x98622))))) % 19.23/19.03 [9863]~E(f341(f113(a857),x98631),f341(a121,x98632))+P85(f341(f341(f95(a1,a850),f341(f113(a1),f341(f341(f89(a1),x98631),a106))),f341(f341(f20(a1,a850,a850),f341(f341(f10(a850,f864(a850,a850),a1),a339),f341(f341(f10(a850,a850,a1),a337),a191))),f341(f341(f20(a1,a850,a850),f341(f341(f10(a850,f864(a850,a850),a1),a344),f341(f341(f10(a850,a850,a1),a337),a191))),f341(f341(f9(a1,a857,a850),f341(f341(f10(a857,f864(a857,a850),a1),a338),a114)),x98632))))) % 19.23/19.03 [9904]E(f341(a121,x99041),f341(f113(a857),x99042))+~P85(f341(f341(f95(a1,a850),f341(f113(a1),f341(f341(f89(a1),x99042),a106))),f341(f341(f20(a1,a850,a850),f341(f341(f10(a850,f864(a850,a850),a1),a339),f341(f341(f10(a850,a850,a1),a337),a191))),f341(f341(f20(a1,a850,a850),f341(f341(f10(a850,f864(a850,a850),a1),a344),f341(f341(f10(a850,a850,a1),a337),a191))),f341(f341(f9(a1,a857,a850),f341(f341(f10(a857,f864(a857,a850),a1),a338),a114)),x99041))))) % 19.23/19.03 [9905]E(f341(f113(a857),x99051),f341(a121,x99052))+~P85(f341(f341(f95(a1,a850),f341(f113(a1),f341(f341(f89(a1),x99051),a106))),f341(f341(f20(a1,a850,a850),f341(f341(f10(a850,f864(a850,a850),a1),a339),f341(f341(f10(a850,a850,a1),a337),a191))),f341(f341(f20(a1,a850,a850),f341(f341(f10(a850,f864(a850,a850),a1),a344),f341(f341(f10(a850,a850,a1),a337),a191))),f341(f341(f9(a1,a857,a850),f341(f341(f10(a857,f864(a857,a850),a1),a338),a114)),x99052))))) % 19.23/19.03 [9680]~P89(x96801)+E(f341(f341(f251(x96801),f341(f113(x96801),a106)),f341(f341(f90(a857),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),x96802)),f87(x96801)) % 19.23/19.03 [9681]~P136(x96811)+E(f341(f341(f251(x96811),f341(f88(x96811),f87(x96811))),f341(f341(f90(a857),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),x96812)),f87(x96811)) % 19.23/19.03 [9684]~P75(x96841)+E(f341(f341(f251(x96841),x96842),f341(f113(a857),f341(f341(f3(a1),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106))),a106))),f341(f341(f90(x96841),f341(f341(f90(x96841),x96842),x96842)),x96842)) % 19.23/19.03 [9884]~P85(f341(f341(f241(a1),f2(a1)),x98842))+E(f60(a1,f341(f341(f89(a1),f87(a1)),f341(f341(f90(a1),f341(f113(a1),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),x98841)),f341(f341(f90(a1),f341(f113(a1),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),x98842)),f341(f341(f89(a1),f87(a1)),f341(f341(f90(a1),f341(f113(a1),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),f60(a1,x98841,x98842)))) % 19.23/19.03 [9907]~P85(f341(f341(f241(a1),f2(a1)),x99072))+E(f341(f341(f51(a1),f341(f341(f89(a1),f87(a1)),f341(f341(f90(a1),f341(f113(a1),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),x99071))),f341(f341(f90(a1),f341(f113(a1),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),x99072)),f341(f341(f51(a1),x99071),x99072)) % 19.23/19.03 [9909]~P85(f341(f341(f241(a1),x99092),f2(a1)))+E(f341(f341(f51(a1),f341(f341(f89(a1),f87(a1)),f341(f341(f90(a1),f341(f113(a1),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),x99091))),f341(f341(f90(a1),f341(f113(a1),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),x99092)),f341(f341(f51(a1),f341(f341(f89(a1),x99091),f87(a1))),x99092)) % 19.23/19.03 [9910]~P85(f341(f341(f241(a1),x99102),f2(a1)))+E(f60(a1,f341(f341(f89(a1),f87(a1)),f341(f341(f90(a1),f341(f113(a1),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),x99101)),f341(f341(f90(a1),f341(f113(a1),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),x99102)),f341(f341(f3(a1),f341(f341(f90(a1),f341(f113(a1),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),f60(a1,f341(f341(f89(a1),x99101),f87(a1)),x99102))),f87(a1))) % 19.23/19.03 [9777]~P89(x97771)+E(f341(f341(f251(x97771),f341(f113(x97771),a106)),f341(a121,f341(f341(f90(a857),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),x97772))),f341(f113(x97771),a106)) % 19.23/19.03 [9779]~P136(x97791)+E(f341(f341(f251(x97791),f341(f88(x97791),f87(x97791))),f341(a121,f341(f341(f90(a857),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),x97792))),f341(f88(x97791),f87(x97791))) % 19.23/19.03 [6006]E(x60061,x60062)+~P38(a25,x60061,x60063,x60062) % 19.23/19.03 [5022]~P35(x50221,x50223)+P35(x50221,f336(x50221,x50222,x50223)) % 19.23/19.03 [5265]~P9(x52651,x52652,x52653)+P9(f858(x52651),f155(x52651,x52652),f153(x52651,x52653)) % 19.23/19.03 [5266]~P46(x52661,x52662,x52663)+P46(f858(x52661),f155(x52661,x52662),f153(x52661,x52663)) % 19.23/19.03 [5376]P53(x53761,x53762,x53763)+~E(f647(x53763,x53762,x53761),f648(x53763,x53762,x53761)) % 19.23/19.03 [5377]P52(x53771,x53772,x53773)+~E(f649(x53773,x53772,x53771),f650(x53773,x53772,x53771)) % 19.23/19.03 [6327]P31(x63271,x63272,x63273)+~P30(x63271,f608(x63273,x63272,x63271),f610(x63273,x63272,x63271)) % 19.23/19.03 [4579]~E(x45791,f188(x45792))+~E(x45791,f341(f235(x45792),x45793)) % 19.23/19.03 [4627]~E(f341(f148(x46272),x46271),x46273)+E(x46271,f341(f148(x46272),x46273)) % 19.23/19.03 [4628]~E(x46282,f341(f148(x46281),x46283))+E(f341(f148(x46281),x46282),x46283) % 19.23/19.03 [4672]E(x46721,x46722)+~E(f341(f235(x46723),x46721),f341(f235(x46723),x46722)) % 19.23/19.03 [4673]E(x46731,x46732)+~E(f341(f148(x46733),x46731),f341(f148(x46733),x46732)) % 19.23/19.03 [4871]~P8(x48713,x48711)+P85(f341(f341(x48711,x48712),x48712)) % 19.23/19.03 [4872]~P48(x48723,x48721)+P85(f341(f341(x48721,x48722),x48722)) % 19.23/19.03 [4874]~P57(x48741,x48742)+P85(f341(f330(x48741,x48742),x48743)) % 19.23/19.03 [4936]~P35(x49361,x49362)+P35(f858(x49361),f341(f139(x49361,x49362),x49363)) % 19.23/19.03 [4940]~P85(f341(x49402,x49403))+~E(f341(f265(x49401),x49402),f185(f864(x49401,a850))) % 19.23/19.03 [4941]~P85(f341(x49412,x49413))+~E(f185(f864(x49411,a850)),f341(f265(x49411),x49412)) % 19.23/19.03 [4978]~P85(f341(x49781,x49783))+P85(f341(x49781,f99(x49782,x49781))) % 19.23/19.03 [5101]~E(x51012,x51013)+P85(f341(f341(f343(x51011),x51012),f341(a338,x51013))) % 19.23/19.03 [5153]E(f341(f148(x51531),x51532),f341(f341(f146(x51531),x51533),f122(x51531)))+~E(x51532,f341(f341(f146(x51531),x51533),f122(x51531))) % 19.23/19.03 [5154]~E(x51543,f341(f341(f146(x51541),x51542),f122(x51541)))+E(f341(f341(f146(x51541),x51542),f122(x51541)),f341(f148(x51541),x51543)) % 19.23/19.03 [5179]~E(x51793,f341(f18(f861(x51792),x51791),f188(x51792)))+E(f174(x51791,x51792,x51793),f185(f864(x51791,a850))) % 19.23/19.03 [5199]E(f341(f50(x51991),f374(x51992,x51993,x51991)),x51992)+~E(f341(f50(x51991),x51993),f341(a121,x51992)) % 19.23/19.03 [5205]~P35(x52051,x52053)+P85(f341(f341(f343(x52051),x52052),f331(x52051,x52053))) % 19.23/19.03 [5208]~E(f341(f148(x52082),x52081),f341(f341(f146(x52082),x52083),f122(x52082)))+E(x52081,f341(f341(f146(x52082),x52083),f122(x52082))) % 19.23/19.03 [5209]~E(f341(f341(f146(x52092),x52093),f122(x52092)),f341(f148(x52092),x52091))+E(x52091,f341(f341(f146(x52092),x52093),f122(x52092))) % 19.23/19.03 [5224]E(x52241,f341(f18(f861(x52242),x52243),f188(x52242)))+~E(f174(x52243,x52242,x52241),f185(f864(x52243,a850))) % 19.23/19.03 [5230]E(f94(f863(a857,a857),f63(x52301,x52302)),x52303)+~P85(f341(f63(x52301,x52302),x52303)) % 19.23/19.03 [5237]~E(x52373,f341(f235(x52371),x52372))+P85(f341(f341(f343(x52371),x52372),f234(x52371,x52373))) % 19.23/19.03 [5328]~E(x53282,f122(x53281))+P85(f341(f341(f343(f858(x53281)),x53282),f155(x53281,x53283))) % 19.23/19.03 [5336]~P46(x53361,x53362,x53363)+P46(x53361,x53362,f341(f287(x53361,x53361),x53363)) % 19.23/19.03 [5337]~P53(x53371,x53372,x53373)+P53(x53371,x53372,f341(f287(x53371,x53371),x53373)) % 19.23/19.03 [5357]~P4(x53571)+E(f60(x53571,f60(x53571,x53572,x53573),x53573),f60(x53571,x53572,x53573)) % 19.23/19.03 [5454]E(x54541,x54542)+~P85(f341(f341(f343(x54543),x54541),f341(a338,x54542))) % 19.23/19.03 [5496]~P112(x54961)+E(f187(x54961,x54962,f2(a857),x54963),x54963) % 19.23/19.03 [5516]P46(x55161,x55162,x55163)+~P46(x55161,x55162,f341(f287(x55161,x55161),x55163)) % 19.23/19.03 [5517]P53(x55171,x55172,x55173)+~P53(x55171,x55172,f341(f287(x55171,x55171),x55173)) % 19.23/19.03 [5539]E(x55391,f341(f235(x55392),x55393))+~P85(f341(f341(f343(x55392),x55393),f234(x55392,x55391))) % 19.23/19.03 [5621]~P85(f341(a26,x56213))+P85(f341(a26,f34(x56211,x56212,x56213))) % 19.23/19.03 [5633]E(f341(f133(x56331,x56332),x56333),f122(x56331))+P85(f341(x56332,f767(x56333,x56332,x56331))) % 19.23/19.03 [5789]~P85(f341(f134(x57891),x57893))+P85(f341(f134(x57891),f157(x57891,x57892,x57893))) % 19.23/19.03 [5790]~P85(f341(f134(x57901),x57902))+P85(f341(f134(x57901),f165(x57901,x57902,x57903))) % 19.23/19.03 [5791]~P85(f341(f134(x57911),x57913))+P85(f341(f134(x57911),f167(x57911,x57912,x57913))) % 19.23/19.03 [5792]~P142(x57921,x57922,x57923)+P85(f341(x57921,f60(a1,x57922,x57923))) % 19.23/19.03 [5892]P85(f341(a26,f33(x58921,x58922,x58923)))+~P85(f341(a26,f341(a29,x58922))) % 19.23/19.03 [5904]~P100(x59041)+E(f341(f341(f111(f864(x59041,a850)),f341(f302(x59041),x59042)),f307(x59041,x59042,x59043)),f185(f864(x59041,a850))) % 19.23/19.03 [5905]~P100(x59051)+E(f341(f341(f111(f864(x59051,a850)),f341(f302(x59051),x59052)),f306(x59051,x59052,x59053)),f185(f864(x59051,a850))) % 19.23/19.03 [5906]~P100(x59061)+E(f341(f341(f111(f864(x59061,a850)),f341(f266(x59061),x59062)),f304(x59061,x59062,x59063)),f185(f864(x59061,a850))) % 19.23/19.03 [6055]P85(f341(a26,x60551))+~P85(f341(a26,f34(x60552,x60553,x60551))) % 19.23/19.03 [6057]P85(f341(a26,x60571))+~P85(f341(a26,f35(x60572,x60573,x60571))) % 19.23/19.03 [6059]P85(f341(a26,x60591))+~P85(f341(a26,f35(x60592,x60591,x60593))) % 19.23/19.03 [6139]E(f341(f133(x61391,x61392),x61393),x61393)+~P85(f341(x61392,f770(x61393,x61392,x61391))) % 19.23/19.03 [6141]E(f341(f341(f311(x61411),f383(x61412,x61413,x61411)),f374(x61412,x61413,x61411)),x61413)+~E(f341(f50(x61411),x61413),f341(a121,x61412)) % 19.23/19.03 [6156]P142(x61561,x61562,x61563)+~P85(f341(x61561,f60(a1,x61562,x61563))) % 19.23/19.03 [6208]E(f167(x62081,x62082,x62083),x62083)+~P85(f341(x62082,f782(x62083,x62082,x62081))) % 19.23/19.03 [6248]~P85(f341(a26,f33(x62482,x62481,x62483)))+P85(f341(a26,f341(a29,x62481))) % 19.23/19.03 [6296]~P85(f341(x62962,f596(x62963,x62962,x62961)))+P85(f341(f254(x62961,x62962),x62963)) % 19.23/19.03 [6555]~P85(f341(f330(x65551,x65552),f831(x65553,x65552,x65551)))+P85(f341(f330(x65551,x65552),x65553)) % 19.23/19.03 [6556]~P85(f341(f330(x65561,x65562),f832(x65563,x65562,x65561)))+P85(f341(f330(x65561,x65562),x65563)) % 19.23/19.03 [7182]~P4(x71821)+E(f341(f341(f89(x71821),f341(f341(f90(x71821),x71822),f341(f341(f51(x71821),x71823),x71822))),f60(x71821,x71823,x71822)),x71823) % 19.23/19.03 [7669]E(f341(f341(f250(x76691,x76691),f407(x76692,x76693,x76691)),f407(x76692,x76693,x76691)),x76693)+~P85(f341(f341(f343(f863(x76691,x76691)),x76693),f269(x76691,x76692))) % 19.23/19.03 [7788]~P85(f341(f341(f343(x77881),f377(x77883,x77882,x77881)),f331(x77881,x77883)))+P85(f341(f341(f343(x77881),x77882),f331(x77881,x77883))) % 19.23/19.03 [7789]~P85(f341(f341(f343(x77891),f628(x77893,x77892,x77891)),f331(x77891,x77893)))+P85(f341(f341(f343(x77891),x77892),f331(x77891,x77893))) % 19.23/19.03 [7790]~P85(f341(f341(f343(x77901),f630(x77903,x77902,x77901)),f331(x77901,x77903)))+P85(f341(f341(f343(x77901),x77902),f331(x77901,x77903))) % 19.23/19.03 [7976]~P4(x79761)+E(f341(f341(f89(x79761),f341(f341(f90(x79761),f341(f341(f51(x79761),x79762),x79763)),x79763)),f60(x79761,x79762,x79763)),x79762) % 19.23/19.03 [8016]~E(f341(f50(x80161),x80162),f341(a121,x80163))+~P85(f341(f341(f343(x80161),f383(x80163,x80162,x80161)),f374(x80163,x80162,x80161))) % 19.23/19.03 [8615]P85(f341(f341(f241(f864(f863(x86151,x86151),a850)),f309(x86151,x86152)),f309(x86151,x86153)))+~P85(f341(f341(f241(f864(f863(x86151,x86151),a850)),x86152),f309(x86151,x86153))) % 19.23/19.03 [8855]E(x88551,f122(x88552))+~P85(f341(f341(f343(f863(f858(x88552),f858(x88552))),f341(f341(f250(f858(x88552),f858(x88552)),x88551),f122(x88552))),f153(x88552,x88553))) % 19.23/19.03 [8881]E(x88811,f122(x88812))+~P85(f341(f341(f343(f863(f858(x88812),f858(x88812))),f341(f341(f250(f858(x88812),f858(x88812)),f122(x88812)),x88811)),f153(x88812,x88813))) % 19.23/19.03 [9007]E(f341(f341(f146(x90071),f760(x90072,x90073,x90071)),f761(x90072,x90073,x90071)),x90073)+~P85(f341(f341(f343(f863(f858(x90071),f858(x90071))),f341(f341(f250(f858(x90071),f858(x90071)),f122(x90071)),x90073)),f143(x90071,x90072))) % 19.23/19.03 [9207]~P121(x92071)+~P85(f341(f341(f242(x92071),f341(f341(f89(x92071),f341(f341(f90(x92071),x92072),x92072)),f341(f341(f90(x92071),x92073),x92073))),f2(x92071))) % 19.23/19.03 [9255]P85(f341(f71(x92551),x92552))+~P85(f341(f341(f343(f863(f864(x92551,a850),f864(x92551,a850))),f341(f341(f250(f864(x92551,a850),f864(x92551,a850)),x92553),x92552)),f308(x92551))) % 19.23/19.03 [9536]~P44(x95361,x95362,x95363)+P85(f341(f341(f242(a1),f341(f341(f82(f863(a1,a1),a1,x95361,f249(a1,a1)),f215(x95361)),f232(x95361,x95362,f229(x95361,x95363)))),f2(a1))) % 19.23/19.03 [9537]~P45(x95371,x95372,x95373)+P85(f341(f341(f241(a1),f341(f341(f82(f863(a1,a1),a1,x95371,f249(a1,a1)),f215(x95371)),f232(x95371,x95372,f229(x95371,x95373)))),f2(a1))) % 19.23/19.03 [9658]P44(x96581,x96582,x96583)+~P85(f341(f341(f242(a1),f341(f341(f82(f863(a1,a1),a1,x96581,f249(a1,a1)),f215(x96581)),f232(x96581,x96582,f229(x96581,x96583)))),f2(a1))) % 19.23/19.03 [9659]P45(x96591,x96592,x96593)+~P85(f341(f341(f241(a1),f341(f341(f82(f863(a1,a1),a1,x96591,f249(a1,a1)),f215(x96591)),f232(x96591,x96592,f229(x96591,x96593)))),f2(a1))) % 19.23/19.03 [9990]~P113(x99901)+~P85(f341(f341(f242(x99901),f341(f341(f89(x99901),f341(f341(f251(x99901),x99902),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106))))),f341(f341(f251(x99901),x99903),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))))),f2(x99901))) % 19.23/19.03 [4656]~E(x46563,f122(x46561))+E(f341(f341(f132(x46561),x46562),x46563),x46562) % 19.23/19.03 [4657]~E(x46572,f122(x46571))+E(f341(f341(f132(x46571),x46572),x46573),x46573) % 19.23/19.03 [4663]~E(x46632,f2(a857))+E(f341(f341(f164(x46631),x46632),x46633),f122(x46631)) % 19.23/19.03 [4667]~E(x46673,f122(x46671))+E(f341(f341(f164(x46671),x46672),x46673),f122(x46671)) % 19.23/19.03 [4706]~E(x47061,x47063)+E(x47061,f341(f341(f132(x47062),f122(x47062)),x47063)) % 19.23/19.03 [4788]~P102(x47882)+E(f341(f185(f864(x47881,x47882)),x47883),f185(x47882)) % 19.23/19.03 [4789]~P107(x47892)+E(f341(f248(f864(x47891,x47892)),x47893),f248(x47892)) % 19.23/19.03 [4808]E(x48081,f122(x48082))+~E(f341(f341(f132(x48082),x48083),x48081),x48083) % 19.23/19.03 [4809]E(x48091,f122(x48092))+~E(f341(f341(f132(x48092),x48091),x48093),x48093) % 19.23/19.03 [4817]E(x48171,f122(x48172))+~E(f341(f341(f132(x48172),x48173),x48171),f122(x48172)) % 19.23/19.03 [4818]E(x48181,f122(x48182))+~E(f341(f341(f132(x48182),x48181),x48183),f122(x48182)) % 19.23/19.03 [4843]~E(x48432,f2(a857))+E(f341(f341(f90(a857),x48431),x48432),f341(f341(f90(a857),x48433),x48432)) % 19.23/19.03 [4845]~E(x48451,f2(a857))+E(f341(f341(f90(a857),x48451),x48452),f341(f341(f90(a857),x48451),x48453)) % 19.23/19.03 [4898]~P86(x48981)+E(f341(f341(f89(x48981),x48982),x48983),f341(f341(f89(x48981),x48983),x48982)) % 19.23/19.03 [4899]~P86(x48991)+E(f341(f341(f90(x48991),x48992),x48993),f341(f341(f90(x48991),x48993),x48992)) % 19.23/19.03 [4901]~P101(x49011)+E(f341(f341(f245(x49011),x49012),x49013),f341(f341(f245(x49011),x49013),x49012)) % 19.23/19.03 [4903]~P101(x49031)+E(f341(f341(f240(x49031),x49032),x49033),f341(f341(f240(x49031),x49033),x49032)) % 19.23/19.03 [4904]~P95(x49041)+E(f341(f341(f110(x49041),x49042),x49043),f341(f341(f110(x49041),x49043),x49042)) % 19.23/19.03 [4906]~P98(x49061)+E(f341(f341(f110(x49061),x49062),x49063),f341(f341(f110(x49061),x49063),x49062)) % 19.23/19.03 [4907]~P95(x49071)+E(f341(f341(f111(x49071),x49072),x49073),f341(f341(f111(x49071),x49073),x49072)) % 19.23/19.03 [4909]~P99(x49091)+E(f341(f341(f111(x49091),x49092),x49093),f341(f341(f111(x49091),x49093),x49092)) % 19.23/19.03 [4973]E(f60(a857,x49731,x49732),f2(a857))+~E(x49731,f341(f341(f90(a857),x49732),x49733)) % 19.23/19.03 [4974]E(f60(a1,x49741,x49742),f2(a1))+~E(x49741,f341(f341(f90(a1),x49742),x49743)) % 19.23/19.03 [5034]E(x50341,x50342)+~E(f341(f341(f89(a857),x50343),x50341),f341(f341(f89(a857),x50343),x50342)) % 19.23/19.03 [5035]E(x50351,x50352)+~E(f341(f341(f89(a857),x50351),x50353),f341(f341(f89(a857),x50352),x50353)) % 19.23/19.03 [5045]~P105(x50451)+E(f341(f341(f89(x50451),x50452),f341(f88(x50451),x50453)),f341(f341(f3(x50451),x50452),x50453)) % 19.23/19.03 [5046]~P70(x50461)+E(f341(f341(f89(x50461),x50462),f341(f88(x50461),x50463)),f341(f341(f3(x50461),x50462),x50463)) % 19.23/19.03 [5047]~P3(x50471)+E(f341(f341(f89(x50471),x50472),f341(f88(x50471),x50473)),f341(f341(f3(x50471),x50472),x50473)) % 19.23/19.03 [5048]~P91(x50481)+E(f341(f341(f111(x50481),x50482),f341(f88(x50481),x50483)),f341(f341(f3(x50481),x50482),x50483)) % 19.23/19.03 [5049]~P70(x50491)+E(f341(f341(f3(x50491),x50492),f341(f88(x50491),x50493)),f341(f341(f89(x50491),x50492),x50493)) % 19.23/19.03 [5095]~P85(f341(x50953,x50952))+P85(f341(f341(f343(x50951),x50952),x50953)) % 19.23/19.03 [5097]~P71(x50972)+E(f341(f341(f11(x50971,x50972),x50973),f185(f864(x50971,a850))),f87(x50972)) % 19.23/19.03 [5099]~P68(x50992)+E(f341(f341(f8(x50991,x50992),x50993),f185(f864(x50991,a850))),f2(x50992)) % 19.23/19.03 [5143]~E(x51432,f341(f341(f89(a857),x51431),x51433))+P85(f341(f341(f241(a857),x51431),x51432)) % 19.23/19.03 [5145]~E(x51452,f185(f864(x51451,a850)))+E(f341(f341(f69(x51451),x51452),x51453),f185(f864(f864(x51451,a850),a850))) % 19.23/19.03 [5146]~E(x51462,f185(f864(x51461,a850)))+E(f185(f864(f864(x51461,a850),a850)),f341(f341(f69(x51461),x51462),x51463)) % 19.23/19.03 [5212]~E(f341(f268(x52122,x52123),x52121),f185(f864(x52123,a850)))+E(x52121,f185(f864(f863(x52122,x52123),a850))) % 19.23/19.03 [5213]~E(f341(f270(x52132,x52133),x52131),f185(f864(x52132,a850)))+E(x52131,f185(f864(f863(x52132,x52133),a850))) % 19.23/19.03 [5243]E(f341(f268(x52431,x52432),x52433),f185(f864(x52432,a850)))+~E(x52433,f185(f864(f863(x52431,x52432),a850))) % 19.23/19.03 [5244]E(f341(f270(x52441,x52442),x52443),f185(f864(x52441,a850)))+~E(x52443,f185(f864(f863(x52441,x52442),a850))) % 19.23/19.03 [5247]E(f278(x52471,x52472,x52473),f341(f341(f3(a108),x52472),x52473))+P85(f341(f341(f242(a108),x52472),x52473)) % 19.23/19.03 [5263]P85(f341(x52631,x52632))+~P85(f341(f341(f343(x52633),x52632),x52631)) % 19.23/19.03 [5299]E(x52991,x52992)+~E(f341(f88(f864(x52993,a850)),x52991),f341(f88(f864(x52993,a850)),x52992)) % 19.23/19.03 [5304]E(f316(x53041,x53042,x53043),f188(f858(a849)))+~P85(f341(f341(f242(a1),x53042),x53043)) % 19.23/19.03 [5309]~E(x53091,f185(f864(x53092,a850)))+~P85(f341(f341(f343(x53092),x53093),x53091)) % 19.23/19.03 [5338]~E(x53382,f341(f341(f89(a1),x53381),f341(f109(a1),x53383)))+P85(f341(f341(f241(a1),x53381),x53382)) % 19.23/19.03 [5354]E(f341(f341(f311(x53541),x53542),x53543),x53543)+~P85(f341(f341(f343(x53541),x53542),x53543)) % 19.23/19.03 [5366]E(x53661,f185(f864(x53662,a850)))+~E(f341(f341(f69(x53662),x53661),x53663),f185(f864(f864(x53662,a850),a850))) % 19.23/19.03 [5367]E(x53671,f185(f864(x53672,a850)))+~E(f185(f864(f864(x53672,a850),a850)),f341(f341(f69(x53672),x53671),x53673)) % 19.23/19.03 [5373]~P123(x53731)+E(f341(f341(f90(x53731),f341(f88(x53731),x53732)),f341(f88(x53731),x53733)),f341(f341(f90(x53731),x53732),x53733)) % 19.23/19.03 [5375]~P59(x53751)+E(f341(f341(f292(x53751),f341(f88(x53751),x53752)),f341(f88(x53751),x53753)),f341(f341(f292(x53751),x53752),x53753)) % 19.23/19.03 [5407]~P85(f341(x54073,x54072))+P85(f341(f341(f343(x54071),x54072),f341(f265(x54071),x54073))) % 19.23/19.03 [5447]E(f157(x54471,x54472,x54473),x54473)+P85(f341(f341(f343(x54471),x54472),f341(f163(x54471),x54473))) % 19.23/19.03 [5525]~P85(f341(f134(x55251),x55253))+P85(f341(f134(x55251),f341(f133(x55251,x55252),x55253))) % 19.23/19.03 [5567]~P4(x55671)+E(f341(f341(f51(x55671),f60(x55671,x55672,x55673)),x55673),f2(x55671)) % 19.23/19.03 [5585]E(f165(x55851,f341(f341(f146(x55851),x55852),f122(x55851)),x55853),f122(x55851))+P85(f341(f341(f343(a857),f2(a857)),x55853)) % 19.23/19.03 [5650]E(x56501,x56502)+~E(f341(f341(f90(a857),f341(a121,x56503)),x56501),f341(f341(f90(a857),f341(a121,x56503)),x56502)) % 19.23/19.03 [5651]~E(x56512,f341(f341(f89(a1),x56511),f341(f109(a1),f341(a121,x56513))))+P85(f341(f341(f242(a1),x56511),x56512)) % 19.23/19.03 [5769]~E(x57693,f122(x57691))+E(f341(f341(f341(f179(f858(x57691),f858(x57691)),x57692),f147(x57691)),x57693),f122(x57691)) % 19.23/19.03 [5773]P85(f341(x57731,x57732))+~P85(f341(f341(f343(x57733),x57732),f341(f265(x57733),x57731))) % 19.23/19.03 [5807]E(x58071,x58072)+~E(f341(f341(f311(x58073),x58071),f185(f864(x58073,a850))),f341(f341(f311(x58073),x58072),f185(f864(x58073,a850)))) % 19.23/19.03 [5817]~P100(x58171)+E(f341(f341(f111(f864(x58171,a850)),f341(f266(x58171),x58172)),f341(f303(x58171,x58172),x58173)),f185(f864(x58171,a850))) % 19.23/19.03 [5878]~P77(x58781)+E(f341(f312(x58781,x58781,f88(x58781)),f341(f303(x58781,x58782),x58783)),f306(x58781,f341(f88(x58781),x58783),f341(f88(x58781),x58782))) % 19.23/19.03 [5886]E(f341(f186(f858(x58861)),f157(x58861,x58862,x58863)),f341(f186(f858(x58861)),x58863))+P85(f341(f341(f343(x58861),x58862),f341(f163(x58861),x58863))) % 19.23/19.03 [5942]~P100(x59421)+E(f341(f341(f111(f864(x59421,a850)),f341(f303(x59421,x59422),x59423)),f341(f267(x59421),x59423)),f185(f864(x59421,a850))) % 19.23/19.03 [5963]~P77(x59631)+E(f341(f312(x59631,x59631,f88(x59631)),f307(x59631,x59632,x59633)),f307(x59631,f341(f88(x59631),x59633),f341(f88(x59631),x59632))) % 19.23/19.03 [5964]~P77(x59641)+E(f341(f312(x59641,x59641,f88(x59641)),f304(x59641,x59642,x59643)),f304(x59641,f341(f88(x59641),x59643),f341(f88(x59641),x59642))) % 19.23/19.03 [6022]E(f165(x60221,f341(f341(f146(x60221),x60222),f122(x60221)),x60223),f341(f341(f146(x60221),x60222),f122(x60221)))+~P85(f341(f341(f343(a857),f2(a857)),x60223)) % 19.23/19.03 [6030]~P77(x60301)+E(f341(f312(x60301,x60301,f88(x60301)),f306(x60301,x60302,x60303)),f341(f303(x60301,f341(f88(x60301),x60303)),f341(f88(x60301),x60302))) % 19.23/19.03 [6050]~P5(x60501)+E(f60(x60501,f341(f88(x60501),f60(x60501,x60502,x60503)),x60503),f60(x60501,f341(f88(x60501),x60502),x60503)) % 19.23/19.03 [6154]~P85(f341(f71(f863(x61542,x61541)),x61543))+P85(f341(f71(x61541),f341(f268(x61542,x61541),x61543))) % 19.23/19.03 [6155]~P85(f341(f71(f863(x61551,x61552)),x61553))+P85(f341(f71(x61551),f341(f270(x61551,x61552),x61553))) % 19.23/19.03 [6160]~P100(x61601)+E(f341(f341(f111(f864(x61601,a850)),f307(x61601,x61602,x61603)),f341(f267(x61601),x61603)),f185(f864(x61601,a850))) % 19.23/19.03 [6161]~P100(x61611)+E(f341(f341(f111(f864(x61611,a850)),f306(x61611,x61612,x61613)),f341(f305(x61611),x61613)),f185(f864(x61611,a850))) % 19.23/19.03 [6162]~P100(x61621)+E(f341(f341(f111(f864(x61621,a850)),f304(x61621,x61622,x61623)),f341(f305(x61621),x61623)),f185(f864(x61621,a850))) % 19.23/19.03 [6230]E(f341(f341(f158(x62301),x62302),f740(x62302,x62303,x62301)),x62303)+~P85(f341(f341(f343(x62301),x62303),f341(f163(x62301),x62302))) % 19.23/19.03 [6382]E(x63821,f122(x63822))+~E(f341(f341(f341(f179(f858(x63822),f858(x63822)),x63823),f147(x63822)),x63821),f122(x63822)) % 19.23/19.03 [6461]P38(x64611,x64612,f355(x64613,x64612,x64611),x64613)+~P85(f341(f341(f192(x64611),x64612),x64613)) % 19.23/19.03 [6462]P38(x64621,x64622,f384(x64623,x64622,x64621),x64623)+~P85(f341(f341(f192(x64621),x64622),x64623)) % 19.23/19.03 [6491]~P85(f341(f71(f863(x64912,x64911)),x64913))+P85(f341(f71(f863(x64911,x64912)),f341(f287(x64912,x64911),x64913))) % 19.23/19.03 [6513]E(x65131,x65132)+~E(f291(a857,f288(a857),x65133,x65131),f341(f341(f311(a857),x65132),f185(f864(a857,a850)))) % 19.23/19.03 [6514]E(x65141,x65142)+~E(f291(a857,f288(a857),x65141,x65142),f341(f341(f311(a857),x65143),f185(f864(a857,a850)))) % 19.23/19.03 [6649]P53(x66491,x66492,x66493)+P85(f341(f341(f343(x66491),f648(x66493,x66492,x66491)),x66492)) % 19.23/19.03 [6650]P53(x66501,x66502,x66503)+P85(f341(f341(f343(x66501),f647(x66503,x66502,x66501)),x66502)) % 19.23/19.03 [6661]P85(f341(f330(x66611,x66612),x66613))+P85(f341(f341(x66612,f831(x66613,x66612,x66611)),x66613)) % 19.23/19.03 [6662]P85(f341(f330(x66621,x66622),x66623))+P85(f341(f341(x66622,f832(x66623,x66622,x66621)),x66623)) % 19.23/19.03 [6693]E(f341(f186(f858(x66931)),f157(x66931,x66932,x66933)),f341(f341(f3(a857),f341(f186(f858(x66931)),x66933)),f87(a857)))+~P85(f341(f341(f343(x66931),x66932),f341(f163(x66931),x66933))) % 19.23/19.03 [6733]P85(f341(f254(x67331,x67332),x67333))+P85(f341(f341(f343(x67331),f596(x67333,x67332,x67331)),x67333)) % 19.23/19.03 [6745]~P85(f341(f71(f863(x67452,x67451)),f341(f287(x67451,x67452),x67453)))+P85(f341(f71(f863(x67451,x67452)),x67453)) % 19.23/19.03 [6806]~P85(f341(f341(f343(x68061),x68062),f341(f163(x68061),f123(x68061,x68063))))+P85(f341(f341(f343(x68061),x68062),f341(f163(x68061),x68063))) % 19.23/19.03 [6813]P31(x68131,x68132,x68133)+P85(f341(f341(f343(f856(x68131)),f610(x68133,x68132,x68131)),x68133)) % 19.23/19.03 [6842]E(f341(f133(x68421,x68422),x68423),x68423)+P85(f341(f341(f343(x68421),f770(x68423,x68422,x68421)),f341(f163(x68421),x68423))) % 19.23/19.03 [6859]E(f341(f133(x68591,x68592),x68593),f122(x68591))+P85(f341(f341(f343(x68591),f767(x68593,x68592,x68591)),f341(f163(x68591),x68593))) % 19.23/19.03 [6887]E(f167(x68871,x68872,x68873),x68873)+P85(f341(f341(f343(x68871),f782(x68873,x68872,x68871)),f341(f163(x68871),x68873))) % 19.23/19.03 [7007]P85(f341(f341(f343(x70071),x70072),f705(x70073,x70072,x70071)))+~P85(f341(f341(f343(x70071),x70072),f52(f864(x70071,a850),x70073))) % 19.23/19.03 [7009]~P68(x70091)+E(f341(f341(f89(x70091),f341(f341(f8(a857,x70091),x70092),f341(f266(a857),x70093))),f341(x70092,x70093)),f341(f341(f8(a857,x70091),x70092),f341(f266(a857),f341(a121,x70093)))) % 19.23/19.03 [7112]~P85(f341(f341(f343(x71121),x71122),f692(x71122,x71123,x71121)))+P85(f341(f341(f343(x71121),x71122),f53(f864(x71121,a850),x71123))) % 19.23/19.03 [7141]~P68(x71411)+E(f341(f341(f89(x71411),f341(f341(f8(a857,x71411),x71412),f341(f302(a857),x71413))),f341(x71412,f341(a121,x71413))),f341(f341(f8(a857,x71411),x71412),f341(f302(a857),f341(a121,x71413)))) % 19.23/19.03 [7295]P85(f341(f341(f343(f858(x72951)),x72952),f155(x72951,x72953)))+P85(f341(f341(f343(x72951),f759(x72953,x72952,x72951)),f341(f163(x72951),x72952))) % 19.23/19.03 [7312]~P85(f341(f341(f343(f858(x73121)),x73122),f155(x73121,f331(x73121,x73123))))+P85(f341(f341(f343(f858(x73121)),x73122),f331(f858(x73121),f152(x73121,x73123)))) % 19.23/19.03 [7340]~P85(f341(f341(f343(f858(x73401)),x73402),f331(f858(x73401),f152(x73401,x73403))))+P85(f341(f341(f343(f858(x73401)),x73402),f155(x73401,f331(x73401,x73403)))) % 19.23/19.03 [7380]E(f341(f341(f341(f179(f858(x73801),f858(x73801)),x73802),f147(x73801)),x73803),x73803)+~P85(f341(f341(f241(a857),f341(f186(f858(x73801)),x73803)),f87(a857))) % 19.23/19.03 [7433]~P26(x74331,x74332,x74333,f248(f864(x74331,a850)))+P26(f858(x74331),f858(x74332),f341(f149(x74331,x74332),x74333),f248(f864(f858(x74331),a850))) % 19.23/19.03 [7590]E(x75901,f341(f341(f89(a857),f341(f341(f90(a857),f341(f249(a857,a857),x75902)),x75903)),f341(f259(a857,a857),x75902)))+~P85(f341(f63(x75901,x75903),x75902)) % 19.23/19.03 [7598]P26(x75981,x75982,x75983,f248(f864(x75981,a850)))+~P26(f858(x75981),f858(x75982),f341(f149(x75981,x75982),x75983),f248(f864(f858(x75981),a850))) % 19.23/19.03 [7641]P85(f341(f341(f343(f864(x76411,a850)),f692(x76412,x76413,x76411)),x76413))+P85(f341(f341(f343(x76411),x76412),f53(f864(x76411,a850),x76413))) % 19.23/19.03 [7730]P85(f341(f341(f343(f858(x77301)),x77302),f155(x77301,x77303)))+~P85(f341(f341(f343(x77301),f759(x77303,x77302,x77301)),x77303)) % 19.23/19.03 [7861]E(x78611,x78612)+~E(f341(f341(f9(x78613,f864(x78613,a850),a850),f343(x78613)),x78611),f341(f341(f9(x78613,f864(x78613,a850),a850),f343(x78613)),x78612)) % 19.23/19.03 [7867]~P85(f341(f341(f343(f863(x78671,x78671)),x78673),f269(x78671,x78672)))+P85(f341(f341(f343(x78671),f407(x78672,x78673,x78671)),x78672)) % 19.23/19.03 [7869]~P85(f341(f341(f343(x78691),x78693),f52(f864(x78691,a850),x78692)))+P85(f341(f341(f343(f864(x78691,a850)),f705(x78692,x78693,x78691)),x78692)) % 19.23/19.03 [8127]E(f341(f237(f861(f858(a849)),f858(a849),f316(x81271,x81272,f341(f341(f89(a1),x81273),f87(a1))),f235(f858(a849))),f341(x81271,x81273)),f316(x81271,x81272,x81273))+P85(f341(f341(f242(a1),x81272),x81273)) % 19.23/19.03 [8225]E(x82251,f122(x82252))+P85(f341(f341(f343(x82252),f341(f249(x82252,f863(a108,a108)),f341(f279(x82252,x82251),x82253))),f341(f163(x82252),x82251))) % 19.23/19.03 [8324]~P2(x83241)+E(f341(f138(x83241,x83241,f341(f9(x83241,x83241,x83241),f89(x83241)),x83242),f341(f148(x83241),x83243)),f341(f138(x83241,x83241,f89(x83241),x83242),x83243)) % 19.23/19.03 [8784]~P101(x87841)+E(f341(f163(x87841),f145(x87841,x87841,f7(x87841),x87842,x87843)),f341(f341(f311(x87841),x87842),f341(f163(x87841),x87843))) % 19.23/19.03 [8793]P85(f341(f341(f242(a857),f2(a857)),f644(x87931,x87932,x87933)))+~P85(f341(f341(f343(f863(x87933,x87933)),x87932),f341(f341(f290(x87933,x87933,x87933),x87931),f309(x87933,x87931)))) % 19.23/19.03 [9059]~P55(x90591,x90592)+~P85(f341(f341(f343(f863(x90591,x90591)),f341(f341(f250(x90591,x90591),x90593),x90593)),f341(f341(f290(x90591,x90591,x90591),x90592),f309(x90591,x90592)))) % 19.23/19.03 [9170]~E(f341(f341(f111(f864(f863(x91701,x91701),a850)),f341(f287(x91701,x91701),x91702)),f309(x91701,x91702)),f185(f864(f863(x91701,x91701),a850)))+~P85(f341(f341(f343(f863(x91701,x91701)),f341(f341(f250(x91701,x91701),x91703),x91703)),f341(f341(f290(x91701,x91701,x91701),x91702),f309(x91701,x91702)))) % 19.23/19.03 [9343]~P85(f341(f71(x93431),x93432))+P85(f341(f341(f241(a857),f341(f50(x93431),f341(f341(f3(f864(x93431,a850)),x93432),f341(f341(f311(x93431),x93433),f185(f864(x93431,a850)))))),f341(f50(x93431),x93432))) % 19.23/19.03 [4956]~E(x49563,f122(x49561))+E(f140(x49561,f341(f341(f146(x49561),x49562),x49563)),x49562) % 19.23/19.03 [4970]~E(x49703,f122(x49701))+E(f123(x49701,f341(f341(f146(x49701),x49702),x49703)),f122(x49701)) % 19.23/19.03 [4999]E(x49991,f122(x49992))+E(f140(x49992,f341(f341(f146(x49992),x49993),x49991)),f140(x49992,x49991)) % 19.23/19.03 [5001]E(x50011,f122(x50012))+E(f140(x50012,f341(f341(f132(x50012),x50013),x50011)),f140(x50012,x50011)) % 19.23/19.03 [5008]~E(x50083,f122(x50081))+E(f140(x50081,f341(f341(f132(x50081),x50082),x50083)),f140(x50081,x50082)) % 19.23/19.03 [5009]~E(x50093,f122(x50091))+E(f123(x50091,f341(f341(f132(x50091),x50092),x50093)),f123(x50091,x50092)) % 19.23/19.03 [5039]E(x50391,f122(x50392))+E(f341(f137(x50392),f341(f341(f132(x50392),x50391),x50393)),f341(f137(x50392),x50391)) % 19.23/19.03 [5070]~E(x50702,f122(x50701))+E(f341(f137(x50701),f341(f341(f132(x50701),x50702),x50703)),f341(f137(x50701),x50703)) % 19.23/19.03 [5120]~P101(x51201)+E(f341(f341(f245(x51201),x51202),f341(f341(f240(x51201),x51202),x51203)),x51202) % 19.23/19.03 [5121]~P101(x51211)+E(f341(f341(f240(x51211),x51212),f341(f341(f245(x51211),x51212),x51213)),x51212) % 19.23/19.03 [5122]~P95(x51221)+E(f341(f341(f110(x51221),x51222),f341(f341(f111(x51221),x51222),x51223)),x51222) % 19.23/19.03 [5123]~P95(x51231)+E(f341(f341(f111(x51231),x51232),f341(f341(f110(x51231),x51232),x51233)),x51232) % 19.23/19.03 [5141]~P4(x51411)+E(f60(x51411,f341(f341(f90(x51411),x51412),x51413),x51413),f2(x51411)) % 19.23/19.03 [5142]~P4(x51421)+E(f60(x51421,f341(f341(f90(x51421),x51422),x51423),x51422),f2(x51421)) % 19.23/19.03 [5207]~P3(x52071)+E(f341(f88(x52071),f341(f341(f3(x52071),x52072),x52073)),f341(f341(f3(x52071),x52073),x52072)) % 19.23/19.03 [5267]E(x52671,f122(x52672))+E(f123(x52672,f341(f341(f146(x52672),x52673),x52671)),f341(f341(f146(x52672),x52673),f123(x52672,x52671))) % 19.23/19.03 [5268]E(x52681,f122(x52682))+E(f123(x52682,f341(f341(f132(x52682),x52683),x52681)),f341(f341(f132(x52682),x52683),f123(x52682,x52681))) % 19.23/19.03 [5269]~P6(x52691)+E(f53(x52691,f341(f341(f311(x52691),x52692),x52693)),f341(f341(f111(x52691),x52692),f53(x52691,x52693))) % 19.23/19.03 [5270]~P6(x52701)+E(f52(x52701,f341(f341(f311(x52701),x52702),x52703)),f341(f341(f110(x52701),x52702),f52(x52701,x52703))) % 19.23/19.03 [5313]~P92(x53131)+E(f341(f341(f90(x53131),x53132),f341(f341(f90(x53131),x53132),x53133)),f341(f341(f90(x53131),x53132),x53133)) % 19.23/19.03 [5315]~P101(x53151)+E(f341(f341(f245(x53151),x53152),f341(f341(f245(x53151),x53152),x53153)),f341(f341(f245(x53151),x53152),x53153)) % 19.23/19.03 [5317]~P101(x53171)+E(f341(f341(f240(x53171),x53172),f341(f341(f240(x53171),x53172),x53173)),f341(f341(f240(x53171),x53172),x53173)) % 19.23/19.03 [5318]~P95(x53181)+E(f341(f341(f110(x53181),x53182),f341(f341(f110(x53181),x53182),x53183)),f341(f341(f110(x53181),x53182),x53183)) % 19.23/19.03 [5320]~P98(x53201)+E(f341(f341(f110(x53201),x53202),f341(f341(f110(x53201),x53202),x53203)),f341(f341(f110(x53201),x53202),x53203)) % 19.23/19.03 [5321]~P95(x53211)+E(f341(f341(f111(x53211),x53212),f341(f341(f111(x53211),x53212),x53213)),f341(f341(f111(x53211),x53212),x53213)) % 19.23/19.03 [5323]~P99(x53231)+E(f341(f341(f111(x53231),x53232),f341(f341(f111(x53231),x53232),x53233)),f341(f341(f111(x53231),x53232),x53233)) % 19.23/19.03 [5331]~P4(x53311)+E(f60(x53311,f341(f341(f89(x53311),x53312),x53313),x53313),f60(x53311,x53312,x53313)) % 19.23/19.03 [5332]~P4(x53321)+E(f60(x53321,f341(f341(f89(x53321),x53322),x53323),x53322),f60(x53321,x53323,x53322)) % 19.23/19.03 [5339]~P123(x53391)+E(f341(f341(f90(x53391),x53392),f341(f88(x53391),x53393)),f341(f88(x53391),f341(f341(f90(x53391),x53392),x53393))) % 19.23/19.03 [5340]~P59(x53401)+E(f341(f341(f292(x53401),x53402),f341(f88(x53401),x53403)),f341(f88(x53401),f341(f341(f292(x53401),x53402),x53403))) % 19.23/19.03 [5341]~P67(x53411)+E(f341(f341(f89(x53411),x53412),f341(f160(x53411),x53413)),f341(f160(x53411),f341(f341(f146(x53411),x53412),x53413))) % 19.23/19.03 [5372]~P123(x53721)+E(f341(f341(f90(x53721),f341(f88(x53721),x53722)),x53723),f341(f341(f90(x53721),x53722),f341(f88(x53721),x53723))) % 19.23/19.03 [5378]~P9(x53781,x53782,x53783)+E(f52(f864(x53781,a850),f341(f341(f69(x53781),x53782),x53783)),x53782) % 19.23/19.03 [5439]~P106(x54391)+E(f341(f341(f90(x54391),x54392),f341(f341(f251(x54391),x54392),x54393)),f341(f341(f251(x54391),x54392),f341(a121,x54393))) % 19.23/19.03 [5440]~P86(x54401)+E(f341(f341(f90(x54401),x54402),f341(f341(f251(x54401),x54402),x54403)),f341(f341(f251(x54401),x54402),f341(a121,x54403))) % 19.23/19.03 [5450]~P70(x54501)+E(f341(f341(f89(x54501),f341(f88(x54501),x54502)),f341(f341(f89(x54501),x54502),x54503)),x54503) % 19.23/19.03 [5469]~P112(x54691)+E(f341(f341(f251(x54691),f341(f109(x54691),x54692)),x54693),f341(f109(x54691),f341(f341(f251(a857),x54692),x54693))) % 19.23/19.03 [5470]~P136(x54701)+E(f341(f341(f251(x54701),f341(f112(x54701),x54702)),x54703),f341(f112(x54701),f341(f341(f251(a1),x54702),x54703))) % 19.23/19.03 [5475]~P79(x54751)+E(f341(f84(x54751),f341(f341(f3(x54751),x54752),x54753)),f341(f84(x54751),f341(f341(f3(x54751),x54753),x54752))) % 19.23/19.03 [5477]~P113(x54771)+E(f341(f341(f90(x54771),f91(x54771,x54772)),f91(x54771,x54773)),f91(x54771,f341(f341(f90(x54771),x54772),x54773))) % 19.23/19.03 [5481]E(x54811,f122(x54812))+E(f341(f341(f132(x54812),f341(f162(x54812),x54811)),x54813),f341(f162(x54812),f341(f341(f132(x54812),x54811),x54813))) % 19.23/19.03 [5487]~E(x54872,f341(a121,f341(f341(f89(a857),x54871),x54873)))+P85(f341(f341(f242(a857),x54871),x54872)) % 19.23/19.03 [5488]~P123(x54881)+E(f341(f341(f90(x54881),f341(f88(x54881),x54882)),x54883),f341(f88(x54881),f341(f341(f90(x54881),x54882),x54883))) % 19.23/19.03 [5489]~P116(x54891)+E(f341(f341(f292(x54891),f341(f88(x54891),x54892)),x54893),f341(f88(x54891),f341(f341(f292(x54891),x54892),x54893))) % 19.23/19.03 [5490]~P113(x54901)+E(f341(f341(f251(x54901),f341(f84(x54901),x54902)),x54903),f341(f84(x54901),f341(f341(f251(x54901),x54902),x54903))) % 19.23/19.03 [5584]E(f380(x55841,x55842,x55843),f382(x55841,x55842,x55843))+E(f341(f341(f111(f864(x55843,a850)),x55842),x55841),f185(f864(x55843,a850))) % 19.23/19.03 [5598]~P71(x55982)+E(f341(f341(f11(x55981,x55982),f341(f18(x55982,x55981),f87(x55982))),x55983),f87(x55982)) % 19.23/19.03 [5599]~P68(x55992)+E(f341(f341(f8(x55991,x55992),f341(f18(x55992,x55991),f2(x55992))),x55993),f2(x55992)) % 19.23/19.03 [5601]~P112(x56011)+E(f341(f341(f89(x56011),f341(f109(x56011),x56012)),f341(f109(x56011),x56013)),f341(f109(x56011),f341(f341(f89(a857),x56012),x56013))) % 19.23/19.03 [5602]~P112(x56021)+E(f341(f341(f90(x56021),f341(f109(x56021),x56022)),f341(f109(x56021),x56023)),f341(f109(x56021),f341(f341(f90(a857),x56022),x56023))) % 19.23/19.03 [5603]~P136(x56031)+E(f341(f341(f89(x56031),f341(f112(x56031),x56032)),f341(f112(x56031),x56033)),f341(f112(x56031),f341(f341(f89(a1),x56032),x56033))) % 19.23/19.03 [5604]~P136(x56041)+E(f341(f341(f90(x56041),f341(f112(x56041),x56042)),f341(f112(x56041),x56043)),f341(f112(x56041),f341(f341(f90(a1),x56042),x56043))) % 19.23/19.03 [5605]~P136(x56051)+E(f341(f341(f3(x56051),f341(f112(x56051),x56052)),f341(f112(x56051),x56053)),f341(f112(x56051),f341(f341(f3(a1),x56052),x56053))) % 19.23/19.03 [5608]~P89(x56081)+E(f341(f341(f3(x56081),f341(f113(x56081),x56082)),f341(f113(x56081),x56083)),f341(f113(x56081),f341(f341(f3(a1),x56082),x56083))) % 19.23/19.03 [5609]~P89(x56091)+E(f341(f341(f89(x56091),f341(f113(x56091),x56092)),f341(f113(x56091),x56093)),f341(f113(x56091),f341(f341(f89(a1),x56092),x56093))) % 19.23/19.03 [5610]~P89(x56101)+E(f341(f341(f90(x56101),f341(f113(x56101),x56102)),f341(f113(x56101),x56103)),f341(f113(x56101),f341(f341(f90(a1),x56102),x56103))) % 19.23/19.03 [5657]~E(x56573,x56572)+P85(f341(f341(f241(f864(x56571,a850)),x56572),x56573)) % 19.23/19.03 [5663]~E(x56632,x56633)+P85(f341(f341(f241(f864(x56631,a850)),x56632),x56633)) % 19.23/19.03 [5668]~P70(x56681)+E(f341(f341(f89(x56681),f341(f88(x56681),x56682)),f341(f88(x56681),x56683)),f341(f88(x56681),f341(f341(f89(x56681),x56683),x56682))) % 19.23/19.03 [5669]~P3(x56691)+E(f341(f341(f89(x56691),f341(f88(x56691),x56692)),f341(f88(x56691),x56693)),f341(f88(x56691),f341(f341(f89(x56691),x56692),x56693))) % 19.23/19.03 [5670]~P69(x56701)+E(f341(f341(f240(x56701),f341(f88(x56701),x56702)),f341(f88(x56701),x56703)),f341(f88(x56701),f341(f341(f245(x56701),x56702),x56703))) % 19.23/19.03 [5671]~P69(x56711)+E(f341(f341(f245(x56711),f341(f88(x56711),x56712)),f341(f88(x56711),x56713)),f341(f88(x56711),f341(f341(f240(x56711),x56712),x56713))) % 19.23/19.03 [5672]~P91(x56721)+E(f341(f341(f111(x56721),f341(f88(x56721),x56722)),f341(f88(x56721),x56723)),f341(f88(x56721),f341(f341(f110(x56721),x56722),x56723))) % 19.23/19.03 [5673]~P91(x56731)+E(f341(f341(f110(x56731),f341(f88(x56731),x56732)),f341(f88(x56731),x56733)),f341(f88(x56731),f341(f341(f111(x56731),x56732),x56733))) % 19.23/19.03 [5674]~P113(x56741)+E(f341(f341(f90(x56741),f341(f84(x56741),x56742)),f341(f84(x56741),x56743)),f341(f84(x56741),f341(f341(f90(x56741),x56742),x56743))) % 19.23/19.03 [5675]~P61(x56751)+E(f341(f341(f292(x56751),f341(f84(x56751),x56752)),f341(f84(x56751),x56753)),f341(f84(x56751),f341(f341(f292(x56751),x56752),x56753))) % 19.23/19.03 [5676]~P67(x56761)+E(f341(f341(f89(x56761),f341(f160(x56761),x56762)),f341(f160(x56761),x56763)),f341(f160(x56761),f341(f341(f132(x56761),x56762),x56763))) % 19.23/19.03 [5677]E(x56771,f185(f864(x56772,a850)))+~E(f341(f341(f110(f864(x56772,a850)),x56773),x56771),f185(f864(x56772,a850))) % 19.23/19.03 [5678]E(x56781,f185(f864(x56782,a850)))+~E(f341(f341(f110(f864(x56782,a850)),x56781),x56783),f185(f864(x56782,a850))) % 19.23/19.03 [5679]~P143(x56791,x56792,x56793)+P85(f341(x56791,f341(f341(f51(a1),x56792),x56793))) % 19.23/19.03 [5741]~P85(f341(f71(x57411),x57413))+P85(f341(f71(x57411),f341(f341(f311(x57411),x57412),x57413))) % 19.23/19.03 [5742]~P85(f341(f134(x57421),x57423))+P85(f341(f134(x57421),f341(f341(f164(x57421),x57422),x57423))) % 19.23/19.03 [5743]~P85(f341(f134(x57431),x57433))+P85(f341(f134(x57431),f341(f341(f135(x57431),x57432),x57433))) % 19.23/19.03 [5774]~P101(x57741)+P85(f341(f341(f241(x57741),x57742),f341(f341(f240(x57741),x57743),x57742))) % 19.23/19.03 [5775]~P101(x57751)+P85(f341(f341(f241(x57751),x57752),f341(f341(f240(x57751),x57752),x57753))) % 19.23/19.03 [5776]~P95(x57761)+P85(f341(f341(f241(x57761),x57762),f341(f341(f110(x57761),x57763),x57762))) % 19.23/19.03 [5777]~P98(x57771)+P85(f341(f341(f241(x57771),x57772),f341(f341(f110(x57771),x57773),x57772))) % 19.23/19.03 [5778]~P95(x57781)+P85(f341(f341(f241(x57781),x57782),f341(f341(f110(x57781),x57782),x57783))) % 19.23/19.03 [5779]~P98(x57791)+P85(f341(f341(f241(x57791),x57792),f341(f341(f110(x57791),x57792),x57793))) % 19.23/19.03 [5780]~P86(x57801)+P85(f341(f341(f288(x57801),x57802),f341(f341(f90(x57801),x57803),x57802))) % 19.23/19.03 [5781]~P86(x57811)+P85(f341(f341(f288(x57811),x57812),f341(f341(f90(x57811),x57812),x57813))) % 19.23/19.03 [5794]~E(x57941,f2(a857))+E(f341(f341(f51(a857),f341(f341(f90(a857),x57941),x57942)),f341(f341(f90(a857),x57941),x57943)),f2(a857)) % 19.23/19.03 [5859]P85(f341(x58591,x58592))+P85(f341(f341(f192(f37(x58591,x58593)),x58592),x58592)) % 19.23/19.03 [5871]~P89(x58711)+E(f341(f341(f3(x58711),f341(f113(x58711),x58712)),f341(f113(x58711),x58713)),f341(f113(x58711),f341(f341(f89(a1),x58712),f341(f88(a1),x58713)))) % 19.23/19.03 [5926]E(x59261,f2(a857))+E(f341(f341(f51(a857),f341(f341(f90(a857),x59261),x59262)),f341(f341(f90(a857),x59261),x59263)),f341(f341(f51(a857),x59262),x59263)) % 19.23/19.03 [5994]P143(x59941,x59942,x59943)+~P85(f341(x59941,f341(f341(f51(a1),x59942),x59943))) % 19.23/19.03 [6071]E(x60711,f122(x60712))+E(f341(f341(f146(x60712),f341(f137(x60712),x60711)),f341(f341(f164(x60712),x60713),f341(f162(x60712),x60711))),f341(f341(f164(x60712),f341(a121,x60713)),x60711)) % 19.23/19.03 [6079]E(f341(f341(f3(f864(x60791,a850)),x60792),x60793),x60792)+~E(f341(f341(f111(f864(x60791,a850)),x60792),x60793),f185(f864(x60791,a850))) % 19.23/19.03 [6123]~P85(f341(f341(f242(a857),x61231),x61233))+P85(f341(f341(f242(a857),x61231),f341(f341(f89(a857),x61232),x61233))) % 19.23/19.03 [6125]~P85(f341(f341(f242(a857),x61251),x61252))+P85(f341(f341(f242(a857),x61251),f341(f341(f89(a857),x61252),x61253))) % 19.23/19.03 [6127]~P85(f341(f341(f241(a857),x61271),x61273))+P85(f341(f341(f241(a857),x61271),f341(f341(f89(a857),x61272),x61273))) % 19.23/19.03 [6129]~P85(f341(f341(f241(a857),x61291),x61292))+P85(f341(f341(f241(a857),x61291),f341(f341(f89(a857),x61292),x61293))) % 19.23/19.03 [6168]P85(f341(f71(x61681),x61682))+~P85(f341(f71(x61681),f341(f341(f311(x61681),x61683),x61682))) % 19.23/19.03 [6169]P85(f341(f134(x61691),x61692))+~P85(f341(f134(x61691),f341(f341(f146(x61691),x61693),x61692))) % 19.23/19.03 [6170]P85(f341(f134(x61701),x61702))+~P85(f341(f134(x61701),f341(f341(f132(x61701),x61703),x61702))) % 19.23/19.03 [6171]P85(f341(f134(x61711),x61712))+~P85(f341(f134(x61711),f341(f341(f132(x61711),x61712),x61713))) % 19.23/19.03 [6216]~E(f60(a1,x62162,x62161),f60(a1,x62163,x62161))+P85(f341(f341(f288(a1),x62161),f341(f341(f3(a1),x62162),x62163))) % 19.23/19.03 [6221]~P86(x62211)+E(f341(f341(f89(x62211),x62212),f341(f341(f90(x62211),x62213),x62212)),f341(f341(f90(x62211),f341(f341(f89(x62211),x62213),f87(x62211))),x62212)) % 19.23/19.03 [6269]~E(x62691,x62692)+~P85(f341(f341(f242(f864(x62693,a850)),x62691),x62692)) % 19.23/19.03 [6317]P85(f341(f341(f343(x63171),x63172),x63173))+P85(f341(f341(f343(x63171),x63172),f341(f88(f864(x63171,a850)),x63173))) % 19.23/19.03 [6324]E(f140(x63241,f341(f341(f135(x63241),x63242),x63243)),f140(x63241,x63243))+~P85(f341(f341(f242(a857),x63242),f341(f186(f858(x63241)),x63243))) % 19.23/19.03 [6325]E(f341(f341(f164(x63251),x63252),f123(x63251,x63253)),f341(f341(f164(x63251),x63252),x63253))+~P85(f341(f341(f242(a857),x63252),f341(f186(f858(x63251)),x63253))) % 19.23/19.03 [6384]E(f341(f341(f341(f179(f858(x63841),f858(x63841)),x63842),f147(x63841)),x63843),x63843)+~E(f60(a857,x63842,f341(f186(f858(x63841)),x63843)),f2(a857)) % 19.23/19.03 [6393]~P9(x63931,x63933,x63932)+E(f341(f341(f290(x63931,x63931,x63931),f341(f287(x63931,x63931),x63932)),x63932),x63932) % 19.23/19.03 [6436]~E(f341(f341(f110(f864(x64361,a850)),x64362),x64363),x64363)+P85(f341(f341(f241(f864(x64361,a850)),x64362),x64363)) % 19.23/19.03 [6441]~P52(x64411,x64411,x64413)+P52(x64411,x64411,f341(f341(f179(f863(x64411,x64411),a850),x64412),x64413)) % 19.23/19.03 [6443]~P85(f341(f341(f343(x64431),x64433),f341(f163(x64431),x64432)))+P85(f341(f341(f242(a857),f2(a857)),f341(f186(f858(x64431)),x64432))) % 19.23/19.03 [6473]~P79(x64731)+E(f341(f84(x64731),f341(f341(f89(x64731),f341(f84(x64731),x64732)),f341(f84(x64731),x64733))),f341(f341(f89(x64731),f341(f84(x64731),x64732)),f341(f84(x64731),x64733))) % 19.23/19.03 [6484]E(f341(f341(f51(a857),f341(f341(f90(a857),x64841),x64842)),f341(f341(f90(a857),x64841),x64843)),f341(f341(f51(a857),x64842),x64843))+~P85(f341(f341(f242(a857),f2(a857)),x64841)) % 19.23/19.03 [6511]E(f60(a1,x65111,x65112),f60(a1,x65113,x65112))+~P85(f341(f341(f288(a1),x65112),f341(f341(f3(a1),x65111),x65113))) % 19.23/19.03 [6624]~P85(f341(f71(x66241),x66243))+E(f341(f341(f74(x66241,f864(x66241,a850),f311(x66241)),x66242),x66243),f341(f341(f110(f864(x66241,a850)),x66243),x66242)) % 19.23/19.03 [6686]E(f341(f341(f110(f864(x66861,a850)),x66862),x66863),x66862)+~P85(f341(f341(f241(f864(x66861,a850)),x66863),x66862)) % 19.23/19.03 [6688]E(f341(f341(f110(f864(x66881,a850)),x66882),x66883),x66883)+~P85(f341(f341(f241(f864(x66881,a850)),x66882),x66883)) % 19.23/19.03 [6689]E(f341(f341(f111(f864(x66891,a850)),x66892),x66893),x66893)+~P85(f341(f341(f241(f864(x66891,a850)),x66893),x66892)) % 19.23/19.03 [6690]E(f341(f341(f111(f864(x66901,a850)),x66902),x66903),x66902)+~P85(f341(f341(f241(f864(x66901,a850)),x66902),x66903)) % 19.23/19.03 [6743]~P85(f341(f134(x67431),x67432))+E(f341(f341(f3(f864(x67431,a850)),f341(f163(x67431),x67432)),f341(f341(f311(x67431),x67433),f185(f864(x67431,a850)))),f341(f163(x67431),f157(x67431,x67433,x67432))) % 19.23/19.03 [6801]P35(x68011,x68012)+~P35(x68011,f341(f341(f179(f863(x68011,x68011),a850),x68013),x68012)) % 19.23/19.03 [6817]~E(x68171,f2(a857))+P85(f341(f341(f288(a857),f341(f341(f90(a857),x68171),x68172)),f341(f341(f90(a857),x68171),x68173))) % 19.23/19.03 [6871]P85(f341(f64(x68711,x68712),f341(a66,x68713)))+~P85(f341(f64(f341(f88(a1),x68711),f341(f88(a1),x68712)),x68713)) % 19.23/19.03 [6876]E(f341(f341(f3(f864(x68761,a850)),f341(f341(f311(x68761),x68762),x68763)),f341(f341(f311(x68761),x68762),f185(f864(x68761,a850)))),x68763)+P85(f341(f341(f343(x68761),x68762),x68763)) % 19.23/19.03 [6895]E(f341(f341(f111(f864(x68951,a850)),f341(f163(x68951),x68952)),f341(f163(x68951),x68953)),f185(f864(x68951,a850)))+~P85(f341(f134(x68951),f341(f341(f132(x68951),x68952),x68953))) % 19.23/19.03 [6912]~P85(f341(f341(f343(x69121),x69122),f341(f163(x69121),x69123)))+~P85(f341(f134(x69121),f341(f341(f146(x69121),x69122),x69123))) % 19.23/19.03 [6988]E(f341(f341(f111(f864(x69881,a850)),x69882),x69883),f185(f864(x69881,a850)))+P85(f341(f341(f343(x69881),f380(x69883,x69882,x69881)),x69882)) % 19.23/19.03 [6989]E(f341(f341(f111(f864(x69891,a850)),x69892),x69893),f185(f864(x69891,a850)))+P85(f341(f341(f343(x69891),f382(x69893,x69892,x69891)),x69893)) % 19.23/19.03 [6993]E(f123(x69931,f341(f341(f164(x69931),x69932),x69933)),f341(f341(f164(x69931),f341(f341(f3(a857),x69932),f87(a857))),x69933))+~P85(f341(f341(f241(a857),x69932),f341(f186(f858(x69931)),x69933))) % 19.23/19.03 [7075]P85(f341(f341(f242(a857),f2(a857)),x70751))+P85(f341(f341(f241(a857),f341(f341(f90(a857),x70752),x70751)),f341(f341(f90(a857),x70753),x70751))) % 19.23/19.03 [7076]P85(f341(f341(f242(a857),f2(a857)),x70761))+P85(f341(f341(f241(a857),f341(f341(f90(a857),x70761),x70762)),f341(f341(f90(a857),x70761),x70763))) % 19.23/19.03 [7079]~P85(f341(f341(f343(x70791),x70792),x70793))+~P85(f341(f341(f343(x70791),x70792),f341(f88(f864(x70791,a850)),x70793))) % 19.23/19.03 [7085]~P85(f341(f341(f242(f864(x70851,a850)),x70852),x70853))+P85(f341(f341(f241(f864(x70851,a850)),x70852),x70853)) % 19.23/19.03 [7189]~P85(f341(f341(f242(a857),x71892),x71893))+P85(f341(f341(f242(a857),f341(f341(f89(a857),x71891),x71892)),f341(f341(f89(a857),x71891),x71893))) % 19.23/19.04 [7190]~P85(f341(f341(f242(a857),x71901),x71903))+P85(f341(f341(f242(a857),f341(f341(f89(a857),x71901),x71902)),f341(f341(f89(a857),x71903),x71902))) % 19.23/19.04 [7191]~P85(f341(f341(f242(a1),x71911),x71913))+P85(f341(f341(f242(a1),f341(f341(f89(a1),x71911),x71912)),f341(f341(f89(a1),x71913),x71912))) % 19.23/19.04 [7194]~P85(f341(f341(f241(a857),x71942),x71943))+P85(f341(f341(f241(a857),f341(f341(f89(a857),x71941),x71942)),f341(f341(f89(a857),x71941),x71943))) % 19.23/19.04 [7195]~P85(f341(f341(f241(a857),x71951),x71953))+P85(f341(f341(f241(a857),f341(f341(f89(a857),x71951),x71952)),f341(f341(f89(a857),x71953),x71952))) % 19.23/19.04 [7197]~P85(f341(f341(f241(a857),x71972),x71973))+P85(f341(f341(f241(a857),f341(f341(f90(a857),x71971),x71972)),f341(f341(f90(a857),x71971),x71973))) % 19.23/19.04 [7199]~P85(f341(f341(f241(a857),x71991),x71993))+P85(f341(f341(f241(a857),f341(f341(f90(a857),x71991),x71992)),f341(f341(f90(a857),x71993),x71992))) % 19.23/19.04 [7200]~P85(f341(f341(f241(a857),x72001),x72003))+P85(f341(f341(f241(a857),f341(f341(f51(a857),x72001),x72002)),f341(f341(f51(a857),x72003),x72002))) % 19.23/19.04 [7201]~P85(f341(f341(f241(a857),x72013),x72012))+P85(f341(f341(f241(a857),f341(f341(f3(a857),x72011),x72012)),f341(f341(f3(a857),x72011),x72013))) % 19.23/19.04 [7202]~P85(f341(f341(f241(a857),x72021),x72023))+P85(f341(f341(f241(a857),f341(f341(f3(a857),x72021),x72022)),f341(f341(f3(a857),x72023),x72022))) % 19.23/19.04 [7203]~P85(f341(f341(f241(a1),x72032),x72033))+P85(f341(f341(f241(a1),f341(f341(f89(a1),x72031),x72032)),f341(f341(f89(a1),x72031),x72033))) % 19.23/19.04 [7206]~P85(f341(f341(f288(a857),x72062),x72063))+P85(f341(f341(f288(a857),f341(f341(f90(a857),x72061),x72062)),f341(f341(f90(a857),x72061),x72063))) % 19.23/19.04 [7294]E(x72941,x72942)+~P85(f341(f341(f343(x72943),x72941),f341(f341(f311(x72943),x72942),f185(f864(x72943,a850))))) % 19.23/19.04 [7296]~E(f341(f341(f111(f864(x72961,a850)),x72962),x72963),f185(f864(x72961,a850)))+P85(f341(f341(f241(f864(x72961,a850)),x72962),f341(f88(f864(x72961,a850)),x72963))) % 19.23/19.04 [7303]P85(f341(f341(f343(f864(x73031,a850)),x73032),f341(f310(x73031),x73033)))+~P85(f341(f341(f241(f864(x73031,a850)),x73032),x73033)) % 19.23/19.04 [7360]E(f341(f341(f146(x73601),f341(f341(f158(x73601),x73602),x73603)),f341(f341(f135(x73601),f341(a121,x73603)),x73602)),f341(f341(f135(x73601),x73603),x73602))+~P85(f341(f341(f242(a857),x73603),f341(f186(f858(x73601)),x73602))) % 19.23/19.04 [7390]P85(f341(f341(f343(f863(x73901,x73901)),x73902),f309(x73901,x73903)))+~P85(f341(f341(f343(f863(x73901,x73901)),x73902),x73903)) % 19.23/19.04 [7400]~P85(f341(f341(f343(f864(x74001,a850)),x74002),f341(f310(x74001),x74003)))+P85(f341(f341(f241(f864(x74001,a850)),x74002),x74003)) % 19.23/19.04 [7441]P85(f341(f341(f241(f864(x74411,a850)),x74412),f52(f864(x74411,a850),x74413)))+~P85(f341(f341(f343(f864(x74411,a850)),x74412),x74413)) % 19.23/19.04 [7469]~P136(x74691)+E(f341(f341(f90(x74691),f341(f341(f251(x74691),f341(f88(x74691),f87(x74691))),x74692)),f341(f341(f251(x74691),x74693),x74692)),f341(f341(f251(x74691),f341(f88(x74691),x74693)),x74692)) % 19.23/19.04 [7491]E(f341(f341(f158(x74911),x74912),f341(f341(f3(a857),f341(f186(f858(x74911)),x74912)),f341(a121,x74913))),f341(f341(f158(x74911),f341(f148(x74911),x74912)),x74913))+~P85(f341(f341(f242(a857),x74913),f341(f186(f858(x74911)),x74912))) % 19.23/19.04 [7508]~E(f341(f341(f111(f864(x75081,a850)),f670(x75083,x75082,x75081)),x75083),f185(f864(x75081,a850)))+E(f341(f341(f111(f864(x75081,a850)),f52(f864(x75081,a850),x75082)),x75083),f185(f864(x75081,a850))) % 19.23/19.04 [7572]~P85(f341(f341(f343(x75723),x75722),f341(f163(x75723),x75721)))+P85(f341(f341(f242(a857),f740(x75721,x75722,x75723)),f341(f186(f858(x75723)),x75721))) % 19.23/19.04 [7580]P85(f341(f341(f343(x75801),f341(f341(f158(x75801),x75802),x75803)),f341(f163(x75801),x75802)))+~P85(f341(f341(f242(a857),x75803),f341(f186(f858(x75801)),x75802))) % 19.23/19.04 [7689]P85(f341(f341(f241(f864(f858(x76891),a850)),f155(x76891,x76892)),f155(x76891,x76893)))+~P85(f341(f341(f241(f864(x76891,a850)),x76892),x76893)) % 19.23/19.04 [7718]E(f341(f341(f111(f864(x77181,a850)),f52(f864(x77181,a850),x77182)),x77183),f185(f864(x77181,a850)))+P85(f341(f341(f343(f864(x77181,a850)),f670(x77183,x77182,x77181)),x77182)) % 19.23/19.04 [7720]~P85(f341(f341(f343(f864(x77201,a850)),x77203),x77202))+P85(f341(f341(f241(f864(x77201,a850)),f53(f864(x77201,a850),x77202)),x77203)) % 19.23/19.04 [7722]E(f341(f341(f111(f864(x77221,a850)),x77222),x77223),f185(f864(x77221,a850)))+~P85(f341(f341(f241(f864(x77221,a850)),x77222),f341(f88(f864(x77221,a850)),x77223))) % 19.23/19.04 [7775]E(f341(f341(f3(a857),f341(f341(f89(a857),f341(f160(a857),x77751)),x77752)),f341(f341(f158(a857),x77751),x77753)),f341(f160(a857),f341(f341(f154(a857,x77751),x77753),x77752)))+~P85(f341(f341(f242(a857),x77753),f341(f186(f858(a857)),x77751))) % 19.23/19.04 [7825]P85(f341(f341(f242(a857),x78251),x78252))+~P85(f341(f341(f242(a857),f341(f341(f89(a857),x78253),x78251)),f341(f341(f89(a857),x78253),x78252))) % 19.23/19.04 [7826]P85(f341(f341(f242(a857),x78261),x78262))+~P85(f341(f341(f242(a857),f341(f341(f90(a857),x78263),x78261)),f341(f341(f90(a857),x78263),x78262))) % 19.23/19.04 [7827]P85(f341(f341(f242(a857),x78271),x78272))+~P85(f341(f341(f242(a857),f341(f341(f90(a857),x78271),x78273)),f341(f341(f90(a857),x78272),x78273))) % 19.23/19.04 [7830]P85(f341(f341(f241(a857),x78301),x78302))+~P85(f341(f341(f241(a857),f341(f341(f89(a857),x78303),x78301)),f341(f341(f89(a857),x78303),x78302))) % 19.23/19.04 [7859]P85(f341(f341(f242(a857),f2(a857)),x78591))+~P85(f341(f341(f242(a857),f341(f341(f90(a857),x78592),x78591)),f341(f341(f90(a857),x78593),x78591))) % 19.23/19.04 [7860]P85(f341(f341(f242(a857),f2(a857)),x78601))+~P85(f341(f341(f242(a857),f341(f341(f90(a857),x78601),x78602)),f341(f341(f90(a857),x78601),x78603))) % 19.23/19.04 [7933]E(f253(x79331,x79332,x79333),x79332)+~P85(f341(f341(f241(f864(x79331,a850)),x79333),f341(f341(f311(x79331),x79332),f185(f864(x79331,a850))))) % 19.23/19.04 [8012]E(f341(f341(f132(x80121),f341(f341(f164(x80121),x80122),x80123)),f341(f341(f146(x80121),f341(f341(f158(x80121),x80123),x80122)),f122(x80121))),f341(f341(f164(x80121),f341(a121,x80122)),x80123))+~P85(f341(f341(f242(a857),x80122),f341(f186(f858(x80121)),x80123))) % 19.23/19.04 [8080]P85(f341(f341(f241(f864(f864(x80801,a850),a850)),f254(x80801,x80802)),f254(x80801,x80803)))+~P85(f341(f341(f241(f864(x80801,a850)),x80802),x80803)) % 19.23/19.04 [8119]~P85(f341(f134(x81191),x81193))+P85(f341(f134(x81191),f341(f341(f341(f179(f858(x81191),f858(x81191)),x81192),f147(x81191)),x81193))) % 19.23/19.04 [8124]~P85(f341(f341(f242(a857),x81242),x81243))+P85(f341(f341(f242(a857),f341(f341(f90(a857),f341(a121,x81241)),x81242)),f341(f341(f90(a857),f341(a121,x81241)),x81243))) % 19.23/19.04 [8145]P85(f341(f341(f241(f864(f864(x81451,a850),a850)),f341(f310(x81451),x81452)),f341(f310(x81451),x81453)))+~P85(f341(f341(f241(f864(x81451,a850)),x81452),x81453)) % 19.23/19.04 [8303]~P85(f341(f341(f241(f864(x83031,a850)),x83033),x83032))+P85(f341(f341(f241(f864(x83031,a850)),f341(f88(f864(x83031,a850)),x83032)),f341(f88(f864(x83031,a850)),x83033))) % 19.23/19.04 [8342]E(f341(f312(a857,a857,f341(f341(f9(a857,a857,a857),f3(a857)),x83421)),f341(f303(a857,x83422),x83423)),f341(f303(a857,f341(f341(f3(a857),x83422),x83421)),f341(f341(f3(a857),x83423),x83421)))+~P85(f341(f341(f242(a857),x83421),x83423)) % 19.23/19.04 [8368]~P67(x83681)+E(f341(f341(f89(x83681),x83682),f341(f138(x83681,x83681,f89(x83681),f2(x83681)),x83683)),f341(f138(x83681,x83681,f89(x83681),x83682),x83683)) % 19.23/19.04 [8448]~P79(x84481)+P85(f341(f341(f241(x84481),f341(f84(x84481),f341(f341(f89(x84481),x84482),x84483))),f341(f341(f89(x84481),f341(f84(x84481),x84482)),f341(f84(x84481),x84483)))) % 19.23/19.04 [8449]~P79(x84491)+P85(f341(f341(f241(x84491),f341(f84(x84491),f341(f341(f3(x84491),x84492),x84493))),f341(f341(f89(x84491),f341(f84(x84491),x84492)),f341(f84(x84491),x84493)))) % 19.23/19.04 [8459]E(f341(f341(f89(a1),f341(f341(f90(a1),x84591),f60(a1,f341(f341(f51(a1),x84592),x84591),x84593))),f60(a1,x84592,x84591)),f60(a1,x84592,f341(f341(f90(a1),x84591),x84593)))+~P85(f341(f341(f242(a1),f2(a1)),x84593)) % 19.23/19.04 [8467]E(f341(f341(f132(x84671),f341(f341(f164(x84671),x84672),x84673)),f341(f341(f146(x84671),f341(f137(x84671),f341(f341(f135(x84671),x84672),x84673))),f122(x84671))),f341(f341(f164(x84671),f341(a121,x84672)),x84673))+~P85(f341(f341(f242(a857),x84672),f341(f186(f858(x84671)),x84673))) % 19.23/19.04 [8486]E(f341(f274(x84861,f341(f341(f149(x84861,f863(a108,x84861)),f341(f250(a108,x84861),f87(a108))),x84862)),f341(a5,x84863)),f341(f341(f158(x84861),x84862),x84863))+~P85(f341(f341(f242(a857),x84863),f341(f186(f858(x84861)),x84862))) % 19.23/19.04 [8543]P85(f341(f341(f343(f863(x85431,x85431)),x85432),f341(f341(f290(x85431,x85431,x85431),x85433),f309(x85431,x85433))))+~P85(f341(f341(f343(f863(x85431,x85431)),x85432),x85433)) % 19.23/19.04 [8560]P85(f341(f341(f241(a857),x85601),x85602))+~P85(f341(f341(f241(a857),f341(f341(f90(a857),f341(a121,x85603)),x85601)),f341(f341(f90(a857),f341(a121,x85603)),x85602))) % 19.23/19.04 [8571]P85(f341(f341(f241(f864(x85711,a850)),x85712),x85713))+~P85(f341(f341(f241(f864(x85711,a850)),f341(f88(f864(x85711,a850)),x85713)),f341(f88(f864(x85711,a850)),x85712))) % 19.23/19.04 [8590]P85(f341(f134(x85901),x85902))+~P85(f341(f134(x85901),f341(f341(f341(f179(f858(x85901),f858(x85901)),x85903),f147(x85901)),x85902))) % 19.23/19.04 [8656]E(f341(f286(x86561,x86561,f309(x86561,x86562)),x86563),x86563)+~P85(f341(f341(f241(f864(x86561,a850)),f341(f286(x86561,x86561,x86562),x86563)),x86563)) % 19.23/19.04 [8658]E(f341(f312(f863(x86581,x86582),x86582,f259(x86581,x86582)),f341(f163(f863(x86581,x86582)),x86583)),f176(x86581,x86582,f171(x86581,x86582,x86583)))+~P85(f341(f134(x86581),f341(f341(f149(f863(x86581,x86582),x86581),f249(x86581,x86582)),x86583))) % 19.23/19.04 [8697]~P101(x86971)+P15(x86971,f341(f133(x86971,f341(f341(f9(x86971,x86971,a850),a338),f341(x86972,x86973))),x86973)) % 19.23/19.04 [8702]~P85(f341(f341(f241(a857),x87021),x87022))+P85(f341(f341(f241(a857),x87021),f341(f138(a857,a857,f89(a857),x87022),x87023))) % 19.23/19.04 [8773]~P85(f341(f341(f343(f863(x87731,x87731)),x87732),f309(x87731,x87733)))+P85(f341(f341(f343(f863(x87731,x87731)),x87732),f341(f341(f179(f863(x87731,x87731),a850),f638(x87733,x87732,x87731)),x87733))) % 19.23/19.04 [8844]~P67(x88441)+E(f341(f341(f89(x88441),x88442),f341(f138(x88441,x88441,f341(f9(x88441,x88441,x88441),f89(x88441)),f2(x88441)),f341(f148(x88441),x88443))),f341(f138(x88441,x88441,f89(x88441),x88442),x88443)) % 19.23/19.04 [9104]P52(x91041,x91042,x91043)+P85(f341(f341(f343(f863(x91041,x91042)),f341(f341(f250(x91041,x91042),f657(x91043,x91042,x91041)),f650(x91043,x91042,x91041))),x91043)) % 19.23/19.04 [9105]P52(x91051,x91052,x91053)+P85(f341(f341(f343(f863(x91051,x91052)),f341(f341(f250(x91051,x91052),f657(x91053,x91052,x91051)),f649(x91053,x91052,x91051))),x91053)) % 19.23/19.04 [9161]~P85(f341(f341(f343(f863(x91611,x91611)),x91612),f341(f341(f290(x91611,x91611,x91611),x91613),f309(x91611,x91613))))+P85(f341(f341(f343(f863(x91611,x91611)),x91612),f341(f341(f179(f863(x91611,x91611),a850),f644(x91613,x91612,x91611)),x91613))) % 19.23/19.04 [9236]~P85(f341(f341(f241(f864(x92361,a850)),x92362),x92363))+P85(f341(f341(f241(f864(x92361,a850)),f341(f341(f9(x92361,f864(x92361,a850),a850),f343(x92361)),x92362)),f341(f341(f9(x92361,f864(x92361,a850),a850),f343(x92361)),x92363))) % 19.23/19.04 [9292]~P85(f341(f341(f343(f863(f864(x92921,a850),f864(x92921,a850))),f341(f341(f250(f864(x92921,a850),f864(x92921,a850)),x92922),x92923)),f308(x92921)))+P85(f341(f341(f242(f864(x92921,a850)),x92922),x92923)) % 19.23/19.04 [9318]P53(x93181,x93182,x93183)+~P85(f341(f341(f343(f863(x93181,x93181)),f341(f341(f250(x93181,x93181),f648(x93183,x93182,x93181)),f647(x93183,x93182,x93181))),x93183)) % 19.23/19.04 [9319]P53(x93191,x93192,x93193)+~P85(f341(f341(f343(f863(x93191,x93191)),f341(f341(f250(x93191,x93191),f647(x93193,x93192,x93191)),f648(x93193,x93192,x93191))),x93193)) % 19.23/19.04 [9353]~P85(f341(f341(f343(f863(f858(x93531),f858(x93531))),f341(f341(f250(f858(x93531),f858(x93531)),x93532),x93532)),f143(x93531,x93533)))+P85(f341(f341(f343(f863(x93531,x93531)),f341(f341(f250(x93531,x93531),f765(x93532,x93533,x93531)),f765(x93532,x93533,x93531))),x93533)) % 19.23/19.04 [9397]P85(f341(f341(f241(f864(x93971,a850)),x93972),x93973))+~P85(f341(f341(f241(f864(x93971,a850)),f341(f341(f9(x93971,f864(x93971,a850),a850),f343(x93971)),x93972)),f341(f341(f9(x93971,f864(x93971,a850),a850),f343(x93971)),x93973))) % 19.23/19.04 [9484]E(f341(f341(f3(a857),f341(f341(f8(a857,a857),x94841),f341(f266(a857),x94842))),f341(f341(f8(a857,a857),x94843),f341(f266(a857),x94842))),f341(f341(f8(a857,a857),f341(f341(f20(a857,a857,a857),f341(f341(f10(a857,f864(a857,a857),a857),f3(a857)),x94841)),x94843)),f341(f266(a857),x94842)))+~P85(f341(f341(f241(a857),f341(x94843,f518(x94842,x94841,x94843))),f341(x94841,f518(x94842,x94841,x94843)))) % 19.23/19.04 [9774]E(f341(f265(f863(x97741,x97742)),f341(f260(x97741,x97742,a850),f341(f341(f9(x97741,f864(x97742,f861(x97742)),f864(x97742,a850)),f341(f341(f10(f864(f861(x97742),a850),f864(f864(x97742,f861(x97742)),f864(x97742,a850)),x97741),f10(f861(x97742),a850,x97742)),f341(f341(f10(f861(x97742),f864(f861(x97742),a850),x97741),a338),f171(x97741,x97742,x97743)))),f235(x97742)))),f341(f163(f863(x97741,x97742)),x97743))+~P85(f341(f134(x97741),f341(f341(f149(f863(x97741,x97742),x97741),f249(x97741,x97742)),x97743))) % 19.23/19.04 [5522]~P70(x55221)+E(f341(f341(f89(x55221),f341(f341(f3(x55221),x55222),x55223)),x55223),x55222) % 19.23/19.04 [5523]~P70(x55231)+E(f341(f341(f3(x55231),f341(f341(f89(x55231),x55232),x55233)),x55233),x55232) % 19.23/19.04 [5749]~P70(x57491)+E(f341(f341(f89(x57491),x57492),f341(f341(f89(x57491),f341(f88(x57491),x57492)),x57493)),x57493) % 19.23/19.04 [5833]~P75(x58331)+E(f341(f341(f90(x58331),f341(f341(f251(x58331),x58332),x58333)),x58332),f341(f341(f251(x58331),x58332),f341(a121,x58333))) % 19.23/19.04 [5834]~P86(x58341)+E(f341(f341(f90(x58341),f341(f341(f251(x58341),x58342),x58343)),x58342),f341(f341(f251(x58341),x58342),f341(a121,x58343))) % 19.23/19.04 [6047]~P113(x60471)+E(f341(f84(x60471),f341(f341(f251(x60471),f341(f88(x60471),x60472)),x60473)),f341(f84(x60471),f341(f341(f251(x60471),x60472),x60473))) % 19.23/19.04 [6099]~P75(x60991)+E(f341(f341(f90(x60991),f341(f341(f251(x60991),x60992),x60993)),x60992),f341(f341(f90(x60991),x60992),f341(f341(f251(x60991),x60992),x60993))) % 19.23/19.04 [6159]E(f341(f341(f3(a108),f341(f341(f89(a108),x61591),x61592)),x61593),f278(x61591,x61592,x61593))+~P85(f341(f341(f242(a108),x61592),x61593)) % 19.23/19.04 [6181]~E(f341(f341(f135(x61811),x61813),x61812),f122(x61811))+P85(f341(f341(f241(a857),f341(f186(f858(x61811)),x61812)),x61813)) % 19.23/19.04 [6322]E(f341(f341(f90(a857),f341(f113(a857),x63221)),f341(f341(f90(a857),f341(f113(a857),x63222)),x63223)),f2(a857))+~P85(f341(f341(f242(a1),x63221),a92)) % 19.23/19.04 [6338]~P59(x63381)+E(f341(f341(f251(x63381),f341(f341(f292(x63381),f87(x63381)),x63382)),x63383),f341(f341(f292(x63381),f87(x63381)),f341(f341(f251(x63381),x63382),x63383))) % 19.23/19.04 [6423]E(f341(f341(f3(a857),f341(f341(f89(a857),x64231),x64232)),x64233),f341(f341(f3(a857),x64231),f341(f341(f3(a857),x64233),x64232)))+~P85(f341(f341(f241(a857),x64232),x64233)) % 19.23/19.04 [6424]E(f341(f341(f3(a857),f341(f341(f89(a857),x64241),x64242)),x64243),f341(f341(f89(a857),x64241),f341(f341(f3(a857),x64242),x64243)))+~P85(f341(f341(f241(a857),x64243),x64242)) % 19.23/19.04 [6464]~P101(x64641)+P85(f341(f341(f241(x64641),f341(f341(f245(x64641),x64642),x64643)),x64643)) % 19.23/19.04 [6465]~P101(x64651)+P85(f341(f341(f241(x64651),f341(f341(f245(x64651),x64652),x64653)),x64652)) % 19.23/19.04 [6466]~P95(x64661)+P85(f341(f341(f241(x64661),f341(f341(f111(x64661),x64662),x64663)),x64663)) % 19.23/19.04 [6467]~P99(x64671)+P85(f341(f341(f241(x64671),f341(f341(f111(x64671),x64672),x64673)),x64673)) % 19.23/19.04 [6468]~P95(x64681)+P85(f341(f341(f241(x64681),f341(f341(f111(x64681),x64682),x64683)),x64682)) % 19.23/19.04 [6469]~P99(x64691)+P85(f341(f341(f241(x64691),f341(f341(f111(x64691),x64692),x64693)),x64692)) % 19.23/19.04 [6483]E(f341(f341(f51(a1),f341(f341(f51(a1),x64831),x64832)),x64833),f341(f341(f51(a1),x64831),f341(f341(f90(a1),x64832),x64833)))+~P85(f341(f341(f242(a1),f2(a1)),x64833)) % 19.23/19.04 [6536]~P86(x65361)+E(f341(f341(f89(x65361),f341(f341(f90(x65361),x65362),x65363)),x65363),f341(f341(f90(x65361),f341(f341(f89(x65361),x65362),f87(x65361))),x65363)) % 19.23/19.04 [6537]~P89(x65371)+E(f341(f341(f90(x65371),f341(f88(x65371),f341(f113(x65371),x65372))),x65373),f341(f341(f90(x65371),f341(f113(x65371),f341(f88(a1),x65372))),x65373)) % 19.23/19.04 [6609]~P67(x66091)+E(f341(f160(x66091),f341(f341(f149(x66092,x66091),f341(f18(x66091,x66092),f2(x66091))),x66093)),f2(x66091)) % 19.23/19.04 [6628]E(f341(f341(f89(a857),f341(f113(a857),x66281)),f341(f341(f89(a857),f341(f113(a857),x66282)),x66283)),f341(f341(f89(a857),f341(f113(a857),x66282)),x66283))+~P85(f341(a191,f341(f113(a1),x66281))) % 19.23/19.04 [6643]~P6(x66431)+E(f53(x66431,f341(f341(f311(x66431),x66432),f341(f341(f311(x66431),x66433),f185(f864(x66431,a850))))),f341(f341(f111(x66431),x66432),x66433)) % 19.23/19.04 [6644]~P6(x66441)+E(f52(x66441,f341(f341(f311(x66441),x66442),f341(f341(f311(x66441),x66443),f185(f864(x66441,a850))))),f341(f341(f110(x66441),x66442),x66443)) % 19.23/19.04 [6668]E(f341(f341(f164(x66681),x66682),x66683),x66683)+~P85(f341(f341(f241(a857),f341(f186(f858(x66681)),x66683)),x66682)) % 19.23/19.04 [6680]E(f341(f341(f135(x66801),x66802),x66803),f122(x66801))+~P85(f341(f341(f241(a857),f341(f186(f858(x66801)),x66803)),x66802)) % 19.23/19.04 [6692]E(f341(f341(f3(a857),f341(f341(f89(a857),x66921),x66922)),x66923),f341(f341(f89(a857),f341(f341(f3(a857),x66921),x66923)),x66922))+~P85(f341(f341(f241(a857),x66923),x66921)) % 19.23/19.04 [6706]~P85(f341(f341(f242(a857),x67061),x67063))+P85(f341(f341(f242(a857),f341(f341(f3(a857),x67061),x67062)),x67063)) % 19.23/19.04 [6734]~P101(x67341)+E(f157(x67341,x67342,f341(f341(f144(x67341,x67341,f7(x67341)),x67342),x67343)),x67343) % 19.23/19.04 [6831]E(f341(f341(f3(a857),f341(f341(f89(a857),x68311),x68312)),f341(a121,x68313)),f341(f341(f3(a857),x68311),f341(a121,f341(f341(f3(a857),x68313),x68312))))+~P85(f341(f341(f241(a857),x68312),x68313)) % 19.23/19.04 [6832]~P113(x68321)+P85(f341(f341(f241(x68321),f2(x68321)),f341(f341(f251(x68321),f341(f84(x68321),x68322)),x68323))) % 19.23/19.04 [6883]P25(x68831,x68832,x68833)+~P85(f341(f341(f241(f864(f856(x68831),a850)),x68833),x68832)) % 19.23/19.04 [6924]~P85(f341(f71(x69241),x69242))+P85(f341(f71(x69241),f341(f341(f3(f864(x69241,a850)),x69242),x69243))) % 19.23/19.04 [6925]~P85(f341(f71(x69251),x69253))+P85(f341(f71(x69251),f341(f341(f111(f864(x69251,a850)),x69252),x69253))) % 19.23/19.04 [6926]~P85(f341(f71(x69261),x69262))+P85(f341(f71(x69261),f341(f341(f111(f864(x69261,a850)),x69262),x69263))) % 19.23/19.04 [7064]~P35(x70641,x70643)+P35(x70641,f341(f341(f111(f864(f863(x70641,x70641),a850)),x70642),x70643)) % 19.23/19.04 [7065]~P35(x70651,x70652)+P35(x70651,f341(f341(f111(f864(f863(x70651,x70651),a850)),x70652),x70653)) % 19.23/19.04 [7184]~P95(x71841)+E(f15(x71841,f341(f163(x71841),f341(f341(f146(x71841),x71842),x71843))),f341(f138(x71841,x71841,f110(x71841),x71842),x71843)) % 19.23/19.04 [7185]~P95(x71851)+E(f12(x71851,f341(f163(x71851),f341(f341(f146(x71851),x71852),x71853))),f341(f138(x71851,x71851,f111(x71851),x71852),x71853)) % 19.23/19.04 [7186]~P101(x71861)+E(f16(x71861,f341(f163(x71861),f341(f341(f146(x71861),x71862),x71863))),f341(f138(x71861,x71861,f240(x71861),x71862),x71863)) % 19.23/19.04 [7187]~P101(x71871)+E(f17(x71871,f341(f163(x71871),f341(f341(f146(x71871),x71872),x71873))),f341(f138(x71871,x71871,f245(x71871),x71872),x71873)) % 19.23/19.04 [7188]~P85(f341(f341(f288(a1),x71881),x71882))+P85(f341(f341(f288(a1),x71881),f341(f341(f89(a1),x71882),f341(f341(f90(a1),x71881),x71883)))) % 19.23/19.04 [7258]~P85(f341(f71(x72581),x72582))+P85(f341(f341(f241(a857),f341(f50(x72581),x72582)),f341(f50(x72581),f341(f341(f311(x72581),x72583),x72582)))) % 19.23/19.04 [7265]E(f341(f341(f110(f864(a857,a850)),f341(f303(a857,x72651),x72652)),f341(f303(a857,x72652),f341(f341(f89(a857),x72652),x72653))),f341(f303(a857,x72651),f341(f341(f89(a857),x72652),x72653)))+~P85(f341(f341(f241(a857),x72651),x72652)) % 19.23/19.04 [7275]P85(f341(f341(f242(a857),x72751),x72752))+~P85(f341(f341(f242(a857),f341(f341(f89(a857),x72751),x72753)),x72752)) % 19.23/19.04 [7278]P85(f341(f341(f241(a857),x72781),x72782))+~P85(f341(f341(f241(a857),f341(f341(f89(a857),x72783),x72781)),x72782)) % 19.23/19.04 [7279]P85(f341(f341(f241(a857),x72791),x72792))+~P85(f341(f341(f241(a857),f341(f341(f89(a857),x72791),x72793)),x72792)) % 19.23/19.04 [7321]~P101(x73211)+E(f13(x73211,f240(x73211),f341(f163(x73211),f341(f341(f146(x73211),x73212),x73213))),f341(f138(x73211,x73211,f240(x73211),x73212),x73213)) % 19.23/19.04 [7322]~P101(x73221)+E(f14(x73221,f245(x73221),f341(f163(x73221),f341(f341(f146(x73221),x73222),x73223))),f341(f138(x73221,x73221,f245(x73221),x73222),x73223)) % 19.23/19.04 [7326]~E(x73262,f185(f864(f863(x73261,x73261),a850)))+P85(f341(f341(f241(f864(f863(x73261,x73261),a850)),x73262),x73263)) % 19.23/19.04 [7434]E(f341(f341(f110(f864(x74341,a850)),x74342),f341(f341(f3(f864(x74341,a850)),x74343),x74342)),x74343)+~P85(f341(f341(f241(f864(x74341,a850)),x74342),x74343)) % 19.23/19.04 [7437]~P85(f341(f341(f242(a857),x74371),f341(f341(f3(a857),x74373),x74372)))+P85(f341(f341(f242(a857),f341(f341(f89(a857),x74371),x74372)),x74373)) % 19.23/19.04 [7438]~P85(f341(f341(f241(a857),x74381),f341(f341(f89(a857),x74383),x74382)))+P85(f341(f341(f241(a857),f341(f341(f3(a857),x74381),x74382)),x74383)) % 19.23/19.04 [7498]E(x74981,f122(x74982))+E(f341(f137(x74982),f341(f341(f341(f179(f858(x74982),f858(x74982)),x74983),f147(x74982)),x74981)),f341(f341(f158(x74982),x74981),f60(a857,x74983,f341(f186(f858(x74982)),x74981)))) % 19.23/19.04 [7507]E(f341(f341(f311(x75071),x75072),f341(f341(f3(f864(x75071,a850)),x75073),f341(f341(f311(x75071),x75072),f185(f864(x75071,a850))))),x75073)+~P85(f341(f341(f343(x75071),x75072),x75073)) % 19.23/19.04 [7671]P85(f341(f341(f242(a857),x76711),f341(f341(f3(a857),x76712),x76713)))+~P85(f341(f341(f242(a857),f341(f341(f89(a857),x76711),x76713)),x76712)) % 19.23/19.04 [7672]P85(f341(f341(f241(a857),x76721),f341(f341(f89(a857),x76722),x76723)))+~P85(f341(f341(f241(a857),f341(f341(f3(a857),x76721),x76723)),x76722)) % 19.23/19.04 [7692]P85(f341(f71(x76921),x76922))+~P85(f341(f71(x76921),f341(f341(f110(f864(x76921,a850)),x76923),x76922))) % 19.23/19.04 [7693]P85(f341(f71(x76931),x76932))+~P85(f341(f71(x76931),f341(f341(f110(f864(x76931,a850)),x76932),x76933))) % 19.23/19.04 [7774]~P43(x77741,x77743)+P85(f341(f341(f343(f863(x77741,x77741)),f341(f341(f250(x77741,x77741),x77742),x77742)),x77743)) % 19.23/19.04 [7824]P85(f341(f341(f288(a1),x78241),x78242))+~P85(f341(f341(f288(a1),x78241),f341(f341(f89(a1),x78242),f341(f341(f90(a1),x78241),x78243)))) % 19.23/19.04 [7904]E(f341(f341(f158(a857),f136(a857,f341(f303(a857,x79041),x79042))),x79043),f341(f341(f89(a857),x79041),x79043))+~P85(f341(f341(f242(a857),f341(f341(f89(a857),x79041),x79043)),x79042)) % 19.23/19.04 [7974]~P85(f341(f341(f192(f341(a29,x79741)),x79742),x79743))+P85(f341(f341(f192(f341(f239(a851),f341(a32,x79741))),x79742),x79743)) % 19.23/19.04 [7978]E(f341(f341(f164(a857),x79781),f136(a857,f341(f303(a857,x79782),x79783))),f136(a857,f341(f303(a857,x79782),f341(f341(f89(a857),x79782),x79781))))+~P85(f341(f341(f241(a857),f341(f341(f89(a857),x79782),x79781)),x79783)) % 19.23/19.04 [8026]~P89(x80261)+E(f341(f341(f251(x80261),x80262),f341(f113(a857),f341(f341(f89(a1),x80263),x80263))),f341(f341(f95(x80261,x80261),f341(f341(f251(x80261),x80262),f341(f113(a857),x80263))),f341(f341(f20(x80261,x80261,x80261),f90(x80261)),f7(x80261)))) % 19.23/19.04 [8224]P85(f341(f341(f192(f341(a29,x82241)),x82242),x82243))+~P85(f341(f341(f192(f341(f239(a851),f341(a32,x82241))),x82242),x82243)) % 19.23/19.04 [8282]E(f341(f341(f132(x82821),f341(f341(f164(x82821),x82822),x82823)),f341(f341(f146(x82821),f341(f341(f158(x82821),x82823),x82822)),f341(f341(f135(x82821),f341(a121,x82822)),x82823))),x82823)+~P85(f341(f341(f242(a857),x82822),f341(f186(f858(x82821)),x82823))) % 19.23/19.04 [8289]P85(f341(f341(f241(f864(x82891,a850)),f330(x82891,x82892)),f330(x82891,x82893)))+~P85(f341(f341(f241(f864(x82891,f864(x82891,a850))),x82893),x82892)) % 19.23/19.04 [8290]~P53(x82901,x82902,x82903)+P53(x82901,x82902,f341(f341(f3(f864(f863(x82901,x82901),a850)),x82903),f309(x82901,f185(f864(f863(x82901,x82901),a850))))) % 19.23/19.04 [8312]P85(f341(f341(f241(f864(x83121,a850)),f331(x83121,x83122)),f331(x83121,x83123)))+~P85(f341(f341(f241(f864(f863(x83121,x83121),a850)),x83123),x83122)) % 19.23/19.04 [8319]~P121(x83191)+P85(f341(f341(f241(x83191),f2(x83191)),f341(f341(f89(x83191),f341(f341(f90(x83191),x83192),x83192)),f341(f341(f90(x83191),x83193),x83193)))) % 19.23/19.04 [8356]P85(f341(f341(f241(f864(x83561,a850)),f341(f285(x83561),x83562)),f341(f285(x83561),x83563)))+~P85(f341(f341(f241(f864(f863(x83561,x83561),a850)),x83562),x83563)) % 19.23/19.04 [8388]~P47(x83881,x83882)+~P85(f341(f341(f343(f863(x83881,x83881)),f341(f341(f250(x83881,x83881),x83883),x83883)),x83882)) % 19.23/19.04 [8390]~P35(x83901,x83902)+~P85(f341(f341(f343(f863(x83901,x83901)),f341(f341(f250(x83901,x83901),x83903),x83903)),x83902)) % 19.23/19.04 [8450]P85(f341(f341(f241(f864(x84501,a850)),f53(f864(x84501,a850),x84502)),f53(f864(x84501,a850),x84503)))+~P85(f341(f341(f241(f864(f864(x84501,a850),a850)),x84503),x84502)) % 19.23/19.04 [8451]P85(f341(f341(f241(f864(x84511,a850)),f52(f864(x84511,a850),x84512)),f52(f864(x84511,a850),x84513)))+~P85(f341(f341(f241(f864(f864(x84511,a850),a850)),x84512),x84513)) % 19.23/19.04 [8505]~P9(x85051,x85053,x85052)+P85(f341(f341(f241(f864(f863(x85051,x85051),a850)),x85052),f341(f341(f257(x85051,x85051),x85053),f341(f18(f864(x85051,a850),x85051),x85053)))) % 19.23/19.04 [8506]~P46(x85061,x85063,x85062)+P85(f341(f341(f241(f864(f863(x85061,x85061),a850)),x85062),f341(f341(f257(x85061,x85061),x85063),f341(f18(f864(x85061,a850),x85061),x85063)))) % 19.23/19.04 [8544]~P79(x85441)+P85(f341(f341(f241(x85441),f341(f341(f3(x85441),f341(f84(x85441),x85442)),f341(f84(x85441),x85443))),f341(f84(x85441),f341(f341(f3(x85441),x85443),x85442)))) % 19.23/19.04 [8545]~P79(x85451)+P85(f341(f341(f241(x85451),f341(f341(f3(x85451),f341(f84(x85451),x85452)),f341(f84(x85451),x85453))),f341(f84(x85451),f341(f341(f3(x85451),x85452),x85453)))) % 19.23/19.04 [8569]P85(f341(f341(f241(f864(f863(x85691,x85691),a850)),f309(x85691,x85692)),f309(x85691,x85693)))+~P85(f341(f341(f241(f864(f863(x85691,x85691),a850)),x85692),x85693)) % 19.23/19.04 [8716]P53(x87161,x87162,x87163)+~P53(x87161,x87162,f341(f341(f3(f864(f863(x87161,x87161),a850)),x87163),f309(x87161,f185(f864(f863(x87161,x87161),a850))))) % 19.23/19.04 [8735]P85(f341(f341(f241(f864(f863(f858(x87351),f858(x87351)),a850)),f153(x87351,x87352)),f153(x87351,x87353)))+~P85(f341(f341(f241(f864(f863(x87351,x87351),a850)),x87352),x87353)) % 19.23/19.04 [8736]P85(f341(f341(f241(f864(f863(f858(x87361),f858(x87361)),a850)),f152(x87361,x87362)),f152(x87361,x87363)))+~P85(f341(f341(f241(f864(f863(x87361,x87361),a850)),x87362),x87363)) % 19.23/19.04 [8753]~P46(x87531,x87533,x87532)+P85(f341(f341(f241(f864(f863(x87531,x87531),a850)),x87532),f341(f341(f290(x87531,x87531,x87531),f341(f287(x87531,x87531),x87532)),x87532))) % 19.23/19.04 [8794]~P85(f341(f134(x87941),x87942))+E(f341(f133(x87941,f341(f341(f9(x87941,f864(x87941,a850),a850),f343(x87941)),f341(f163(x87941),f165(x87941,x87942,x87943)))),x87942),f165(x87941,x87942,x87943)) % 19.23/19.04 [8842]E(x88421,x88422)+~P85(f341(f341(f343(f863(x88423,x88423)),f341(f341(f250(x88423,x88423),x88421),x88422)),f309(x88423,f185(f864(f863(x88423,x88423),a850))))) % 19.23/19.04 [8924]P85(f341(f341(f343(x89241),x89242),f331(x89241,x89243)))+P85(f341(f341(f343(f863(x89241,x89241)),f341(f341(f250(x89241,x89241),f377(x89243,x89242,x89241)),x89242)),x89243)) % 19.23/19.04 [8925]P85(f341(f341(f343(x89251),x89252),f331(x89251,x89253)))+P85(f341(f341(f343(f863(x89251,x89251)),f341(f341(f250(x89251,x89251),f628(x89253,x89252,x89251)),x89252)),x89253)) % 19.23/19.04 [8926]P85(f341(f341(f343(x89261),x89262),f331(x89261,x89263)))+P85(f341(f341(f343(f863(x89261,x89261)),f341(f341(f250(x89261,x89261),f630(x89263,x89262,x89261)),x89262)),x89263)) % 19.23/19.04 [9030]P85(f341(x90303,x90302))+E(f341(f265(x90301),f341(f341(f20(x90301,a850,a850),f341(f341(f10(a850,f864(a850,a850),x90301),a339),f341(a338,x90302))),x90303)),f185(f864(x90301,a850))) % 19.23/19.04 [9050]~P79(x90501)+P85(f341(f341(f241(x90501),f341(f84(x90501),f341(f341(f3(x90501),f341(f84(x90501),x90502)),f341(f84(x90501),x90503)))),f341(f84(x90501),f341(f341(f3(x90501),x90502),x90503)))) % 19.23/19.04 [9063]~P85(f341(x90633,x90632))+E(f341(f265(x90631),f341(f341(f20(x90631,a850,a850),f341(f341(f10(a850,f864(a850,a850),x90631),a339),f341(a338,x90632))),x90633)),f341(f341(f311(x90631),x90632),f185(f864(x90631,a850)))) % 19.23/19.04 [9069]~P85(f341(f341(f343(f864(x90691,a850)),x90693),f341(f310(x90691),x90692)))+P85(f341(f254(x90691,f341(f341(f9(x90691,f864(x90691,a850),a850),f343(x90691)),x90692)),x90693)) % 19.23/19.04 [9103]P35(x91031,x91032)+P85(f341(f341(f343(f863(x91031,x91031)),f341(f341(f250(x91031,x91031),f341(f589(x91032,x91031),f341(a121,x91033))),f341(f589(x91032,x91031),x91033))),x91032)) % 19.23/19.04 [9228]P85(f341(f341(f343(f864(x92281,a850)),x92282),f341(f310(x92281),x92283)))+~P85(f341(f254(x92281,f341(f341(f9(x92281,f864(x92281,a850),a850),f343(x92281)),x92283)),x92282)) % 19.23/19.04 [9288]P85(f341(f341(f343(x92881),f341(f274(x92881,x92882),x92883)),f341(f163(x92881),f341(f341(f149(f863(a108,x92881),x92881),f259(a108,x92881)),x92882))))+~P85(f341(f341(f242(a108),x92883),f341(f160(a108),f341(f341(f149(f863(a108,x92881),a108),f249(a108,x92881)),x92882)))) % 19.23/19.04 [9336]P85(f341(f341(f241(f864(f863(f858(x93361),f858(x93361)),a850)),f153(x93361,x93362)),f341(f341(f257(f858(x93361),f858(x93361)),f155(x93361,x93363)),f341(f18(f864(f858(x93361),a850),f858(x93361)),f155(x93361,x93363)))))+~P85(f341(f341(f241(f864(f863(x93361,x93361),a850)),x93362),f341(f341(f257(x93361,x93361),x93363),f341(f18(f864(x93361,a850),x93361),x93363)))) % 19.23/19.04 [9356]P85(f341(f341(f343(x93561),f341(f249(x93561,f863(a108,a108)),f341(f272(x93561,x93562),x93563))),f341(f163(x93561),f341(f341(f149(f863(a108,x93561),x93561),f259(a108,x93561)),x93562))))+~P85(f341(f341(f242(a108),f2(a108)),f341(f160(a108),f341(f341(f149(f863(a108,x93561),a108),f249(a108,x93561)),x93562)))) % 19.23/19.04 [9370]~P85(f341(f341(f241(f864(f863(x93701,x93701),a850)),x93702),f341(f341(f257(x93701,x93701),x93703),f341(f18(f864(x93701,a850),x93701),x93703))))+P85(f341(f341(f241(f864(f863(x93701,x93701),a850)),f341(f341(f290(x93701,x93701,x93701),x93702),f309(x93701,x93702))),f341(f341(f257(x93701,x93701),x93703),f341(f18(f864(x93701,a850),x93701),x93703)))) % 19.23/19.04 [9661]~P35(x96611,x96612)+~P85(f341(f341(f343(f863(x96611,x96611)),f341(f341(f250(x96611,x96611),f341(x96613,f341(a121,f590(x96612,x96611,x96613)))),f341(x96613,f590(x96612,x96611,x96613)))),x96612)) % 19.23/19.04 [9662]~P35(x96621,x96622)+~P85(f341(f341(f343(f863(x96621,x96621)),f341(f341(f250(x96621,x96621),f341(x96623,f341(a121,f640(x96623,x96622,x96621)))),f341(x96623,f640(x96623,x96622,x96621)))),x96622)) % 19.23/19.04 [9916]P85(f341(f341(f241(f864(f863(f864(x99161,a850),f864(x99161,a850)),a850)),f341(f341(f290(f864(x99161,a850),f864(x99161,a850),f864(x99161,a850)),f333(x99161,x99162)),f341(f341(f110(f864(f863(f864(x99161,a850),f864(x99161,a850)),a850)),f333(x99161,x99163)),f341(f341(f311(f863(f864(x99161,a850),f864(x99161,a850))),f341(f341(f250(f864(x99161,a850),f864(x99161,a850)),f185(f864(x99161,a850))),f185(f864(x99161,a850)))),f185(f864(f863(f864(x99161,a850),f864(x99161,a850)),a850)))))),f333(x99161,x99162)))+~P85(f341(f341(f241(f864(f863(x99161,x99161),a850)),f341(f341(f290(x99161,x99161,x99161),x99162),x99163)),x99162)) % 19.23/19.04 [9917]P85(f341(f341(f241(f864(f863(f864(x99171,a850),f864(x99171,a850)),a850)),f341(f341(f290(f864(x99171,a850),f864(x99171,a850),f864(x99171,a850)),f334(x99171,x99172)),f341(f341(f110(f864(f863(f864(x99171,a850),f864(x99171,a850)),a850)),f334(x99171,x99173)),f341(f341(f311(f863(f864(x99171,a850),f864(x99171,a850))),f341(f341(f250(f864(x99171,a850),f864(x99171,a850)),f185(f864(x99171,a850))),f185(f864(x99171,a850)))),f185(f864(f863(f864(x99171,a850),f864(x99171,a850)),a850)))))),f334(x99171,x99172)))+~P85(f341(f341(f241(f864(f863(x99171,x99171),a850)),f341(f341(f290(x99171,x99171,x99171),x99172),x99173)),x99172)) % 19.23/19.04 [7183]~P85(f341(f341(f241(a857),x71832),x71831))+E(f341(f341(f3(a857),f341(a121,f341(f341(f3(a857),x71831),x71832))),x71833),f341(f341(f3(a857),f341(a121,x71831)),f341(f341(f89(a857),x71832),x71833))) % 19.23/19.04 [7223]~P4(x72231)+E(f341(f341(f89(x72231),f60(x72231,x72232,x72233)),f341(f341(f90(x72231),f341(f341(f51(x72231),x72232),x72233)),x72233)),x72232) % 19.23/19.04 [7442]E(f341(f341(f90(a857),f341(f113(a857),x74421)),f341(f341(f90(a857),f341(f113(a857),x74422)),x74423)),f341(f341(f90(a857),f341(f113(a857),f341(f341(f90(a1),x74421),x74422))),x74423))+P85(f341(f341(f242(a1),x74421),a92)) % 19.23/19.04 [7915]~P85(f341(f341(f241(a857),x79153),x79152))+P85(f341(f341(f241(a857),x79151),f341(f341(f3(a857),f341(f341(f89(a857),x79152),x79151)),x79153))) % 19.23/19.04 [8109]~P85(f341(f341(f241(a857),x81091),x81092))+E(f341(f341(f132(a857),f136(a857,f341(f303(a857,x81091),x81092))),f136(a857,f341(f303(a857,x81092),f341(f341(f89(a857),x81092),x81093)))),f136(a857,f341(f303(a857,x81091),f341(f341(f89(a857),x81092),x81093)))) % 19.23/19.04 [8365]~P85(f341(f71(x83651),x83652))+E(f341(a121,f341(f50(x83651),f341(f341(f3(f864(x83651,a850)),x83652),f341(f341(f311(x83651),x83653),f185(f864(x83651,a850)))))),f341(f50(x83651),f341(f341(f311(x83651),x83653),x83652))) % 19.23/19.04 [8409]~P85(f341(f71(x84091),x84092))+E(f341(f341(f89(a857),f87(a857)),f341(f50(x84091),f341(f341(f3(f864(x84091,a850)),x84092),f341(f341(f311(x84091),x84093),f185(f864(x84091,a850)))))),f341(f50(x84091),f341(f341(f311(x84091),x84093),x84092))) % 19.23/19.04 [8578]E(f341(f341(f3(a857),f341(f50(x85781),x85782)),f341(f50(x85781),f341(f341(f111(f864(x85781,a850)),x85782),x85783))),f341(f50(x85781),f341(f341(f3(f864(x85781,a850)),x85782),x85783)))+~P85(f341(f71(x85781),f341(f341(f111(f864(x85781,a850)),x85782),x85783))) % 19.23/19.04 [8791]~P7(f341(x87912,f410(x87912,x87913,x87911)))+E(f341(f109(a1),f341(f341(f11(x87911,a857),f341(f341(f10(a1,a857,x87911),a114),x87912)),x87913)),f341(f341(f11(x87911,a1),x87912),x87913)) % 19.23/19.04 [8792]~P7(f341(x87922,f513(x87922,x87923,x87921)))+E(f341(f109(a1),f341(f341(f8(x87921,a857),f341(f341(f10(a1,a857,x87921),a114),x87922)),x87923)),f341(f341(f8(x87921,a1),x87922),x87923)) % 19.23/19.04 [8827]~P85(f341(f71(x88271),x88273))+P85(f341(f341(f241(a857),f341(f341(f3(a857),f341(f50(x88271),x88272)),f341(f50(x88271),x88273))),f341(f50(x88271),f341(f341(f3(f864(x88271,a850)),x88272),x88273)))) % 19.23/19.04 [8850]P85(f341(f341(f343(x88501),f410(x88502,x88503,x88501)),x88503))+E(f341(f109(a1),f341(f341(f11(x88501,a857),f341(f341(f10(a1,a857,x88501),a114),x88502)),x88503)),f341(f341(f11(x88501,a1),x88502),x88503)) % 19.23/19.04 [8851]P85(f341(f341(f343(x88511),f513(x88512,x88513,x88511)),x88513))+E(f341(f109(a1),f341(f341(f8(x88511,a857),f341(f341(f10(a1,a857,x88511),a114),x88512)),x88513)),f341(f341(f8(x88511,a1),x88512),x88513)) % 19.23/19.04 [8918]E(f94(x89181,f341(f341(f9(x89181,f864(x89181,a850),a850),f343(x89181)),f341(f341(f3(f864(x89181,a850)),x89182),f341(f341(f311(x89181),x89183),f185(f864(x89181,a850)))))),f253(x89181,x89183,x89182))+P85(f341(f341(f241(f864(x89181,a850)),x89182),f341(f341(f311(x89181),x89183),f185(f864(x89181,a850))))) % 19.23/19.04 [9229]E(f341(f341(f149(f858(x92291),x92291),f341(f341(f9(f858(x92291),a857,x92291),f158(x92291)),x92292)),f341(f133(f858(x92291),f341(f341(f10(a857,a850,f858(x92291)),f341(f242(a857),x92292)),f186(f858(x92291)))),x92293)),f341(f341(f158(f858(x92291)),f169(x92291,x92293)),x92292))+~P85(f341(f341(f242(a857),x92292),f341(f186(f858(f858(x92291))),f169(x92291,x92293)))) % 19.23/19.04 [9529]~P85(f341(f341(f343(f863(x95291,x95291)),x95292),f309(x95291,x95293)))+P85(f341(f341(f343(f863(x95291,x95291)),x95292),f341(f341(f54(a857,f864(f863(x95291,x95291),a850)),f248(f864(a857,a850))),f341(f341(f9(a857,f864(f863(x95291,x95291),a850),f864(f863(x95291,x95291),a850)),f179(f863(x95291,x95291),a850)),x95293)))) % 19.23/19.04 [9586]~P85(f341(f341(f241(f864(x95861,a850)),f341(f341(f54(a857,f864(x95861,a850)),f341(f303(a857,f2(a857)),f534(x95863,x95862,x95861))),x95862)),x95863))+P85(f341(f341(f241(f864(x95861,a850)),f341(f341(f54(a857,f864(x95861,a850)),f248(f864(a857,a850))),x95862)),x95863)) % 19.23/19.04 [9638]~P85(f341(f341(f242(a1),f2(a1)),x96383))+P85(f341(f341(f242(a1),x96381),f341(f341(f89(a1),x96382),f341(f341(f90(a1),f341(f341(f89(a1),f341(f84(a1),f341(f341(f3(a1),x96382),x96381))),f87(a1))),x96383)))) % 19.23/19.04 [9648]~P35(x96481,f341(f341(f110(f864(f863(x96481,x96481),a850)),x96482),x96483))+P35(x96481,f341(f341(f110(f864(f863(x96481,x96481),a850)),f341(f341(f110(f864(f863(x96481,x96481),a850)),f341(f341(f290(x96481,x96481,x96481),x96482),x96482)),f341(f341(f290(x96481,x96481,x96481),x96483),x96482))),x96483)) % 19.23/19.04 [9713]P35(x97131,f341(f341(f110(f864(f863(x97131,x97131),a850)),x97132),x97133))+~P35(x97131,f341(f341(f110(f864(f863(x97131,x97131),a850)),f341(f341(f110(f864(f863(x97131,x97131),a850)),f341(f341(f290(x97131,x97131,x97131),x97132),x97132)),f341(f341(f290(x97131,x97131,x97131),x97133),x97132))),x97133)) % 19.23/19.04 [9311]~P136(x93111)+E(f341(f112(x93111),f341(a98,f341(f286(f863(a857,a857),f863(a857,a857),a118),f341(f341(f311(f863(a857,a857)),f341(f341(f250(a857,a857),x93112),x93113)),f185(f864(f863(a857,a857),a850)))))),f341(f341(f3(x93111),f341(f109(x93111),x93112)),f341(f109(x93111),x93113))) % 19.23/19.04 [9388]P85(f341(x93883,x93882))+E(f341(f265(x93881),f341(f341(f20(x93881,a850,a850),f341(f341(f10(a850,f864(a850,a850),x93881),a339),f341(f341(f9(x93881,x93881,a850),a338),x93882))),x93883)),f185(f864(x93881,a850))) % 19.23/19.04 [9390]~P85(f341(x93903,x93902))+E(f341(f265(x93901),f341(f341(f20(x93901,a850,a850),f341(f341(f10(a850,f864(a850,a850),x93901),a339),f341(f341(f9(x93901,x93901,a850),a338),x93902))),x93903)),f341(f341(f311(x93901),x93902),f185(f864(x93901,a850)))) % 19.23/19.04 [9705]~P85(f341(f71(x97051),x97053))+E(f341(f341(f74(x97051,f864(x97051,a850),f341(f341(f10(f864(x97051,a850),f864(f864(x97051,a850),f864(x97051,a850)),x97051),f341(f9(f864(x97051,a850),f864(x97051,a850),f864(x97051,a850)),f3(f864(x97051,a850)))),f341(f341(f9(x97051,f864(x97051,a850),f864(x97051,a850)),f311(x97051)),f185(f864(x97051,a850))))),x97052),x97053),f341(f341(f3(f864(x97051,a850)),x97052),x97053)) % 19.23/19.04 [9738]~P85(f341(f341(f242(a1),f2(a1)),x97383))+P85(f341(f341(f242(a1),f341(f341(f3(a1),x97381),f341(f341(f90(a1),f341(f341(f89(a1),f341(f84(a1),f341(f341(f3(a1),x97381),x97382))),f87(a1))),x97383))),x97382)) % 19.23/19.04 [9986]~P85(f341(f341(f343(x99861),x99863),f331(x99861,x99862)))+P85(f341(f330(x99861,f341(f341(f9(x99861,f864(f863(x99861,x99861),a850),f864(x99861,a850)),f341(f341(f10(f864(x99861,f864(f864(f863(x99861,x99861),a850),a850)),f864(f864(f863(x99861,x99861),a850),f864(x99861,a850)),x99861),f9(x99861,f864(f863(x99861,x99861),a850),a850)),f341(f341(f10(f864(x99861,f863(x99861,x99861)),f864(x99861,f864(f864(f863(x99861,x99861),a850),a850)),x99861),f341(f10(f863(x99861,x99861),f864(f864(f863(x99861,x99861),a850),a850),x99861),f343(f863(x99861,x99861)))),f250(x99861,x99861)))),x99862)),x99863)) % 19.23/19.04 [9998]P85(f341(f341(f343(x99981),x99982),f331(x99981,x99983)))+~P85(f341(f330(x99981,f341(f341(f9(x99981,f864(f863(x99981,x99981),a850),f864(x99981,a850)),f341(f341(f10(f864(x99981,f864(f864(f863(x99981,x99981),a850),a850)),f864(f864(f863(x99981,x99981),a850),f864(x99981,a850)),x99981),f9(x99981,f864(f863(x99981,x99981),a850),a850)),f341(f341(f10(f864(x99981,f863(x99981,x99981)),f864(x99981,f864(f864(f863(x99981,x99981),a850),a850)),x99981),f341(f10(f863(x99981,x99981),f864(f864(f863(x99981,x99981),a850),a850),x99981),f343(f863(x99981,x99981)))),f250(x99981,x99981)))),x99983)),x99982)) % 19.23/19.04 [9584]~P85(f341(f71(x95841),f341(f265(x95841),x95843)))+P85(f341(f71(x95841),f341(f265(x95841),f341(f341(f20(x95841,a850,a850),f341(f341(f10(a850,f864(a850,a850),x95841),a339),x95842)),x95843)))) % 19.23/19.04 [9585]~P85(f341(f71(x95851),f341(f265(x95851),x95852)))+P85(f341(f71(x95851),f341(f265(x95851),f341(f341(f20(x95851,a850,a850),f341(f341(f10(a850,f864(a850,a850),x95851),a339),x95852)),x95853)))) % 19.23/19.04 [9672]P85(f341(f71(x96721),f341(f265(x96721),x96722)))+~P85(f341(f71(x96721),f341(f265(x96721),f341(f341(f20(x96721,a850,a850),f341(f341(f10(a850,f864(a850,a850),x96721),a340),x96723)),x96722)))) % 19.23/19.04 [9673]P85(f341(f71(x96731),f341(f265(x96731),x96732)))+~P85(f341(f71(x96731),f341(f265(x96731),f341(f341(f20(x96731,a850,a850),f341(f341(f10(a850,f864(a850,a850),x96731),a340),x96732)),x96733)))) % 19.23/19.04 [9971]~P85(f341(f71(x99711),x99712))+P85(f341(f71(f858(x99711)),f341(f265(f858(x99711)),f341(f341(f20(f858(x99711),a850,a850),f341(f341(f10(a850,f864(a850,a850),f858(x99711)),a339),f341(f341(f9(f858(x99711),f864(x99711,a850),a850),f341(f341(f10(f864(x99711,a850),f864(f864(x99711,a850),a850),f858(x99711)),f241(f864(x99711,a850))),f163(x99711))),x99712))),f341(f341(f9(f858(x99711),a857,a850),f341(f341(f10(a857,f864(a857,a850),f858(x99711)),a338),f186(f858(x99711)))),x99713))))) % 19.23/19.04 [9972]~P85(f341(f71(x99721),x99722))+P85(f341(f71(f858(x99721)),f341(f265(f858(x99721)),f341(f341(f20(f858(x99721),a850,a850),f341(f341(f10(a850,f864(a850,a850),f858(x99721)),a339),f341(f341(f9(f858(x99721),f864(x99721,a850),a850),f341(f341(f10(f864(x99721,a850),f864(f864(x99721,a850),a850),f858(x99721)),f241(f864(x99721,a850))),f163(x99721))),x99722))),f341(f341(f9(f858(x99721),a857,a850),f341(f341(f10(a857,f864(a857,a850),f858(x99721)),f241(a857)),f186(f858(x99721)))),x99723))))) % 19.23/19.04 [9686]~P86(x96861)+E(f341(f341(f251(x96861),x96862),f341(f341(f90(a857),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),x96863)),f341(f341(f90(x96861),f341(f341(f251(x96861),x96862),x96863)),f341(f341(f251(x96861),x96862),x96863))) % 19.23/19.04 [9717]~P75(x97171)+E(f341(f341(f251(x97171),f341(f341(f251(x97171),x97172),x97173)),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),f341(f341(f251(x97171),x97172),f341(f341(f90(a857),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),x97173))) % 19.23/19.04 [9778]~P136(x97781)+E(f341(f341(f251(x97781),f341(f88(x97781),x97782)),f341(f341(f90(a857),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),x97783)),f341(f341(f251(x97781),x97782),f341(f341(f90(a857),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),x97783))) % 19.23/19.04 [9921]~P113(x99211)+P85(f341(f341(f241(x99211),f2(x99211)),f341(f341(f89(x99211),f341(f341(f251(x99211),x99212),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106))))),f341(f341(f251(x99211),x99213),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106))))))) % 19.23/19.04 [9788]~P86(x97881)+E(f341(f341(f251(x97881),x97882),f341(a121,f341(f341(f90(a857),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),x97883))),f341(f341(f90(x97881),x97882),f341(f341(f90(x97881),f341(f341(f251(x97881),x97882),x97883)),f341(f341(f251(x97881),x97882),x97883)))) % 19.23/19.04 [9840]~P75(x98401)+E(f341(f341(f90(x98401),x98402),f341(f341(f251(x98401),f341(f341(f251(x98401),x98402),x98403)),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106))))),f341(f341(f251(x98401),x98402),f341(a121,f341(f341(f90(a857),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),x98403)))) % 19.23/19.04 [9883]~P113(x98831)+P85(f341(f341(f241(x98831),f2(x98831)),f341(f341(f251(x98831),x98832),f341(f341(f90(a857),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),x98833)))) % 19.23/19.04 [9950]~P89(x99501)+E(f341(f341(f89(x99501),f341(f341(f89(x99501),f341(f341(f251(x99501),x99502),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106))))),f341(f341(f251(x99501),x99503),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))))),f341(f341(f90(x99501),f341(f341(f90(x99501),f341(f113(x99501),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),x99502)),x99503)),f341(f341(f251(x99501),f341(f341(f89(x99501),x99502),x99503)),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106))))) % 19.23/19.04 [9951]~P89(x99511)+E(f341(f341(f3(x99511),f341(f341(f89(x99511),f341(f341(f251(x99511),x99512),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106))))),f341(f341(f251(x99511),x99513),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))))),f341(f341(f90(x99511),f341(f341(f90(x99511),f341(f113(x99511),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),x99512)),x99513)),f341(f341(f251(x99511),f341(f341(f3(x99511),x99512),x99513)),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106))))) % 19.23/19.04 [4594]E(x45941,x45942)+~E(f30(x45943,x45941),f30(x45944,x45942)) % 19.23/19.04 [4595]E(x45951,x45952)+~E(f30(x45951,x45953),f30(x45952,x45954)) % 19.23/19.04 [4596]E(x45961,x45962)+~E(f38(x45963,x45961),f38(x45964,x45962)) % 19.23/19.04 [4597]E(x45971,x45972)+~E(f38(x45971,x45973),f38(x45972,x45974)) % 19.23/19.04 [4598]E(x45981,x45982)+~E(f37(x45983,x45981),f37(x45984,x45982)) % 19.23/19.04 [4599]E(x45991,x45992)+~E(f37(x45991,x45993),f37(x45992,x45994)) % 19.23/19.04 [5714]P38(f37(x57141,x57143),x57142,x57144,x57142)+P85(f341(x57141,x57142)) % 19.23/19.04 [6870]~P38(x68701,x68702,x68703,x68704)+P38(x68701,x68702,f341(a121,x68703),x68704) % 19.23/19.04 [7712]P26(x77121,x77122,x77123,x77124)+~E(f451(x77124,x77123,x77122,x77121),f453(x77124,x77123,x77122,x77121)) % 19.23/19.04 [8209]~P26(x82091,f861(x82092),x82094,f174(x82091,x82092,x82094))+P26(x82091,f861(x82092),f175(x82091,x82092,x82093,x82094),f174(x82091,x82092,x82094)) % 19.23/19.04 [8423]~P26(x84231,f861(x84232),f175(x84231,x84232,x84234,x84233),f174(x84231,x84232,x84233))+P26(x84231,f861(x84232),x84233,f174(x84231,x84232,x84233)) % 19.23/19.04 [4961]~P18(x49613,x49611,x49614)+E(f341(f341(x49611,x49612),x49612),x49612) % 19.23/19.04 [4962]~P28(x49624,x49621,x49623)+E(f341(f341(x49621,x49622),x49623),x49622) % 19.23/19.04 [4965]E(x49651,x49652)+~E(f341(f322(x49653,x49654),x49651),f341(f322(x49653,x49654),x49652)) % 19.23/19.04 [4967]E(x49671,x49672)+~E(f341(f313(x49673,x49674),x49671),f341(f313(x49673,x49674),x49672)) % 19.23/19.04 [5240]~E(x52404,f185(f864(x52401,a850)))+E(f341(f312(x52401,x52402,x52403),x52404),f185(f864(x52402,a850))) % 19.23/19.04 [5503]~E(f341(f312(x55032,x55033,x55034),x55031),f185(f864(x55033,a850)))+E(x55031,f185(f864(x55032,a850))) % 19.23/19.04 [5795]~P101(x57952)+E(f341(f341(f144(x57951,x57952,x57953),x57954),f122(x57951)),f341(f341(f146(x57951),x57954),f122(x57951))) % 19.23/19.04 [5831]E(f341(x58311,x58312),f188(x58313))+P85(f341(f341(f343(x58314),x58312),f174(x58314,x58313,x58311))) % 19.23/19.04 [6153]~E(x61531,f185(f864(x61532,a850)))+~P85(f341(f72(x61532,x61533,x61531),x61534)) % 19.23/19.04 [6174]~P56(x61741,x61743,x61744,x61742)+P85(f341(f71(x61741),x61742)) % 19.23/19.04 [6175]~P56(x61751,x61753,x61752,x61754)+P85(f341(f71(x61751),x61752)) % 19.23/19.04 [6182]~P56(x61822,x61823,x61824,x61821)+~E(x61821,f185(f864(x61822,a850))) % 19.23/19.04 [6214]~P100(x62141)+E(f341(f341(f111(f864(x62141,a850)),f341(f303(x62141,x62142),x62143)),f304(x62141,x62143,x62144)),f185(f864(x62141,a850))) % 19.23/19.04 [6242]~P85(f341(f341(x62423,x62424),x62422))+P85(f341(f341(f343(x62421),x62422),f296(x62421,x62423,x62424))) % 19.23/19.04 [6243]~P85(f341(f341(x62433,x62434),x62432))+P85(f341(f341(f343(x62431),x62432),f295(x62431,x62433,x62434))) % 19.23/19.04 [6244]~P85(f341(f341(x62443,x62442),x62444))+P85(f341(f341(f343(x62441),x62442),f299(x62441,x62443,x62444))) % 19.23/19.04 [6245]~P85(f341(f341(x62453,x62452),x62454))+P85(f341(f341(f343(x62451),x62452),f297(x62451,x62453,x62454))) % 19.23/19.04 [6397]~P100(x63971)+E(f341(f341(f111(f864(x63971,a850)),f307(x63971,x63972,x63973)),f304(x63971,x63973,x63974)),f185(f864(x63971,a850))) % 19.23/19.04 [6398]~P100(x63981)+E(f341(f341(f111(f864(x63981,a850)),f306(x63981,x63982,x63983)),f307(x63981,x63983,x63984)),f185(f864(x63981,a850))) % 19.23/19.04 [6399]~P100(x63991)+E(f341(f341(f111(f864(x63991,a850)),f306(x63991,x63992,x63993)),f306(x63991,x63993,x63994)),f185(f864(x63991,a850))) % 19.23/19.04 [6400]~P100(x64001)+E(f341(f341(f111(f864(x64001,a850)),f304(x64001,x64002,x64003)),f307(x64001,x64003,x64004)),f185(f864(x64001,a850))) % 19.23/19.04 [6401]~P100(x64011)+E(f341(f341(f111(f864(x64011,a850)),f304(x64011,x64012,x64013)),f306(x64011,x64013,x64014)),f185(f864(x64011,a850))) % 19.23/19.04 [6439]P85(f341(f341(x64391,x64392),f597(x64392,x64391)))+~P85(f341(f255(x64393,x64394,x64391),x64392)) % 19.23/19.04 [6492]~E(f341(x64921,x64922),f188(x64923))+~P85(f341(f341(f343(x64924),x64922),f174(x64924,x64923,x64921))) % 19.23/19.04 [6574]~P112(x65741)+E(f187(x65741,x65742,f341(a121,x65743),x65744),f187(x65741,x65742,x65743,f341(x65742,x65744))) % 19.23/19.04 [6637]~P85(f341(f341(f343(x66374),x66373),f296(x66374,x66371,x66372)))+P85(f341(f341(x66371,x66372),x66373)) % 19.23/19.04 [6638]~P85(f341(f341(f343(x66384),x66383),f295(x66384,x66381,x66382)))+P85(f341(f341(x66381,x66382),x66383)) % 19.23/19.04 [6639]~P85(f341(f341(f343(x66394),x66392),f299(x66394,x66391,x66393)))+P85(f341(f341(x66391,x66392),x66393)) % 19.23/19.04 [6640]~P85(f341(f341(f343(x66404),x66402),f297(x66404,x66401,x66403)))+P85(f341(f341(x66401,x66402),x66403)) % 19.23/19.04 [6721]E(f341(f50(f865(x67211,x67212)),f323(x67211,x67212,x67213,x67214)),f2(a857))+P85(f341(f71(x67212),x67214)) % 19.23/19.04 [6722]E(f341(f50(f865(x67221,x67222)),f323(x67221,x67222,x67223,x67224)),f2(a857))+P85(f341(f71(x67221),x67223)) % 19.23/19.04 [6931]~P16(x69314,x69311,x69312)+E(f341(f82(x69311,x69311,x69311,f341(x69312,x69313)),f341(x69312,x69313)),f341(x69312,x69313)) % 19.23/19.04 [7168]E(f281(x71681,x71682,x71683,x71684),f341(f250(f864(a108,f864(a850,f861(f859(x71681)))),f863(a108,a108)),f56(x71681)))+~P85(f341(f341(f241(a108),x71683),f2(a108))) % 19.23/19.04 [7234]~P38(f341(a29,x72341),x72342,f341(a121,x72343),x72344)+P38(f341(f239(a851),f341(a32,x72341)),x72342,x72343,x72344) % 19.23/19.04 [7271]P38(f341(a29,x72711),x72712,f341(a121,x72713),x72714)+~P38(f341(f239(a851),f341(a32,x72711)),x72712,x72713,x72714) % 19.23/19.04 [7570]~P38(f341(a29,x75704),x75703,x75702,x75701)+E(f341(a121,f542(x75701,x75702,x75703,x75704)),x75702) % 19.23/19.04 [7840]~E(x78402,x78403)+P85(f341(f341(f343(f863(x78401,x78401)),f341(f341(f250(x78401,x78401),x78402),x78403)),f309(x78401,x78404))) % 19.23/19.04 [7866]~P26(x78661,x78662,x78663,f248(f864(x78661,a850)))+E(f341(f86(x78661,x78662,f248(f864(x78661,a850)),x78663),f341(x78663,x78664)),x78664) % 19.23/19.04 [7958]~P85(f341(f341(f343(f858(x79581)),f341(f341(f146(x79581),x79584),x79582)),f155(x79581,x79583)))+P85(f341(f341(f343(f858(x79581)),x79582),f155(x79581,x79583))) % 19.23/19.04 [7959]~P85(f341(f341(f343(f858(x79591)),f341(f341(f132(x79591),x79594),x79592)),f155(x79591,x79593)))+P85(f341(f341(f343(f858(x79591)),x79592),f155(x79591,x79593))) % 19.23/19.04 [7960]~P85(f341(f341(f343(f858(x79601)),f341(f341(f132(x79601),x79602),x79604)),f155(x79601,x79603)))+P85(f341(f341(f343(f858(x79601)),x79602),f155(x79601,x79603))) % 19.23/19.04 [8033]~P38(f341(a29,x80331),x80332,x80334,x80333)+P38(f341(f239(a851),f341(a32,x80331)),x80332,f542(x80333,x80334,x80332,x80331),x80333) % 19.23/19.04 [8070]P26(x80704,x80703,x80701,x80702)+E(f341(x80701,f451(x80702,x80701,x80703,x80704)),f341(x80701,f453(x80702,x80701,x80703,x80704))) % 19.23/19.04 [8079]E(f175(x80791,x80792,x80793,x80794),f175(x80791,x80792,x80794,x80793))+~E(f341(f341(f111(f864(x80791,a850)),f174(x80791,x80792,x80793)),f174(x80791,x80792,x80794)),f185(f864(x80791,a850))) % 19.23/19.04 [8174]~P26(x81742,x81741,x81744,x81743)+P26(x81741,x81742,f86(x81742,x81741,x81743,x81744),f341(f312(x81742,x81741,x81744),x81743)) % 19.23/19.04 [8310]P35(f863(x83102,x83104),f284(x83102,x83104,x83101,x83103))+P85(f341(x83101,f587(x83102,x83103,x83104,x83101))) % 19.23/19.04 [8430]E(x84301,x84302)+~P85(f341(f341(f343(f863(x84303,x84303)),f341(f341(f250(x84303,x84303),x84301),x84302)),f269(x84303,x84304))) % 19.23/19.04 [8497]~P85(f341(f71(f865(x84973,x84971)),f323(x84973,x84971,x84974,x84972)))+P85(f341(f71(x84971),x84972)) % 19.23/19.04 [8498]~P85(f341(f71(f865(x84981,x84983)),f323(x84981,x84983,x84982,x84984)))+P85(f341(f71(x84981),x84982)) % 19.23/19.04 [8660]P35(f863(x86601,x86602),f284(x86601,x86602,x86603,x86604))+~P35(x86602,f341(x86604,f587(x86601,x86604,x86602,x86603))) % 19.23/19.04 [9164]E(f341(f341(f154(x91641,x91642),f747(x91643,x91644,x91642,x91641)),f748(x91643,x91644,x91642,x91641)),x91644)+~P85(f341(f341(f343(f863(f858(x91641),f858(x91641))),f341(f341(f250(f858(x91641),f858(x91641)),x91642),x91644)),f152(x91641,x91643))) % 19.23/19.04 [9168]~P85(f341(f341(f343(f863(f858(x91681),f858(x91681))),f341(f341(f250(f858(x91681),f858(x91681)),x91682),x91683)),f141(x91681,x91684)))+P85(f341(f341(f343(f863(f858(x91681),f858(x91681))),f341(f341(f250(f858(x91681),f858(x91681)),x91682),x91683)),f143(x91681,x91684))) % 19.23/19.04 [9263]P85(f341(f71(x92631),x92632))+~P85(f341(f341(f343(f863(f864(x92631,a850),f864(x92631,a850))),f341(f341(f250(f864(x92631,a850),f864(x92631,a850)),x92633),x92632)),f334(x92631,x92634))) % 19.23/19.04 [9264]P85(f341(f71(x92641),x92642))+~P85(f341(f341(f343(f863(f864(x92641,a850),f864(x92641,a850))),f341(f341(f250(f864(x92641,a850),f864(x92641,a850)),x92642),x92643)),f334(x92641,x92644))) % 19.23/19.04 [9267]~E(x92671,f185(f864(x92672,a850)))+~P85(f341(f341(f343(f863(f864(x92672,a850),f864(x92672,a850))),f341(f341(f250(f864(x92672,a850),f864(x92672,a850)),x92673),x92671)),f334(x92672,x92674))) % 19.23/19.04 [9894]P13(x98941,x98942,x98943,x98944)+~P85(f341(f341(f260(x98941,x98941,a850),f341(f341(f9(x98941,f864(x98941,x98942),f864(x98941,a850)),f341(f341(f10(f864(x98942,a850),f864(f864(x98941,x98942),f864(x98941,a850)),x98941),f10(x98942,a850,x98941)),f341(f341(f10(x98942,f864(x98942,a850),x98941),a338),x98944))),x98944)),f604(x98944,x98943,x98942,x98941))) % 19.23/19.04 [4864]~E(x48644,f122(x48641))+E(f341(f341(f149(x48641,x48642),x48643),x48644),f122(x48642)) % 19.23/19.04 [4865]~E(x48654,f188(x48651))+E(f341(f341(f204(x48651,x48652),x48653),x48654),f188(x48652)) % 19.23/19.04 [4866]~E(x48662,f122(x48661))+E(f341(f341(f154(x48661,x48662),x48663),x48664),f122(x48661)) % 19.23/19.04 [5103]E(x51031,f188(x51032))+~E(f341(f341(f204(x51032,x51033),x51034),x51031),f188(x51033)) % 19.23/19.04 [5104]E(x51041,f122(x51042))+~E(f341(f341(f149(x51042,x51043),x51044),x51041),f122(x51043)) % 19.23/19.04 [5105]E(x51051,f122(x51052))+~E(f341(f341(f154(x51052,x51051),x51053),x51054),f122(x51052)) % 19.23/19.04 [5134]E(x51341,x51342)+~E(f341(f341(f132(x51343),x51344),x51341),f341(f341(f132(x51343),x51344),x51342)) % 19.23/19.04 [5135]E(x51351,x51352)+~E(f341(f341(f132(x51353),x51351),x51354),f341(f341(f132(x51353),x51352),x51354)) % 19.23/19.04 [5275]P85(f341(x52753,x52752))+E(f157(x52751,x52752,f341(f133(x52751,x52753),x52754)),f341(f133(x52751,x52753),x52754)) % 19.23/19.04 [5286]E(x52861,x52862)+~E(f136(a857,f341(f303(a857,x52861),x52863)),f341(f341(f146(a857),x52862),x52864)) % 19.23/19.04 [5334]~P27(x53342,x53343)+P27(x53341,f341(f341(f83(x53342,x53341),x53343),x53344)) % 19.23/19.04 [5335]~P35(x53352,x53353)+P35(x53351,f341(f341(f289(x53352,x53351),x53353),x53354)) % 19.23/19.04 [5544]~E(x55441,f122(x55442))+~E(f341(f341(f132(x55442),x55443),f341(f341(f146(x55442),x55444),f122(x55442))),x55441) % 19.23/19.04 [5577]E(f140(x55771,x55772),x55773)+~E(f341(f341(f132(x55771),x55774),f341(f341(f146(x55771),x55773),f122(x55771))),x55772) % 19.23/19.04 [5578]E(f123(x55781,x55782),x55783)+~E(f341(f341(f132(x55781),x55783),f341(f341(f146(x55781),x55784),f122(x55781))),x55782) % 19.23/19.04 [5686]~E(f136(a857,f341(f303(a857,x56861),x56862)),f341(f341(f146(a857),x56863),x56864))+P85(f341(f341(f242(a857),x56861),x56862)) % 19.23/19.04 [5894]E(x58941,f341(f341(f132(x58942),f341(f148(x58942),x58943)),f341(f341(f146(x58942),x58944),f122(x58942))))+~E(f341(f148(x58942),x58941),f341(f341(f146(x58942),x58944),x58943)) % 19.23/19.04 [6075]~P100(x60751)+E(f341(f341(f111(f864(x60751,a850)),f341(f303(x60751,x60752),x60753)),f341(f303(x60751,x60753),x60754)),f185(f864(x60751,a850))) % 19.23/19.04 [6110]~P68(x61101)+E(f341(f160(x61101),f341(f341(f149(a1,x61101),x61102),f168(x61103,x61104))),f341(f341(f8(a1,x61101),x61102),f341(f163(a1),f168(x61103,x61104)))) % 19.23/19.04 [6111]~P68(x61111)+E(f341(f341(f8(a1,x61111),x61112),f341(f163(a1),f168(x61113,x61114))),f341(f160(x61111),f341(f341(f149(a1,x61111),x61112),f168(x61113,x61114)))) % 19.23/19.04 [6257]~E(x62572,f341(f341(f132(x62571),f341(f148(x62571),x62574)),f341(f341(f146(x62571),x62573),f122(x62571))))+E(f341(f148(x62571),x62572),f341(f341(f146(x62571),x62573),x62574)) % 19.23/19.04 [6273]~P20(x62732,x62733,x62734,x62731)+E(f341(x62731,f185(f864(x62732,a850))),f41(x62733)) % 19.23/19.04 [6303]~P100(x63031)+E(f341(f341(f111(f864(x63031,a850)),f307(x63031,x63032,x63033)),f341(f303(x63031,x63033),x63034)),f185(f864(x63031,a850))) % 19.23/19.04 [6390]~P38(x63901,x63902,x63904,x63903)+P85(f341(f341(f192(x63901),x63902),x63903)) % 19.23/19.04 [6523]E(x65231,f185(f864(x65232,a850)))+~E(f323(x65233,x65232,x65234,x65231),f185(f864(f865(x65233,x65232),a850))) % 19.23/19.04 [6524]E(x65241,f185(f864(x65242,a850)))+~E(f323(x65242,x65243,x65241,x65244),f185(f864(f865(x65242,x65243),a850))) % 19.23/19.04 [6603]~P85(f341(f256(x66033,x66034,x66031),x66032))+P85(f341(f341(x66031,f586(x66032,x66031)),x66032)) % 19.23/19.04 [6651]~P85(f341(f71(x66512),x66514))+P85(f341(f71(x66511),f341(f312(x66512,x66511,x66513),x66514))) % 19.23/19.04 [6891]~P26(x68912,x68911,x68913,x68914)+E(f341(f50(x68911),f341(f312(x68912,x68911,x68913),x68914)),f341(f50(x68912),x68914)) % 19.23/19.04 [6911]E(f341(f312(x69111,x69112,x69113),f341(f314(x69111,x69112,x69113),x69114)),x69114)+~E(f341(f312(x69111,x69112,x69113),f248(f864(x69111,a850))),f248(f864(x69112,a850))) % 19.23/19.04 [7335]~P26(x73351,x73352,x73353,f248(f864(x73351,a850)))+E(f341(f314(x73351,x73352,x73353),f341(f312(x73351,x73352,x73353),x73354)),x73354) % 19.23/19.04 [7674]P85(f341(x76741,x76742))+~P85(f341(f341(f343(x76743),x76742),f341(f163(x76743),f167(x76743,x76741,x76744)))) % 19.23/19.04 [7784]~P85(f341(f341(f343(f858(x77841)),f341(f341(f146(x77841),x77842),x77844)),f155(x77841,x77843)))+P85(f341(f341(f343(x77841),x77842),x77843)) % 19.23/19.04 [7911]~P85(f341(f341(f343(x79111),x79112),f341(f163(x79111),f157(x79111,x79114,x79113))))+P85(f341(f341(f343(x79111),x79112),f341(f163(x79111),x79113))) % 19.23/19.04 [7913]~P85(f341(f341(f343(x79131),x79132),f341(f163(x79131),f165(x79131,x79133,x79134))))+P85(f341(f341(f343(x79131),x79132),f341(f163(x79131),x79133))) % 19.23/19.04 [7914]~P85(f341(f341(f343(x79141),x79142),f341(f163(x79141),f167(x79141,x79144,x79143))))+P85(f341(f341(f343(x79141),x79142),f341(f163(x79141),x79143))) % 19.23/19.04 [8207]~P68(x82071)+E(f341(f341(f8(a857,x82071),f341(f341(f10(a857,x82071,a857),x82072),a121)),f341(f303(a857,x82073),x82074)),f341(f341(f8(a857,x82071),x82072),f341(f303(a857,f341(a121,x82073)),f341(a121,x82074)))) % 19.23/19.04 [8216]~P68(x82161)+E(f341(f341(f8(a857,x82161),f341(f341(f10(a857,x82161,a857),x82162),a121)),f304(a857,x82163,x82164)),f341(f341(f8(a857,x82161),x82162),f304(a857,f341(a121,x82163),f341(a121,x82164)))) % 19.23/19.04 [8349]~P26(x83491,x83493,x83494,f248(f864(x83491,a850)))+P26(x83491,f864(x83492,x83493),f341(f341(f10(x83493,f864(x83492,x83493),x83491),f18(x83493,x83492)),x83494),f248(f864(x83491,a850))) % 19.23/19.04 [8439]~P26(x84392,x84391,x84394,x84393)+E(f341(f312(x84391,x84392,f86(x84392,x84391,x84393,x84394)),f341(f312(x84392,x84391,x84394),x84393)),x84393) % 19.23/19.04 [8499]~P85(f341(f341(f343(f863(x84991,x84991)),f341(f341(f250(x84991,x84991),x84992),x84994)),f269(x84991,x84993)))+P85(f341(f341(f343(x84991),x84992),x84993)) % 19.23/19.04 [8574]E(f341(f341(f341(f81(x85741,f861(x85742)),f341(f18(f861(x85742),x85741),f188(x85742))),x85743),f341(f235(x85742),f523(x85743,x85744,x85742,x85741))),x85744)+~E(f174(x85741,x85742,x85744),f341(f341(f311(x85741),x85743),f185(f864(x85741,a850)))) % 19.23/19.04 [8693]~E(f341(f341(f8(x86931,a857),x86934),x86933),f341(a121,x86932))+P85(f341(f341(f343(x86931),f617(x86932,x86933,x86934,x86931)),x86933)) % 19.23/19.04 [8709]~E(f341(f341(f8(x87094,a857),x87091),x87093),f341(a121,x87092))+P85(f341(f341(f242(a857),f2(a857)),f341(x87091,f617(x87092,x87093,x87091,x87094)))) % 19.23/19.04 [8719]~P85(f341(f71(x87192),x87194))+P85(f341(f341(f241(a857),f341(f50(x87191),f341(f312(x87192,x87191,x87193),x87194))),f341(f50(x87192),x87194))) % 19.23/19.04 [8720]E(f341(f341(f250(x87201,x87202),f709(x87203,x87204,x87202,x87201)),f710(x87203,x87204,x87202,x87201)),x87204)+~P85(f341(f341(f343(f863(x87201,x87202)),x87204),f341(f287(x87202,x87201),x87203))) % 19.23/19.04 [8729]P26(x87291,x87292,x87293,x87294)+P85(f341(f341(f343(x87291),f451(x87294,x87293,x87292,x87291)),x87294)) % 19.23/19.04 [8730]P26(x87301,x87302,x87303,x87304)+P85(f341(f341(f343(x87301),f453(x87304,x87303,x87302,x87301)),x87304)) % 19.23/19.04 [8783]P13(x87831,x87832,x87833,x87834)+P85(f341(f341(f343(f863(x87831,x87831)),f604(x87834,x87833,x87832,x87831)),x87833)) % 19.23/19.04 [8833]P85(f341(x88331,x88332))+~P85(f341(x88331,f341(f341(f250(x88333,x88334),f837(x88334,x88333,x88331)),f839(x88334,x88333,x88331)))) % 19.23/19.04 [8845]E(f341(f186(f858(x88451)),x88452),f341(f186(f858(x88451)),x88453))+~P85(f341(f341(f343(f863(f858(x88451),f858(x88451))),f341(f341(f250(f858(x88451),f858(x88451)),x88452),x88453)),f141(x88451,x88454))) % 19.23/19.04 [8848]E(f341(f186(f858(x88481)),x88482),f341(f186(f858(x88481)),x88483))+~P85(f341(f341(f343(f863(f858(x88481),f858(x88481))),f341(f341(f250(f858(x88481),f858(x88481)),x88482),x88483)),f153(x88481,x88484))) % 19.23/19.04 [8849]E(f341(f186(f858(x88491)),x88492),f341(f186(f858(x88491)),x88493))+~P85(f341(f341(f343(f863(f858(x88491),f858(x88491))),f341(f341(f250(f858(x88491),f858(x88491)),x88492),x88493)),f152(x88491,x88494))) % 19.23/19.04 [8922]P85(f341(f341(f241(a857),f150(x89221,x89222,x89223)),f150(x89221,x89224,x89223)))+P85(f341(f341(f343(x89221),f769(x89224,x89222,x89223,x89221)),f341(f163(x89221),x89223))) % 19.23/19.04 [8923]E(f341(f186(f858(x89231)),x89232),f341(f186(f858(x89231)),x89233))+~P85(f341(f341(f343(f863(f858(x89231),f858(x89231))),f341(f341(f250(f858(x89231),f858(x89231)),x89232),x89233)),f309(f858(x89231),f152(x89231,x89234)))) % 19.23/19.04 [9035]P85(f341(f341(f288(a857),x90351),x90352))+P85(f341(f341(f241(f864(a857,a850)),f291(a857,f288(a857),x90351,x90352)),f291(a857,f288(a857),x90353,x90354))) % 19.23/19.04 [9145]~P26(x91451,x91452,x91453,x91454)+~P85(f341(f341(f242(a857),f341(f50(x91452),f341(f312(x91451,x91452,x91453),x91454))),f341(f50(x91451),x91454))) % 19.23/19.04 [9174]~P85(f341(f341(f343(f863(f858(x91741),f858(x91741))),f341(f341(f250(f858(x91741),f858(x91741)),x91742),x91743)),f152(x91741,x91744)))+P85(f341(f341(f343(f863(f858(x91741),f858(x91741))),f341(f341(f250(f858(x91741),f858(x91741)),x91742),x91743)),f153(x91741,f309(x91741,x91744)))) % 19.23/19.04 [9177]~P85(f341(f341(f343(f863(f858(x91771),f858(x91771))),f341(f341(f250(f858(x91771),f858(x91771)),x91772),x91773)),f153(x91771,x91774)))+P85(f341(f341(f343(f863(f858(x91771),f858(x91771))),f341(f341(f250(f858(x91771),f858(x91771)),x91772),x91773)),f309(f858(x91771),f152(x91771,x91774)))) % 19.23/19.04 [9191]P85(f341(f341(f343(f863(x91911,x91911)),f341(f341(f250(x91911,x91911),x91912),x91913)),f309(x91911,x91914)))+~P85(f341(f341(f343(f863(x91911,x91911)),f341(f341(f250(x91911,x91911),x91912),x91913)),f341(f341(f290(x91911,x91911,x91911),x91914),f309(x91911,x91914)))) % 19.23/19.04 [9259]P85(f341(f341(f288(a857),x92591),x92592))+~P85(f341(f341(f242(f864(a857,a850)),f291(a857,f288(a857),x92593,x92594)),f291(a857,f288(a857),x92591,x92592))) % 19.23/19.04 [9371]E(f341(f341(f132(x93711),f752(x93712,x93713,x93714,x93711)),f341(f341(f146(x93711),f753(x93712,x93713,x93714,x93711)),f755(x93712,x93713,x93714,x93711))),x93714)+~P85(f341(f341(f343(f863(f858(x93711),f858(x93711))),f341(f341(f250(f858(x93711),f858(x93711)),x93714),x93713)),f152(x93711,x93712))) % 19.23/19.04 [9372]E(f341(f341(f132(x93721),f752(x93722,x93723,x93724,x93721)),f341(f341(f146(x93721),f754(x93722,x93723,x93724,x93721)),f755(x93722,x93723,x93724,x93721))),x93723)+~P85(f341(f341(f343(f863(f858(x93721),f858(x93721))),f341(f341(f250(f858(x93721),f858(x93721)),x93724),x93723)),f152(x93721,x93722))) % 19.23/19.04 [9444]P85(f341(f341(f343(f863(x94441,x94441)),f341(f341(f250(x94441,x94441),x94442),f668(x94443,x94444,x94442,x94441))),f309(x94441,x94443)))+~P85(f341(f341(f343(f863(x94441,x94441)),f341(f341(f250(x94441,x94441),x94442),x94444)),f341(f341(f290(x94441,x94441,x94441),x94443),f309(x94441,x94443)))) % 19.23/19.04 [9512]P85(f341(f341(f241(a857),f150(x95121,x95122,x95123)),f150(x95121,x95124,x95123)))+~P85(f341(f341(f242(a857),f341(x95122,f769(x95124,x95122,x95123,x95121))),f341(x95124,f769(x95124,x95122,x95123,x95121)))) % 19.23/19.04 [9581]P85(f341(f341(f343(f863(x95811,x95811)),f341(f341(f250(x95811,x95811),f662(x95812,x95813,x95814,x95811)),x95813)),f309(x95811,x95812)))+~P85(f341(f341(f343(f863(x95811,x95811)),f341(f341(f250(x95811,x95811),x95814),x95813)),f341(f341(f290(x95811,x95811,x95811),x95812),f309(x95811,x95812)))) % 19.23/19.04 [5115]~E(x51152,x51153)+E(f157(x51151,x51152,f341(f341(f146(x51151),x51153),x51154)),x51154) % 19.23/19.04 [5298]~P84(x52982)+E(f341(f341(f88(f864(x52981,x52982)),x52983),x52984),f341(f88(x52982),f341(x52983,x52984))) % 19.23/19.04 [5310]~E(x53102,f2(a857))+E(f341(f341(f135(x53101),x53102),f341(f341(f146(x53101),x53103),x53104)),f341(f341(f146(x53101),x53103),x53104)) % 19.23/19.04 [5311]P85(f341(x53112,x53113))+E(f341(f133(x53111,x53112),f341(f341(f146(x53111),x53113),x53114)),f341(f133(x53111,x53112),x53114)) % 19.23/19.04 [5445]~E(x54452,x54454)+P85(f341(f341(f341(f311(x54451),x54452),x54453),x54454)) % 19.23/19.04 [5453]E(x54531,f122(x54532))+E(f140(x54533,f341(f341(f149(x54532,x54533),x54534),x54531)),f341(x54534,f140(x54532,x54531))) % 19.23/19.04 [5464]~E(x54641,f73(x54642,x54644))+E(f341(x54641,f341(f341(f311(x54642),x54643),f185(f864(x54642,a850)))),x54643) % 19.23/19.04 [5498]E(x54981,f122(x54982))+E(f341(f137(x54983),f341(f341(f149(x54982,x54983),x54984),x54981)),f341(x54984,f341(f137(x54982),x54981))) % 19.23/19.04 [5596]~P85(f341(x55963,x55964))+P85(f341(f341(f341(f311(x55961),x55962),x55963),x55964)) % 19.23/19.04 [5721]~P19(x57212,x57214,x57211)+E(f341(x57211,f341(f341(f311(x57212),x57213),f185(f864(x57212,a850)))),x57213) % 19.23/19.04 [5746]~E(x57462,x57463)+P85(f341(f341(f343(x57461),x57462),f341(f341(f311(x57461),x57463),x57464))) % 19.23/19.04 [5750]~P86(x57501)+E(f341(f341(f89(x57501),x57502),f341(f341(f89(x57501),x57503),x57504)),f341(f341(f89(x57501),x57503),f341(f341(f89(x57501),x57502),x57504))) % 19.23/19.04 [5751]~P86(x57511)+E(f341(f341(f90(x57511),x57512),f341(f341(f90(x57511),x57513),x57514)),f341(f341(f90(x57511),x57513),f341(f341(f90(x57511),x57512),x57514))) % 19.23/19.04 [5753]~P101(x57531)+E(f341(f341(f245(x57531),x57532),f341(f341(f245(x57531),x57533),x57534)),f341(f341(f245(x57531),x57533),f341(f341(f245(x57531),x57532),x57534))) % 19.23/19.04 [5755]~P101(x57551)+E(f341(f341(f240(x57551),x57552),f341(f341(f240(x57551),x57553),x57554)),f341(f341(f240(x57551),x57553),f341(f341(f240(x57551),x57552),x57554))) % 19.23/19.04 [5756]~P95(x57561)+E(f341(f341(f110(x57561),x57562),f341(f341(f110(x57561),x57563),x57564)),f341(f341(f110(x57561),x57563),f341(f341(f110(x57561),x57562),x57564))) % 19.23/19.04 [5758]~P98(x57581)+E(f341(f341(f110(x57581),x57582),f341(f341(f110(x57581),x57583),x57584)),f341(f341(f110(x57581),x57583),f341(f341(f110(x57581),x57582),x57584))) % 19.23/19.04 [5759]~P95(x57591)+E(f341(f341(f111(x57591),x57592),f341(f341(f111(x57591),x57593),x57594)),f341(f341(f111(x57591),x57593),f341(f341(f111(x57591),x57592),x57594))) % 19.23/19.04 [5761]~P99(x57611)+E(f341(f341(f111(x57611),x57612),f341(f341(f111(x57611),x57613),x57614)),f341(f341(f111(x57611),x57613),f341(f341(f111(x57611),x57612),x57614))) % 19.23/19.04 [5768]E(x57681,x57682)+E(f157(x57683,x57681,f341(f341(f146(x57683),x57682),x57684)),f341(f341(f146(x57683),x57682),f157(x57683,x57681,x57684))) % 19.23/19.04 [5783]~P85(f341(x57832,x57833))+E(f341(f133(x57831,x57832),f341(f341(f146(x57831),x57833),x57834)),f341(f341(f146(x57831),x57833),f341(f133(x57831,x57832),x57834))) % 19.23/19.04 [5978]E(x59781,f185(f864(x59782,a850)))+E(f341(f341(f54(x59782,f864(x59783,a850)),x59781),f341(f18(f864(x59783,a850),x59782),x59784)),x59784) % 19.23/19.04 [5979]E(x59791,f185(f864(x59792,a850)))+E(f341(f341(f55(x59792,f864(x59793,a850)),x59791),f341(f18(f864(x59793,a850),x59792),x59794)),x59794) % 19.23/19.04 [5988]~E(x59884,f185(f864(x59882,a850)))+E(f341(f341(f257(x59881,x59882),x59883),f341(f18(f864(x59882,a850),x59881),x59884)),f185(f864(f863(x59881,x59882),a850))) % 19.23/19.04 [5989]~E(x59893,f185(f864(x59891,a850)))+E(f341(f341(f257(x59891,x59892),x59893),f341(f18(f864(x59892,a850),x59891),x59894)),f185(f864(f863(x59891,x59892),a850))) % 19.23/19.04 [6040]E(x60401,f2(a857))+E(f341(f341(f135(x60402),x60401),f341(f341(f146(x60402),x60403),x60404)),f341(f341(f135(x60402),f341(f341(f3(a857),x60401),f87(a857))),x60404)) % 19.23/19.04 [6067]E(x60671,f185(f864(x60672,a850)))+E(f341(f312(x60672,x60673,f341(f18(x60673,x60672),x60674)),x60671),f341(f341(f311(x60673),x60674),f185(f864(x60673,a850)))) % 19.23/19.04 [6070]E(f341(f314(x60701,x60702,f341(f18(x60702,x60701),x60703)),x60704),f185(f864(x60701,a850)))+P85(f341(f341(f343(x60702),x60703),x60704)) % 19.23/19.04 [6137]~E(x61373,f185(f864(x61371,a850)))+E(f341(f341(f54(x61371,f864(x61372,a850)),x61373),f341(f18(f864(x61372,a850),x61371),x61374)),f185(f864(x61372,a850))) % 19.23/19.04 [6138]~E(x61383,f185(f864(x61381,a850)))+E(f341(f341(f55(x61381,f864(x61382,a850)),x61383),f341(f18(f864(x61382,a850),x61381),x61384)),f248(f864(x61382,a850))) % 19.23/19.04 [6140]~P4(x61401)+E(f60(x61401,f341(f341(f90(x61401),x61402),x61403),f341(f341(f90(x61401),x61402),x61404)),f341(f341(f90(x61401),x61402),f60(x61401,x61403,x61404))) % 19.23/19.04 [6313]E(f341(f314(x63131,x63132,f341(f18(x63132,x63131),x63133)),x63134),f248(f864(x63131,a850)))+~P85(f341(f341(f343(x63132),x63133),x63134)) % 19.23/19.04 [6336]~P85(f341(f341(f343(x63361),x63362),x63364))+P85(f341(f341(f343(x63361),x63362),f341(f341(f311(x63361),x63363),x63364))) % 19.23/19.04 [6349]~E(x63493,f341(f341(f3(a857),f341(f186(f858(x63491)),x63492)),f87(a857)))+E(f123(x63491,f341(f341(f154(x63491,x63492),x63493),x63494)),f123(x63491,x63492)) % 19.23/19.04 [6374]~P101(x63741)+E(f341(f341(f111(f864(x63741,a850)),f341(f302(x63741),x63742)),f304(x63741,x63743,x63744)),f304(x63741,x63743,f341(f341(f245(x63741),x63742),x63744))) % 19.23/19.04 [6375]~P101(x63751)+E(f341(f341(f111(f864(x63751,a850)),f341(f267(x63751),x63752)),f304(x63751,x63753,x63754)),f304(x63751,f341(f341(f240(x63751),x63752),x63753),x63754)) % 19.23/19.04 [6392]E(f341(f341(f111(f864(x63921,a850)),x63922),f341(f341(f311(x63921),x63923),x63924)),f341(f341(f111(f864(x63921,a850)),x63922),x63924))+P85(f341(f341(f343(x63921),x63923),x63922)) % 19.23/19.04 [6404]E(f157(x64041,x64042,f341(f341(f132(x64041),x64043),x64044)),f341(f341(f132(x64041),x64043),f157(x64041,x64042,x64044)))+P85(f341(f341(f343(x64041),x64042),f341(f163(x64041),x64043))) % 19.23/19.04 [6409]~P75(x64091)+E(f341(f341(f90(x64091),f341(f341(f251(x64091),x64092),x64093)),f341(f341(f251(x64091),x64092),x64094)),f341(f341(f251(x64091),x64092),f341(f341(f89(a857),x64093),x64094))) % 19.23/19.04 [6410]~P86(x64101)+E(f341(f341(f90(x64101),f341(f341(f251(x64101),x64102),x64103)),f341(f341(f251(x64101),x64102),x64104)),f341(f341(f251(x64101),x64102),f341(f341(f89(a857),x64103),x64104))) % 19.23/19.04 [6446]~P86(x64461)+E(f341(f341(f89(x64461),f341(f341(f90(x64461),x64462),x64463)),f341(f341(f90(x64461),x64462),x64464)),f341(f341(f90(x64461),x64462),f341(f341(f89(x64461),x64463),x64464))) % 19.23/19.04 [6447]~P101(x64471)+E(f341(f341(f240(x64471),f341(f341(f245(x64471),x64472),x64473)),f341(f341(f245(x64471),x64472),x64474)),f341(f341(f245(x64471),x64472),f341(f341(f240(x64471),x64473),x64474))) % 19.23/19.04 [6448]~P101(x64481)+E(f341(f341(f245(x64481),f341(f341(f240(x64481),x64482),x64483)),f341(f341(f240(x64481),x64482),x64484)),f341(f341(f240(x64481),x64482),f341(f341(f245(x64481),x64483),x64484))) % 19.23/19.04 [6449]~P96(x64491)+E(f341(f341(f111(x64491),f341(f341(f110(x64491),x64492),x64493)),f341(f341(f110(x64491),x64492),x64494)),f341(f341(f110(x64491),x64492),f341(f341(f111(x64491),x64493),x64494))) % 19.23/19.04 [6450]~P96(x64501)+E(f341(f341(f110(x64501),f341(f341(f111(x64501),x64502),x64503)),f341(f341(f111(x64501),x64502),x64504)),f341(f341(f111(x64501),x64502),f341(f341(f110(x64501),x64503),x64504))) % 19.23/19.04 [6486]~P4(x64861)+E(f60(x64861,f341(f341(f90(x64861),x64862),x64863),f341(f341(f90(x64861),x64864),x64863)),f341(f341(f90(x64861),f60(x64861,x64862,x64864)),x64863)) % 19.23/19.04 [6489]~E(f341(f186(f858(x64891)),x64893),f341(f186(f858(x64892)),x64894))+E(f341(f341(f149(f863(x64891,x64892),x64892),f259(x64891,x64892)),f341(f341(f172(x64891,x64892),x64893),x64894)),x64894) % 19.23/19.04 [6490]~E(f341(f186(f858(x64901)),x64903),f341(f186(f858(x64902)),x64904))+E(f341(f341(f149(f863(x64901,x64902),x64901),f249(x64901,x64902)),f341(f341(f172(x64901,x64902),x64903),x64904)),x64903) % 19.23/19.04 [6501]~P4(x65011)+E(f60(x65011,f341(f341(f90(x65011),x65012),f60(x65011,x65013,x65014)),x65014),f60(x65011,f341(f341(f90(x65011),x65012),x65013),x65014)) % 19.23/19.04 [6502]~P5(x65021)+E(f60(x65021,f341(f341(f3(x65021),x65022),f60(x65021,x65023,x65024)),x65024),f60(x65021,f341(f341(f3(x65021),x65022),x65023),x65024)) % 19.23/19.04 [6503]~P4(x65031)+E(f60(x65031,f341(f341(f89(x65031),x65032),f60(x65031,x65033,x65034)),x65034),f60(x65031,f341(f341(f89(x65031),x65032),x65033),x65034)) % 19.23/19.04 [6586]~P101(x65861)+E(f341(f341(f111(f864(x65861,a850)),f304(x65861,x65862,x65863)),f341(f302(x65861),x65864)),f304(x65861,x65862,f341(f341(f245(x65861),x65863),x65864))) % 19.23/19.04 [6587]~P101(x65871)+E(f341(f341(f111(f864(x65871,a850)),f304(x65871,x65872,x65873)),f341(f267(x65871),x65874)),f304(x65871,f341(f341(f240(x65871),x65872),x65874),x65873)) % 19.23/19.04 [6590]~E(f341(f186(f858(x65901)),x65903),f341(f186(f858(x65902)),x65904))+E(f341(f341(f172(x65901,x65902),f341(f148(x65901),x65903)),f341(f148(x65902),x65904)),f341(f148(f863(x65901,x65902)),f341(f341(f172(x65901,x65902),x65903),x65904))) % 19.23/19.04 [6599]E(x65991,f341(f341(f3(a857),f341(f186(f858(x65992)),x65993)),f87(a857)))+E(f123(x65992,f341(f341(f154(x65992,x65993),x65991),x65994)),f341(f341(f154(x65992,f123(x65992,x65993)),x65991),x65994)) % 19.23/19.04 [6616]~P85(f341(f134(x66162),x66164))+P85(f341(f134(f863(x66161,x66162)),f341(f341(f172(x66161,x66162),x66163),x66164))) % 19.23/19.04 [6617]~P85(f341(f134(x66171),x66173))+P85(f341(f134(f863(x66171,x66172)),f341(f341(f172(x66171,x66172),x66173),x66174))) % 19.23/19.04 [6714]E(x67141,f341(f341(f341(a194,x67142),x67143),f341(x67144,x67142)))+~P85(f341(f341(f192(f30(x67143,x67144)),x67142),x67141)) % 19.23/19.04 [6894]E(f341(f341(f51(a857),x68941),x68942),x68943)+~P85(f341(f63(x68941,x68942),f341(f341(f250(a857,a857),x68943),x68944))) % 19.23/19.04 [6920]E(f60(a857,x69201,x69202),x69203)+~P85(f341(f63(x69201,x69202),f341(f341(f250(a857,a857),x69204),x69203))) % 19.23/19.04 [6923]P85(f341(f134(x69231),x69232))+~P85(f341(f134(x69233),f341(f341(f149(x69231,x69233),x69234),x69232))) % 19.23/19.04 [7002]E(f157(x70021,x70022,f341(f341(f132(x70021),x70023),x70024)),f341(f341(f132(x70021),f157(x70021,x70022,x70023)),x70024))+~P85(f341(f341(f343(x70021),x70022),f341(f163(x70021),x70023))) % 19.23/19.04 [7098]~P5(x70981)+E(f60(x70981,f341(f341(f3(x70981),f60(x70981,x70982,x70983)),x70984),x70983),f60(x70981,f341(f341(f3(x70981),x70982),x70984),x70983)) % 19.23/19.04 [7099]~P4(x70991)+E(f60(x70991,f341(f341(f89(x70991),f60(x70991,x70992,x70993)),x70994),x70993),f60(x70991,f341(f341(f89(x70991),x70992),x70994),x70993)) % 19.23/19.04 [7100]~P4(x71001)+E(f60(x71001,f341(f341(f90(x71001),f60(x71001,x71002,x71003)),x71004),x71003),f60(x71001,f341(f341(f90(x71001),x71002),x71004),x71003)) % 19.23/19.04 [7305]~E(x73051,f341(f341(f146(x73052),x73053),x73054))+~P85(f341(f341(f241(a857),f341(f186(f858(x73052)),x73051)),f341(f186(f858(x73052)),x73054))) % 19.23/19.04 [7476]~E(f171(x74761,x74762,x74763),f171(x74761,x74762,x74764))+E(f341(f312(f863(x74761,x74762),x74761,f249(x74761,x74762)),f341(f163(f863(x74761,x74762)),x74763)),f341(f312(f863(x74761,x74762),x74761,f249(x74761,x74762)),f341(f163(f863(x74761,x74762)),x74764))) % 19.23/19.04 [7519]P26(x75191,x75192,x75193,f341(f163(x75191),x75194))+~P85(f341(f134(x75192),f341(f341(f149(x75191,x75192),x75193),x75194))) % 19.23/19.04 [7596]~P85(f341(f341(f241(f864(x75961,a850)),x75962),x75964))+P85(f341(f341(f241(f864(x75961,a850)),x75962),f341(f341(f311(x75961),x75963),x75964))) % 19.23/19.04 [7631]~P4(x76311)+E(f60(x76311,f341(f341(f89(x76311),f60(x76311,x76312,x76313)),f60(x76311,x76314,x76313)),x76313),f60(x76311,f341(f341(f89(x76311),x76312),x76314),x76313)) % 19.23/19.04 [7632]~P4(x76321)+E(f60(x76321,f341(f341(f90(x76321),f60(x76321,x76322,x76323)),f60(x76321,x76324,x76323)),x76323),f60(x76321,f341(f341(f90(x76321),x76322),x76324),x76323)) % 19.23/19.04 [7633]~P5(x76331)+E(f60(x76331,f341(f341(f3(x76331),f60(x76331,x76332,x76333)),f60(x76331,x76334,x76333)),x76333),f60(x76331,f341(f341(f3(x76331),x76332),x76334),x76333)) % 19.23/19.04 [7734]~E(f341(x77344,f409(x77344,x77343,x77341,x77342)),f185(f864(x77342,a850)))+E(f341(f341(f54(x77341,f864(x77342,a850)),x77343),x77344),f185(f864(x77342,a850))) % 19.23/19.04 [7735]~E(f341(x77354,f671(x77354,x77353,x77351,x77352)),f248(f864(x77352,a850)))+E(f341(f341(f55(x77351,f864(x77352,a850)),x77353),x77354),f248(f864(x77352,a850))) % 19.23/19.04 [7736]~E(f341(x77364,f423(x77364,x77363,x77362,x77361)),f185(f864(x77362,a850)))+E(f341(f341(f54(x77361,f864(x77362,a850)),x77363),x77364),f185(f864(x77362,a850))) % 19.23/19.04 [7737]~E(f341(x77374,f674(x77374,x77373,x77372,x77371)),f248(f864(x77372,a850)))+E(f341(f341(f55(x77371,f864(x77372,a850)),x77373),x77374),f248(f864(x77372,a850))) % 19.23/19.04 [8126]P85(f341(x81261,x81262))+~P85(f341(f341(f343(x81263),x81262),f341(f341(f111(f864(x81263,a850)),x81264),f341(f265(x81263),x81261)))) % 19.23/19.04 [8164]~P85(f341(f341(f241(f864(x81641,a850)),x81643),x81644))+P85(f341(f341(f241(f864(x81641,a850)),f341(f341(f311(x81641),x81642),x81643)),f341(f341(f311(x81641),x81642),x81644))) % 19.23/19.04 [8332]P85(f341(f341(f192(x83321),x83322),f367(x83323,x83322,x83324,x83321)))+~P85(f341(f341(f192(f38(x83321,x83324)),x83322),x83323)) % 19.23/19.04 [8333]P85(f341(f341(f192(x83331),x83332),f381(x83333,x83332,x83334,x83331)))+~P85(f341(f341(f192(f38(x83331,x83334)),x83332),x83333)) % 19.23/19.04 [8453]~P85(f341(f341(f242(a857),f341(x84534,x84532)),f341(x84534,x84533)))+P85(f341(f341(f343(f863(x84531,x84531)),f341(f341(f250(x84531,x84531),x84532),x84533)),f341(f341(f289(a857,x84531),a246),x84534))) % 19.23/19.04 [8600]P26(f858(x86001),f858(x86002),f341(f149(x86001,x86002),x86003),x86004)+~P26(x86001,x86002,x86003,f52(f864(x86001,a850),f341(f312(f858(x86001),f864(x86001,a850),f163(x86001)),x86004))) % 19.23/19.04 [8710]E(f341(f341(f54(x87101,f864(x87102,a850)),x87103),x87104),f185(f864(x87102,a850)))+P85(f341(f341(f343(x87101),f409(x87104,x87103,x87101,x87102)),x87103)) % 19.23/19.04 [8711]E(f341(f341(f55(x87111,f864(x87112,a850)),x87113),x87114),f248(f864(x87112,a850)))+P85(f341(f341(f343(x87111),f671(x87114,x87113,x87111,x87112)),x87113)) % 19.23/19.04 [8712]E(f341(f341(f54(x87121,f864(x87122,a850)),x87123),x87124),f185(f864(x87122,a850)))+P85(f341(f341(f343(x87121),f423(x87124,x87123,x87122,x87121)),x87123)) % 19.23/19.04 [8713]E(f341(f341(f55(x87131,f864(x87132,a850)),x87133),x87134),f248(f864(x87132,a850)))+P85(f341(f341(f343(x87131),f674(x87134,x87133,x87132,x87131)),x87133)) % 19.23/19.04 [8748]P85(f341(f341(f242(a857),f341(x87481,x87482)),f341(x87481,x87483)))+~P85(f341(f341(f343(f863(x87484,x87484)),f341(f341(f250(x87484,x87484),x87482),x87483)),f341(f341(f289(a857,x87484),a246),x87481))) % 19.23/19.04 [8797]P85(f341(f341(f192(x87971),f367(x87972,x87973,x87971,x87974)),x87972))+~P85(f341(f341(f192(f38(x87974,x87971)),x87973),x87972)) % 19.23/19.04 [8798]P85(f341(f341(f192(x87981),f381(x87982,x87983,x87981,x87984)),x87982))+~P85(f341(f341(f192(f38(x87984,x87981)),x87983),x87982)) % 19.23/19.04 [8911]P85(f341(f341(f343(x89111),f385(x89112,x89113,x89114,x89111)),x89113))+~P85(f341(f341(f343(f864(x89111,a850)),x89114),f341(f341(f69(x89111),x89113),x89112))) % 19.23/19.04 [8914]E(x89141,x89142)+~P85(f341(f341(f343(f863(x89143,x89143)),f341(f341(f250(x89143,x89143),x89141),x89142)),f341(f341(f179(f863(x89143,x89143),a850),f2(a857)),x89144))) % 19.23/19.04 [8985]E(f341(f286(x89851,x89851,x89852),f341(f341(f311(x89851),f385(x89852,x89853,x89854,x89851)),f185(f864(x89851,a850)))),x89854)+~P85(f341(f341(f343(f864(x89851,a850)),x89854),f341(f341(f69(x89851),x89853),x89852))) % 19.23/19.04 [8996]~P85(f341(f341(f343(f863(x89961,x89961)),f341(f341(f250(x89961,x89961),x89963),x89962)),f309(x89961,x89964)))+P85(f341(f341(f343(f863(x89961,x89961)),f341(f341(f250(x89961,x89961),x89962),x89963)),f309(x89961,f341(f287(x89961,x89961),x89964)))) % 19.23/19.04 [9009]~P4(x90091)+E(f341(f341(f89(x90091),f341(f341(f89(x90091),f341(f341(f90(x90091),x90092),f341(f341(f51(x90091),x90093),x90092))),f60(x90091,x90093,x90092))),x90094),f341(f341(f89(x90091),x90093),x90094)) % 19.23/19.04 [9017]~P85(f341(f341(f343(x90171),x90173),x90174))+P85(f341(f341(f343(f864(x90171,a850)),f341(f286(x90171,x90171,x90172),f341(f341(f311(x90171),x90173),f185(f864(x90171,a850))))),f341(f341(f69(x90171),x90174),x90172))) % 19.23/19.04 [9027]P85(f341(f341(f343(f863(x90271,x90271)),f341(f341(f250(x90271,x90271),x90272),x90273)),f309(x90271,x90274)))+~P85(f341(f341(f343(f863(x90271,x90271)),f341(f341(f250(x90271,x90271),x90273),x90272)),f309(x90271,f341(f287(x90271,x90271),x90274)))) % 19.23/19.04 [9111]E(f341(f341(f154(x91111,f341(f148(x91111),x91112)),f341(f341(f3(a857),f341(f341(f3(a857),f341(f186(f858(x91111)),x91112)),x91113)),f87(a857))),x91114),f341(f148(x91111),f341(f341(f154(x91111,x91112),x91113),x91114)))+~P85(f341(f341(f242(a857),x91113),f341(f186(f858(x91111)),x91112))) % 19.23/19.04 [9149]~P26(x91492,x91491,x91493,f248(f864(x91492,a850)))+P85(f341(f341(f241(f864(x91491,a850)),f341(f312(x91492,x91491,x91493),f341(f88(f864(x91492,a850)),x91494))),f341(f88(f864(x91491,a850)),f341(f312(x91492,x91491,x91493),x91494)))) % 19.23/19.04 [9157]~P6(x91571)+E(f341(f138(x91571,x91572,f341(f9(x91572,x91571,x91571),f341(f341(f10(x91571,f864(x91571,x91571),x91572),f110(x91571)),x91573)),f185(x91571)),x91574),f341(f341(f54(x91572,x91571),f341(f163(x91572),x91574)),x91573)) % 19.23/19.04 [9158]~P6(x91581)+E(f341(f138(x91581,x91582,f341(f9(x91582,x91581,x91581),f341(f341(f10(x91581,f864(x91581,x91581),x91582),f111(x91581)),x91583)),f248(x91581)),x91584),f341(f341(f55(x91582,x91581),f341(f163(x91582),x91584)),x91583)) % 19.23/19.04 [9222]~P85(f341(f341(f343(f863(f858(x92224),f858(x92224))),f341(f341(f250(f858(x92224),f858(x92224)),x92223),x92222)),f152(x92224,x92221)))+P85(f341(f341(f242(a857),f747(x92221,x92222,x92223,x92224)),f341(f186(f858(x92224)),x92223))) % 19.23/19.04 [9223]~P4(x92231)+E(f341(f341(f89(x92231),f341(f341(f89(x92231),f341(f341(f90(x92231),f341(f341(f51(x92231),x92232),x92233)),x92233)),f60(x92231,x92232,x92233))),x92234),f341(f341(f89(x92231),x92232),x92234)) % 19.23/19.04 [9251]~P85(f341(f341(f343(f863(f858(x92511),f858(x92511))),f341(f341(f250(f858(x92511),f858(x92511)),x92512),x92513)),f341(f287(f858(x92511),f858(x92511)),f152(x92511,x92514))))+P85(f341(f341(f343(f863(f858(x92511),f858(x92511))),f341(f341(f250(f858(x92511),f858(x92511)),x92512),x92513)),f152(x92511,f341(f287(x92511,x92511),x92514)))) % 19.23/19.04 [9252]P85(f341(f341(f343(f863(f858(x92521),f858(x92521))),f341(f341(f250(f858(x92521),f858(x92521)),x92522),x92523)),f341(f287(f858(x92521),f858(x92521)),f152(x92521,x92524))))+~P85(f341(f341(f343(f863(f858(x92521),f858(x92521))),f341(f341(f250(f858(x92521),f858(x92521)),x92522),x92523)),f152(x92521,f341(f287(x92521,x92521),x92524)))) % 19.23/19.04 [9290]~P85(f341(f341(f343(x92901),x92903),f341(f270(x92901,x92902),x92904)))+P85(f341(f341(f343(f863(x92901,x92902)),f341(f341(f250(x92901,x92902),x92903),f598(x92904,x92902,x92903,x92901))),x92904)) % 19.23/19.04 [9291]~P85(f341(f341(f343(x92911),x92913),f341(f270(x92911,x92912),x92914)))+P85(f341(f341(f343(f863(x92911,x92912)),f341(f341(f250(x92911,x92912),x92913),f599(x92914,x92912,x92913,x92911))),x92914)) % 19.23/19.04 [9417]~P85(f341(f71(f861(x94171)),f341(f312(x94172,f861(x94171),x94173),f248(f864(x94172,a850)))))+P85(f341(f71(f861(x94171)),f341(f312(x94172,f861(x94171),f175(x94172,x94171,x94173,f171(x94172,x94171,x94174))),f248(f864(x94172,a850))))) % 19.23/19.04 [9439]~P85(f341(f341(f343(f863(x94391,x94391)),f341(f341(f250(x94391,x94391),x94392),x94394)),f341(f341(f290(x94391,x94391,x94391),x94393),f309(x94391,x94393))))+P85(f341(f341(f343(f863(x94391,x94391)),f341(f341(f250(x94391,x94391),x94392),f662(x94393,x94394,x94392,x94391))),x94393)) % 19.23/19.04 [9608]~P85(f341(f341(f343(f863(x96082,x96081)),x96084),f341(f287(x96081,x96082),x96083)))+P85(f341(f341(f343(f863(x96081,x96082)),f341(f341(f250(x96081,x96082),f710(x96083,x96084,x96081,x96082)),f709(x96083,x96084,x96081,x96082))),x96083)) % 19.23/19.04 [9632]~P85(f341(f341(f343(f863(f858(x96321),f858(x96321))),f341(f341(f250(f858(x96321),f858(x96321)),x96324),x96323)),f152(x96321,x96322)))+P85(f341(f341(f343(f863(x96321,x96321)),f341(f341(f250(x96321,x96321),f753(x96322,x96323,x96324,x96321)),f754(x96322,x96323,x96324,x96321))),x96322)) % 19.23/19.04 [9707]~P85(f341(f341(f343(f863(f858(x97071),f858(x97071))),f341(f341(f250(f858(x97071),f858(x97071)),x97072),x97074)),f152(x97071,x97073)))+P85(f341(f341(f343(f863(x97071,x97071)),f341(f341(f250(x97071,x97071),f341(f341(f158(x97071),x97072),f747(x97073,x97074,x97072,x97071))),f748(x97073,x97074,x97072,x97071))),x97073)) % 19.23/19.04 [9728]~P85(f341(f71(x97282),x97284))+E(f341(f341(f341(f75(f864(x97281,a850),x97282,f110(f864(x97281,a850))),f341(f341(f9(x97282,f864(x97281,a850),f864(x97281,a850)),f341(f341(f10(x97281,f864(f864(x97281,a850),f864(x97281,a850)),x97282),f311(x97281)),x97283)),f185(f864(x97281,a850)))),f185(f864(x97281,a850))),x97284),f341(f312(x97282,x97281,x97283),x97284)) % 19.23/19.04 [9848]~P26(x98481,x98482,x98483,f248(f864(x98481,a850)))+P85(f341(f341(f241(f864(x98481,a850)),f341(f314(x98481,x98482,x98483),f341(f341(f311(x98482),x98484),f185(f864(x98482,a850))))),f341(f341(f311(x98481),f94(x98481,f341(f341(f9(x98481,x98482,a850),f341(f341(f10(x98482,f864(x98482,a850),x98481),a338),x98483)),x98484))),f185(f864(x98481,a850))))) % 19.23/19.04 [5507]~E(f341(f341(f132(x55071),x55072),x55074),x55073)+E(f341(f341(f164(x55071),f341(f186(f858(x55071)),x55072)),x55073),x55072) % 19.23/19.04 [5508]~E(f341(f341(f132(x55082),x55083),x55081),x55084)+E(x55081,f341(f341(f135(x55082),f341(f186(f858(x55082)),x55083)),x55084)) % 19.23/19.04 [5519]~E(x55194,f2(a857))+E(f341(f341(f158(x55191),f341(f341(f146(x55191),x55192),x55193)),x55194),x55192) % 19.23/19.04 [6051]~P86(x60511)+E(f341(f341(f251(x60511),f341(f341(f251(x60511),x60512),x60513)),x60514),f341(f341(f251(x60511),x60512),f341(f341(f90(a857),x60513),x60514))) % 19.23/19.04 [6052]~P75(x60521)+E(f341(f341(f251(x60521),f341(f341(f251(x60521),x60522),x60523)),x60524),f341(f341(f251(x60521),x60522),f341(f341(f90(a857),x60523),x60524))) % 19.23/19.04 [6068]E(x60681,f2(a857))+E(f341(f341(f158(x60682),f341(f341(f146(x60682),x60683),x60684)),x60681),f341(f341(f158(x60682),x60684),f341(f341(f3(a857),x60681),f87(a857)))) % 19.23/19.04 [6094]~P116(x60941)+E(f341(f341(f292(x60941),f341(f341(f90(x60941),x60942),x60943)),x60944),f341(f341(f90(x60941),x60942),f341(f341(f292(x60941),x60943),x60944))) % 19.23/19.04 [6095]~P2(x60951)+E(f341(f341(f89(x60951),f341(f341(f89(x60951),x60952),x60953)),x60954),f341(f341(f89(x60951),x60952),f341(f341(f89(x60951),x60953),x60954))) % 19.23/19.04 [6096]~P86(x60961)+E(f341(f341(f89(x60961),f341(f341(f89(x60961),x60962),x60963)),x60964),f341(f341(f89(x60961),x60962),f341(f341(f89(x60961),x60963),x60964))) % 19.23/19.04 [6097]~P86(x60971)+E(f341(f341(f90(x60971),f341(f341(f90(x60971),x60972),x60973)),x60974),f341(f341(f90(x60971),x60972),f341(f341(f90(x60971),x60973),x60974))) % 19.23/19.04 [6098]~P65(x60981)+E(f341(f341(f90(x60981),f341(f341(f90(x60981),x60982),x60983)),x60984),f341(f341(f90(x60981),x60982),f341(f341(f90(x60981),x60983),x60984))) % 19.23/19.04 [6101]~P101(x61011)+E(f341(f341(f245(x61011),f341(f341(f245(x61011),x61012),x61013)),x61014),f341(f341(f245(x61011),x61012),f341(f341(f245(x61011),x61013),x61014))) % 19.23/19.04 [6103]~P101(x61031)+E(f341(f341(f240(x61031),f341(f341(f240(x61031),x61032),x61033)),x61034),f341(f341(f240(x61031),x61032),f341(f341(f240(x61031),x61033),x61034))) % 19.23/19.04 [6104]~P95(x61041)+E(f341(f341(f110(x61041),f341(f341(f110(x61041),x61042),x61043)),x61044),f341(f341(f110(x61041),x61042),f341(f341(f110(x61041),x61043),x61044))) % 19.23/19.04 [6106]~P98(x61061)+E(f341(f341(f110(x61061),f341(f341(f110(x61061),x61062),x61063)),x61064),f341(f341(f110(x61061),x61062),f341(f341(f110(x61061),x61063),x61064))) % 19.23/19.04 [6107]~P95(x61071)+E(f341(f341(f111(x61071),f341(f341(f111(x61071),x61072),x61073)),x61074),f341(f341(f111(x61071),x61072),f341(f341(f111(x61071),x61073),x61074))) % 19.23/19.04 [6109]~P99(x61091)+E(f341(f341(f111(x61091),f341(f341(f111(x61091),x61092),x61093)),x61094),f341(f341(f111(x61091),x61092),f341(f341(f111(x61091),x61093),x61094))) % 19.23/19.04 [6120]~P4(x61201)+E(f60(x61201,f341(f341(f89(x61201),x61202),f341(f341(f90(x61201),x61203),x61204)),x61204),f60(x61201,x61202,x61204)) % 19.23/19.04 [6121]~P4(x61211)+E(f60(x61211,f341(f341(f89(x61211),x61212),f341(f341(f90(x61211),x61213),x61214)),x61213),f60(x61211,x61212,x61213)) % 19.23/19.04 [6258]E(f341(f341(f158(x62581),f341(f341(f164(x62581),x62582),x62583)),x62584),f341(f341(f158(x62581),x62583),x62584))+~P85(f341(f341(f242(a857),x62584),x62582)) % 19.23/19.04 [6444]~P86(x64441)+E(f341(f341(f89(x64441),f341(f341(f89(x64441),x64442),x64443)),x64444),f341(f341(f89(x64441),f341(f341(f89(x64441),x64442),x64444)),x64443)) % 19.23/19.04 [6445]~P86(x64451)+E(f341(f341(f90(x64451),f341(f341(f90(x64451),x64452),x64453)),x64454),f341(f341(f90(x64451),f341(f341(f90(x64451),x64452),x64454)),x64453)) % 19.23/19.04 [6506]~P112(x65062)+E(f341(f341(f8(x65061,x65062),f341(f18(x65062,x65061),x65063)),x65064),f341(f341(f90(x65062),f341(f109(x65062),f341(f50(x65061),x65064))),x65063)) % 19.23/19.04 [6683]E(f341(f341(f111(f864(x66831,a850)),f341(f341(f311(x66831),x66832),x66833)),x66834),f341(f341(f111(f864(x66831,a850)),x66833),x66834))+P85(f341(f341(f343(x66831),x66832),x66834)) % 19.23/19.04 [6757]~P74(x67571)+E(f341(f341(f245(x67571),f341(f341(f89(x67571),x67572),x67573)),f341(f341(f89(x67571),x67574),x67573)),f341(f341(f89(x67571),f341(f341(f245(x67571),x67572),x67574)),x67573)) % 19.23/19.04 [6758]~P74(x67581)+E(f341(f341(f240(x67581),f341(f341(f89(x67581),x67582),x67583)),f341(f341(f89(x67581),x67584),x67583)),f341(f341(f89(x67581),f341(f341(f240(x67581),x67582),x67584)),x67583)) % 19.23/19.04 [6760]~P110(x67601)+E(f341(f341(f89(x67601),f341(f341(f90(x67601),x67602),x67603)),f341(f341(f90(x67601),x67604),x67603)),f341(f341(f90(x67601),f341(f341(f89(x67601),x67602),x67604)),x67603)) % 19.23/19.04 [6761]~P77(x67611)+E(f341(f341(f245(x67611),f341(f341(f3(x67611),x67612),x67613)),f341(f341(f3(x67611),x67614),x67613)),f341(f341(f3(x67611),f341(f341(f245(x67611),x67612),x67614)),x67613)) % 19.23/19.04 [6762]~P77(x67621)+E(f341(f341(f240(x67621),f341(f341(f3(x67621),x67622),x67623)),f341(f341(f3(x67621),x67624),x67623)),f341(f341(f3(x67621),f341(f341(f240(x67621),x67622),x67624)),x67623)) % 19.23/19.04 [6763]~P86(x67631)+E(f341(f341(f90(x67631),f341(f341(f251(x67631),x67632),x67633)),f341(f341(f251(x67631),x67634),x67633)),f341(f341(f251(x67631),f341(f341(f90(x67631),x67632),x67634)),x67633)) % 19.23/19.04 [6764]~P71(x67641)+E(f341(f341(f90(x67641),f341(f341(f251(x67641),x67642),x67643)),f341(f341(f251(x67641),x67644),x67643)),f341(f341(f251(x67641),f341(f341(f90(x67641),x67642),x67644)),x67643)) % 19.23/19.04 [6765]~P59(x67651)+E(f341(f341(f292(x67651),f341(f341(f251(x67651),x67652),x67653)),f341(f341(f251(x67651),x67654),x67653)),f341(f341(f251(x67651),f341(f341(f292(x67651),x67652),x67654)),x67653)) % 19.23/19.04 [6766]~P116(x67661)+E(f341(f341(f89(x67661),f341(f341(f292(x67661),x67662),x67663)),f341(f341(f292(x67661),x67664),x67663)),f341(f341(f292(x67661),f341(f341(f89(x67661),x67662),x67664)),x67663)) % 19.23/19.04 [6767]~P116(x67671)+E(f341(f341(f3(x67671),f341(f341(f292(x67671),x67672),x67673)),f341(f341(f292(x67671),x67674),x67673)),f341(f341(f292(x67671),f341(f341(f3(x67671),x67672),x67674)),x67673)) % 19.23/19.04 [6768]~P101(x67681)+E(f341(f341(f240(x67681),f341(f341(f245(x67681),x67682),x67683)),f341(f341(f245(x67681),x67684),x67683)),f341(f341(f245(x67681),f341(f341(f240(x67681),x67682),x67684)),x67683)) % 19.23/19.04 [6769]~P101(x67691)+E(f341(f341(f245(x67691),f341(f341(f240(x67691),x67692),x67693)),f341(f341(f240(x67691),x67694),x67693)),f341(f341(f240(x67691),f341(f341(f245(x67691),x67692),x67694)),x67693)) % 19.23/19.04 [6770]~P96(x67701)+E(f341(f341(f111(x67701),f341(f341(f110(x67701),x67702),x67703)),f341(f341(f110(x67701),x67704),x67703)),f341(f341(f110(x67701),f341(f341(f111(x67701),x67702),x67704)),x67703)) % 19.23/19.04 [6771]~P96(x67711)+E(f341(f341(f110(x67711),f341(f341(f111(x67711),x67712),x67713)),f341(f341(f111(x67711),x67714),x67713)),f341(f341(f111(x67711),f341(f341(f110(x67711),x67712),x67714)),x67713)) % 19.23/19.04 [6772]~P86(x67721)+E(f341(f341(f89(x67721),f341(f341(f90(x67721),x67722),x67723)),f341(f341(f90(x67721),x67724),x67723)),f341(f341(f90(x67721),f341(f341(f89(x67721),x67722),x67724)),x67723)) % 19.23/19.04 [6807]E(f341(f341(f154(x68071,x68072),x68073),x68074),x68072)+~P85(f341(f341(f241(a857),f341(f186(f858(x68071)),x68072)),x68073)) % 19.23/19.04 [6834]~P85(f341(x68343,x68344))+P85(f341(f341(f341(f110(f864(x68341,a850)),x68342),x68343),x68344)) % 19.23/19.04 [6836]~P85(f341(x68362,x68364))+P85(f341(f341(f341(f110(f864(x68361,a850)),x68362),x68363),x68364)) % 19.23/19.04 [6858]E(f341(f341(f158(x68581),f341(f341(f132(x68581),x68582),x68583)),x68584),f341(f341(f158(x68581),x68582),x68584))+~P85(f341(f341(f242(a857),x68584),f341(f186(f858(x68581)),x68582))) % 19.23/19.04 [6868]E(f341(f341(f3(f864(x68681,a850)),f341(f341(f311(x68681),x68682),x68683)),x68684),f341(f341(f3(f864(x68681,a850)),x68683),x68684))+~P85(f341(f341(f343(x68681),x68682),x68684)) % 19.23/19.04 [6909]~E(f136(a857,f341(f303(a857,x69091),x69092)),f341(f341(f146(a857),x69094),x69093))+E(f136(a857,f341(f303(a857,f341(f341(f89(a857),x69091),f87(a857))),x69092)),x69093) % 19.23/19.04 [6977]E(x69771,f2(a857))+E(f341(f341(f146(x69772),x69773),f341(f341(f164(x69772),f341(f341(f3(a857),x69771),f87(a857))),x69774)),f341(f341(f164(x69772),x69771),f341(f341(f146(x69772),x69773),x69774))) % 19.23/19.04 [7081]E(f341(f341(f158(x70811),x70812),f341(f341(f3(a857),x70813),f341(f186(f858(x70811)),x70814))),f341(f341(f158(x70811),f341(f341(f132(x70811),x70814),x70812)),x70813))+P85(f341(f341(f242(a857),x70813),f341(f186(f858(x70811)),x70814))) % 19.23/19.04 [7108]E(f341(f341(f111(f864(x71081,a850)),x71082),f341(f341(f311(x71081),x71083),x71084)),f341(f341(f311(x71081),x71083),f341(f341(f111(f864(x71081,a850)),x71082),x71084)))+~P85(f341(f341(f343(x71081),x71083),x71082)) % 19.23/19.04 [7142]E(f341(f341(f158(x71421),f341(f341(f154(x71421,x71422),x71423),x71424)),x71423),x71424)+~P85(f341(f341(f242(a857),x71423),f341(f186(f858(x71421)),x71422))) % 19.23/19.04 [7163]E(x71631,f185(f864(x71632,a850)))+E(f341(f312(f863(x71633,x71632),x71633,f249(x71633,x71632)),f341(f341(f257(x71633,x71632),x71634),f341(f18(f864(x71632,a850),x71633),x71631))),x71634) % 19.23/19.04 [7164]E(x71641,f185(f864(x71642,a850)))+E(f341(f312(f863(x71642,x71643),x71643,f259(x71642,x71643)),f341(f341(f257(x71642,x71643),x71641),f341(f18(f864(x71643,a850),x71642),x71644))),x71644) % 19.23/19.04 [7248]E(f341(f341(f3(f864(x72481,a850)),f341(f341(f311(x72481),x72482),x72483)),x72484),f341(f341(f311(x72481),x72482),f341(f341(f3(f864(x72481,a850)),x72483),x72484)))+P85(f341(f341(f343(x72481),x72482),x72484)) % 19.23/19.04 [7289]~E(x72894,f185(f864(x72892,a850)))+E(f341(f312(f863(x72891,x72892),x72891,f249(x72891,x72892)),f341(f341(f257(x72891,x72892),x72893),f341(f18(f864(x72892,a850),x72891),x72894))),f185(f864(x72891,a850))) % 19.23/19.04 [7290]~E(x72903,f185(f864(x72901,a850)))+E(f341(f312(f863(x72901,x72902),x72902,f259(x72901,x72902)),f341(f341(f257(x72901,x72902),x72903),f341(f18(f864(x72902,a850),x72901),x72904))),f185(f864(x72902,a850))) % 19.23/19.04 [7349]~P85(f341(f341(f343(x73491),x73492),x73494))+P85(f341(f341(f343(x73491),x73492),f341(f341(f110(f864(x73491,a850)),x73493),x73494))) % 19.23/19.04 [7352]~P85(f341(f341(f343(x73521),x73522),x73523))+P85(f341(f341(f343(x73521),x73522),f341(f341(f110(f864(x73521,a850)),x73523),x73524))) % 19.23/19.04 [7374]E(f341(f341(f111(f864(x73741,a850)),f341(f341(f311(x73741),x73742),x73743)),x73744),f341(f341(f311(x73741),x73742),f341(f341(f111(f864(x73741,a850)),x73743),x73744)))+~P85(f341(f341(f343(x73741),x73742),x73744)) % 19.23/19.04 [7652]P85(f341(x76521,x76522))+~P85(f341(f341(f341(f111(f864(x76523,a850)),x76524),x76521),x76522)) % 19.23/19.04 [7653]P85(f341(x76531,x76532))+~P85(f341(f341(f341(f111(f864(x76533,a850)),x76531),x76534),x76532)) % 19.23/19.04 [7656]E(f341(f341(f8(x76561,a857),x76562),f341(f341(f3(f864(x76561,a850)),x76563),f341(f341(f311(x76561),x76564),f185(f864(x76561,a850))))),f341(f341(f8(x76561,a857),x76562),x76563))+P85(f341(f341(f343(x76561),x76564),x76563)) % 19.23/19.04 [7662]~P68(x76621)+E(f341(f160(x76621),f341(f341(f149(a857,x76621),x76622),f136(a857,f341(f303(a857,x76623),x76624)))),f341(f341(f8(a857,x76621),x76622),f341(f163(a857),f136(a857,f341(f303(a857,x76623),x76624))))) % 19.23/19.04 [7663]~P68(x76631)+E(f341(f341(f8(a857,x76631),x76632),f341(f163(a857),f136(a857,f341(f303(a857,x76633),x76634)))),f341(f160(x76631),f341(f341(f149(a857,x76631),x76632),f136(a857,f341(f303(a857,x76633),x76634))))) % 19.23/19.04 [7777]~E(x77773,x77774)+P85(f341(f72(x77771,x77772,f341(f341(f311(x77771),x77773),f185(f864(x77771,a850)))),x77774)) % 19.23/19.04 [7873]P85(f341(f341(f343(x78731),x78732),f341(f163(x78731),x78733)))+~P85(f341(f341(f343(x78731),x78732),f341(f163(x78731),f341(f341(f164(x78731),x78734),x78733)))) % 19.23/19.04 [7874]P85(f341(f341(f343(x78741),x78742),f341(f163(x78741),x78743)))+~P85(f341(f341(f343(x78741),x78742),f341(f163(x78741),f341(f341(f135(x78741),x78744),x78743)))) % 19.23/19.04 [7948]P85(f341(f341(f343(x79481),x79482),x79483))+~P85(f341(f341(f343(x79481),x79482),f341(f341(f3(f864(x79481,a850)),x79483),x79484))) % 19.23/19.04 [7950]P85(f341(f341(f343(x79501),x79502),x79503))+~P85(f341(f341(f343(x79501),x79502),f341(f341(f111(f864(x79501,a850)),x79504),x79503))) % 19.23/19.04 [7953]P85(f341(f341(f343(x79531),x79532),x79533))+~P85(f341(f341(f343(x79531),x79532),f341(f341(f111(f864(x79531,a850)),x79533),x79534))) % 19.23/19.04 [7970]E(f341(f341(f132(x79701),f341(f341(f164(x79701),x79702),x79703)),f341(f341(f146(x79701),x79704),f341(f341(f135(x79701),f341(a121,x79702)),x79703))),f341(f341(f154(x79701,x79703),x79702),x79704))+~P85(f341(f341(f242(a857),x79702),f341(f186(f858(x79701)),x79703))) % 19.23/19.04 [7993]P85(f341(f341(f343(x79931),x79932),x79933))+~P85(f341(f341(f241(f864(x79931,a850)),f341(f341(f311(x79931),x79932),x79934)),x79933)) % 19.23/19.04 [8022]~P85(f341(f341(f343(x80221),x80222),x80223))+~P85(f341(f341(f343(x80221),x80222),f341(f341(f3(f864(x80221,a850)),x80224),x80223))) % 19.23/19.04 [8055]~P85(f341(f341(f242(a857),x80554),f341(f186(f858(x80551)),x80553)))+P85(f341(f341(f343(x80551),x80552),f341(f163(x80551),f341(f341(f154(x80551,x80553),x80554),x80552)))) % 19.23/19.04 [8105]E(f341(f341(f158(x81051),f341(f341(f135(x81051),x81052),x81053)),x81054),f341(f341(f158(x81051),x81053),f341(f341(f89(a857),x81052),x81054)))+~P85(f341(f341(f241(a857),f341(f341(f89(a857),x81052),x81054)),f341(f186(f858(x81051)),x81053))) % 19.23/19.04 [8114]~P112(x81142)+E(f341(f341(f8(x81141,x81142),f341(f341(f10(a857,x81142,x81141),f109(x81142)),x81143)),x81144),f341(f109(x81142),f341(f341(f8(x81141,a857),x81143),x81144))) % 19.23/19.04 [8115]~P136(x81152)+E(f341(f341(f8(x81151,x81152),f341(f341(f10(a1,x81152,x81151),f112(x81152)),x81153)),x81154),f341(f112(x81152),f341(f341(f8(x81151,a1),x81153),x81154))) % 19.23/19.04 [8166]~P62(x81662)+E(f341(f341(f11(x81661,x81662),f341(f341(f10(x81662,x81662,x81661),f84(x81662)),x81663)),x81664),f341(f84(x81662),f341(f341(f11(x81661,x81662),x81663),x81664))) % 19.23/19.04 [8167]~P3(x81672)+E(f341(f341(f8(x81671,x81672),f341(f341(f10(x81672,x81672,x81671),f88(x81672)),x81673)),x81674),f341(f88(x81672),f341(f341(f8(x81671,x81672),x81673),x81674))) % 19.23/19.04 [8169]E(f341(f341(f8(x81691,a857),x81692),f341(f341(f3(f864(x81691,a850)),x81693),f341(f341(f311(x81691),x81694),f185(f864(x81691,a850))))),f341(f341(f3(a857),f341(f341(f8(x81691,a857),x81692),x81693)),f341(x81692,x81694)))+~P85(f341(f341(f343(x81691),x81694),x81693)) % 19.23/19.04 [8188]P85(f341(f341(f241(f864(x81881,a850)),x81882),x81883))+~P85(f341(f341(f241(f864(x81881,a850)),f341(f341(f311(x81881),x81884),x81882)),x81883)) % 19.23/19.04 [8397]P35(x83971,x83972)+~P35(x83971,f341(f341(f311(f863(x83971,x83971)),f341(f341(f250(x83971,x83971),x83973),x83974)),x83972)) % 19.23/19.04 [8398]P55(x83981,x83982)+~P55(x83981,f341(f341(f311(f863(x83981,x83981)),f341(f341(f250(x83981,x83981),x83983),x83984)),x83982)) % 19.23/19.04 [8406]~P101(x84061)+E(f341(f341(f144(x84061,x84061,f7(x84061)),x84062),f341(f341(f144(x84061,x84061,f7(x84061)),x84063),x84064)),f341(f341(f144(x84061,x84061,f7(x84061)),x84063),f341(f341(f144(x84061,x84061,f7(x84061)),x84062),x84064))) % 19.23/19.04 [8416]E(x84161,x84162)+~P85(f341(f72(x84163,x84164,f341(f341(f311(x84163),x84161),f185(f864(x84163,a850)))),x84162)) % 19.23/19.04 [8420]E(f341(f171(x84201,x84202,x84203),x84204),f188(x84202))+P85(f341(f341(f343(x84201),x84204),f341(f312(f863(x84201,x84202),x84201,f249(x84201,x84202)),f341(f163(f863(x84201,x84202)),x84203)))) % 19.23/19.04 [8426]E(f341(f341(f132(x84261),f341(f341(f164(x84261),x84262),x84263)),f341(f341(f164(x84261),x84264),f341(f341(f135(x84261),x84262),x84263))),f341(f341(f164(x84261),f341(f341(f89(a857),x84262),x84264)),x84263))+~P85(f341(f341(f241(a857),f341(f341(f89(a857),x84262),x84264)),f341(f186(f858(x84261)),x84263))) % 19.23/19.04 [8469]P85(f341(f71(x84691),x84692))+~E(x84692,f341(f312(a857,x84691,x84693),f341(f265(a857),f341(f341(f9(a857,a857,a850),f242(a857)),x84694)))) % 19.23/19.04 [8489]~P83(x84891)+E(f341(f138(x84891,x84891,f89(x84891),f341(f341(f89(x84891),x84892),x84893)),x84894),f341(f341(f89(x84891),x84892),f341(f138(x84891,x84891,f89(x84891),x84893),x84894))) % 19.23/19.04 [8521]P85(f341(f341(f241(f864(x85211,a850)),f341(f270(x85211,x85212),x85213)),f341(f270(x85211,x85212),x85214)))+~P85(f341(f341(f241(f864(f863(x85211,x85212),a850)),x85213),x85214)) % 19.23/19.04 [8532]~P85(f341(f341(f241(a857),x85322),x85324))+P85(f341(f341(f241(f864(x85321,a850)),f341(f163(x85321),f341(f341(f164(x85321),x85322),x85323))),f341(f163(x85321),f341(f341(f164(x85321),x85324),x85323)))) % 19.23/19.04 [8533]~P85(f341(f341(f241(a857),x85334),x85332))+P85(f341(f341(f241(f864(x85331,a850)),f341(f163(x85331),f341(f341(f135(x85331),x85332),x85333))),f341(f163(x85331),f341(f341(f135(x85331),x85334),x85333)))) % 19.23/19.04 [8576]~P85(f341(f71(x85761),f341(f341(f3(f864(x85761,a850)),x85762),x85764)))+P85(f341(f71(x85761),f341(f341(f3(f864(x85761,a850)),x85762),f341(f341(f311(x85761),x85763),x85764)))) % 19.23/19.04 [8611]P85(f341(f341(f343(f863(x86111,x86111)),x86112),f309(x86111,x86113)))+~P85(f341(f341(f343(f863(x86111,x86111)),x86112),f341(f341(f179(f863(x86111,x86111),a850),x86114),x86113))) % 19.23/19.04 [8686]~P85(f341(f71(x86861),f341(f341(f3(f864(x86861,a850)),x86862),f341(f341(f311(x86861),x86864),x86863))))+P85(f341(f71(x86861),f341(f341(f3(f864(x86861,a850)),x86862),x86863))) % 19.23/19.04 [8832]~E(f341(f171(x88321,x88322,x88323),x88324),f188(x88322))+~P85(f341(f341(f343(x88321),x88324),f341(f312(f863(x88321,x88322),x88321,f249(x88321,x88322)),f341(f163(f863(x88321,x88322)),x88323)))) % 19.23/19.04 [8868]~P101(x88681)+P85(f341(f341(f241(x88681),f341(f341(f240(x88681),x88682),f341(f341(f245(x88681),x88683),x88684))),f341(f341(f245(x88681),f341(f341(f240(x88681),x88682),x88683)),f341(f341(f240(x88681),x88682),x88684)))) % 19.23/19.04 [8869]~P95(x88691)+P85(f341(f341(f241(x88691),f341(f341(f110(x88691),x88692),f341(f341(f111(x88691),x88693),x88694))),f341(f341(f111(x88691),f341(f341(f110(x88691),x88692),x88693)),f341(f341(f110(x88691),x88692),x88694)))) % 19.23/19.04 [9012]E(x90121,x90122)+~P85(f341(f341(f343(f863(x90123,x90123)),f341(f341(f250(x90123,x90123),x90121),x90122)),f341(f163(f863(x90123,x90123)),f341(f341(f172(x90123,x90123),x90124),x90124)))) % 19.23/19.04 [9044]~P85(f341(f341(f343(f863(x90441,x90441)),f341(f341(f250(x90441,x90441),x90443),x90442)),f309(x90441,x90444)))+~P35(x90441,f341(f341(f311(f863(x90441,x90441)),f341(f341(f250(x90441,x90441),x90442),x90443)),x90444)) % 19.23/19.04 [9045]~P85(f341(f341(f343(f863(x90451,x90451)),f341(f341(f250(x90451,x90451),x90453),x90452)),f309(x90451,x90454)))+~P55(x90451,f341(f341(f311(f863(x90451,x90451)),f341(f341(f250(x90451,x90451),x90452),x90453)),x90454)) % 19.23/19.04 [9090]~P101(x90901)+P85(f341(f341(f241(x90901),f341(f341(f240(x90901),f341(f341(f245(x90901),x90902),x90903)),f341(f341(f245(x90901),x90902),x90904))),f341(f341(f245(x90901),x90902),f341(f341(f240(x90901),x90903),x90904)))) % 19.23/19.04 [9091]~P95(x90911)+P85(f341(f341(f241(x90911),f341(f341(f110(x90911),f341(f341(f111(x90911),x90912),x90913)),f341(f341(f111(x90911),x90912),x90914))),f341(f341(f111(x90911),x90912),f341(f341(f110(x90911),x90913),x90914)))) % 19.23/19.04 [9154]~E(f341(f312(x91542,x91541,x91543),f248(f864(x91542,a850))),f248(f864(x91541,a850)))+P85(f341(f341(f241(f864(x91541,a850)),f341(f88(f864(x91541,a850)),f341(f312(x91542,x91541,x91543),x91544))),f341(f312(x91542,x91541,x91543),f341(f88(f864(x91542,a850)),x91544)))) % 19.23/19.04 [9454]P85(f341(f341(f343(f863(x94541,x94541)),f341(f341(f250(x94541,x94541),x94542),x94543)),f341(f287(x94541,x94541),f341(f341(f290(x94541,x94541,x94541),x94544),f309(x94541,x94544)))))+~P85(f341(f341(f343(f863(x94541,x94541)),f341(f341(f250(x94541,x94541),x94542),x94543)),f341(f341(f290(x94541,x94541,x94541),f341(f287(x94541,x94541),x94544)),f309(x94541,f341(f287(x94541,x94541),x94544))))) % 19.23/19.04 [9455]~P85(f341(f341(f343(f863(x94551,x94551)),f341(f341(f250(x94551,x94551),x94552),x94553)),f341(f287(x94551,x94551),f341(f341(f290(x94551,x94551,x94551),x94554),f309(x94551,x94554)))))+P85(f341(f341(f343(f863(x94551,x94551)),f341(f341(f250(x94551,x94551),x94552),x94553)),f341(f341(f290(x94551,x94551,x94551),f341(f287(x94551,x94551),x94554)),f309(x94551,f341(f287(x94551,x94551),x94554))))) % 19.23/19.04 [9481]~P85(f341(f341(f343(x94812),x94814),f341(f268(x94811,x94812),x94813)))+P85(f341(f341(f343(f863(x94811,x94812)),f341(f341(f250(x94811,x94812),f593(x94813,x94811,x94814,x94812)),x94814)),x94813)) % 19.23/19.04 [9482]~P85(f341(f341(f343(x94822),x94824),f341(f268(x94821,x94822),x94823)))+P85(f341(f341(f343(f863(x94821,x94822)),f341(f341(f250(x94821,x94822),f594(x94823,x94821,x94824,x94822)),x94824)),x94823)) % 19.23/19.04 [9502]~P85(f341(f341(f343(x95021),x95024),f341(f341(f110(f864(x95021,a850)),x95022),x95023)))+P85(f341(f341(f341(f110(f864(x95021,a850)),f341(f341(f9(x95021,f864(x95021,a850),a850),f343(x95021)),x95022)),f341(f341(f9(x95021,f864(x95021,a850),a850),f343(x95021)),x95023)),x95024)) % 19.23/19.04 [9503]~P85(f341(f341(f343(x95031),x95034),f341(f341(f111(f864(x95031,a850)),x95032),x95033)))+P85(f341(f341(f341(f111(f864(x95031,a850)),f341(f341(f9(x95031,f864(x95031,a850),a850),f343(x95031)),x95032)),f341(f341(f9(x95031,f864(x95031,a850),a850),f343(x95031)),x95033)),x95034)) % 19.23/19.04 [9579]~P85(f341(f341(f343(f863(x95791,x95791)),f341(f341(f250(x95791,x95791),x95794),x95793)),f341(f341(f290(x95791,x95791,x95791),x95792),f309(x95791,x95792))))+P85(f341(f341(f343(f863(x95791,x95791)),f341(f341(f250(x95791,x95791),f668(x95792,x95793,x95794,x95791)),x95793)),x95792)) % 19.23/19.04 [9619]P85(f341(f341(f343(x96191),x96192),f341(f341(f110(f864(x96191,a850)),x96193),x96194)))+~P85(f341(f341(f341(f110(f864(x96191,a850)),f341(f341(f9(x96191,f864(x96191,a850),a850),f343(x96191)),x96193)),f341(f341(f9(x96191,f864(x96191,a850),a850),f343(x96191)),x96194)),x96192)) % 19.23/19.04 [9620]P85(f341(f341(f343(x96201),x96202),f341(f341(f111(f864(x96201,a850)),x96203),x96204)))+~P85(f341(f341(f341(f111(f864(x96201,a850)),f341(f341(f9(x96201,f864(x96201,a850),a850),f343(x96201)),x96203)),f341(f341(f9(x96201,f864(x96201,a850),a850),f343(x96201)),x96204)),x96202)) % 19.23/19.04 [9899]P33(x98991,f341(f341(f9(x98991,f864(f863(x98991,x98991),a850),f864(x98991,a850)),f341(f341(f10(f864(x98991,f864(f864(f863(x98991,x98991),a850),a850)),f864(f864(f863(x98991,x98991),a850),f864(x98991,a850)),x98991),f9(x98991,f864(f863(x98991,x98991),a850),a850)),f341(f341(f10(f864(x98991,f863(x98991,x98991)),f864(x98991,f864(f864(f863(x98991,x98991),a850),a850)),x98991),f341(f10(f863(x98991,x98991),f864(f864(f863(x98991,x98991),a850),a850),x98991),f343(f863(x98991,x98991)))),f250(x98991,x98991)))),x98992),x98993,x98994)+~P85(f341(f341(f343(f863(f858(x98991),f858(x98991))),f341(f341(f250(f858(x98991),f858(x98991)),x98993),x98994)),f153(x98991,x98992))) % 19.23/19.04 [9903]P56(x99031,f341(f341(f9(x99031,f864(f863(x99031,x99031),a850),f864(x99031,a850)),f341(f341(f10(f864(x99031,f864(f864(f863(x99031,x99031),a850),a850)),f864(f864(f863(x99031,x99031),a850),f864(x99031,a850)),x99031),f9(x99031,f864(f863(x99031,x99031),a850),a850)),f341(f341(f10(f864(x99031,f863(x99031,x99031)),f864(x99031,f864(f864(f863(x99031,x99031),a850),a850)),x99031),f341(f10(f863(x99031,x99031),f864(f864(f863(x99031,x99031),a850),a850),x99031),f343(f863(x99031,x99031)))),f250(x99031,x99031)))),x99032),x99033,x99034)+~P85(f341(f341(f343(f863(f864(x99031,a850),f864(x99031,a850))),f341(f341(f250(f864(x99031,a850),f864(x99031,a850)),x99033),x99034)),f334(x99031,x99032))) % 19.23/19.04 [9930]E(x99301,x99302)+~E(f341(f341(f9(x99303,f864(f863(x99303,x99304),a850),f864(x99304,a850)),f341(f341(f10(f864(x99304,f864(f864(f863(x99303,x99304),a850),a850)),f864(f864(f863(x99303,x99304),a850),f864(x99304,a850)),x99303),f9(x99304,f864(f863(x99303,x99304),a850),a850)),f341(f341(f10(f864(x99304,f863(x99303,x99304)),f864(x99304,f864(f864(f863(x99303,x99304),a850),a850)),x99303),f341(f10(f863(x99303,x99304),f864(f864(f863(x99303,x99304),a850),a850),x99304),f343(f863(x99303,x99304)))),f250(x99303,x99304)))),x99301),f341(f341(f9(x99303,f864(f863(x99303,x99304),a850),f864(x99304,a850)),f341(f341(f10(f864(x99304,f864(f864(f863(x99303,x99304),a850),a850)),f864(f864(f863(x99303,x99304),a850),f864(x99304,a850)),x99303),f9(x99304,f864(f863(x99303,x99304),a850),a850)),f341(f341(f10(f864(x99304,f863(x99303,x99304)),f864(x99304,f864(f864(f863(x99303,x99304),a850),a850)),x99303),f341(f10(f863(x99303,x99304),f864(f864(f863(x99303,x99304),a850),a850),x99304),f343(f863(x99303,x99304)))),f250(x99303,x99304)))),x99302)) % 19.23/19.04 [9933]~P33(x99331,f341(f341(f9(x99331,f864(f863(x99331,x99331),a850),f864(x99331,a850)),f341(f341(f10(f864(x99331,f864(f864(f863(x99331,x99331),a850),a850)),f864(f864(f863(x99331,x99331),a850),f864(x99331,a850)),x99331),f9(x99331,f864(f863(x99331,x99331),a850),a850)),f341(f341(f10(f864(x99331,f863(x99331,x99331)),f864(x99331,f864(f864(f863(x99331,x99331),a850),a850)),x99331),f341(f10(f863(x99331,x99331),f864(f864(f863(x99331,x99331),a850),a850),x99331),f343(f863(x99331,x99331)))),f250(x99331,x99331)))),x99334),x99332,x99333)+P85(f341(f341(f343(f863(f858(x99331),f858(x99331))),f341(f341(f250(f858(x99331),f858(x99331)),x99332),x99333)),f153(x99331,x99334))) % 19.23/19.04 [9934]~P56(x99341,f341(f341(f9(x99341,f864(f863(x99341,x99341),a850),f864(x99341,a850)),f341(f341(f10(f864(x99341,f864(f864(f863(x99341,x99341),a850),a850)),f864(f864(f863(x99341,x99341),a850),f864(x99341,a850)),x99341),f9(x99341,f864(f863(x99341,x99341),a850),a850)),f341(f341(f10(f864(x99341,f863(x99341,x99341)),f864(x99341,f864(f864(f863(x99341,x99341),a850),a850)),x99341),f341(f10(f863(x99341,x99341),f864(f864(f863(x99341,x99341),a850),a850),x99341),f343(f863(x99341,x99341)))),f250(x99341,x99341)))),x99344),x99342,x99343)+P85(f341(f341(f343(f863(f864(x99341,a850),f864(x99341,a850))),f341(f341(f250(f864(x99341,a850),f864(x99341,a850)),x99342),x99343)),f334(x99341,x99344))) % 19.23/19.04 [7422]~P89(x74221)+E(f341(f341(f89(x74221),f341(f113(x74221),x74222)),f341(f341(f89(x74221),f341(f113(x74221),x74223)),x74224)),f341(f341(f89(x74221),f341(f113(x74221),f341(f341(f89(a1),x74222),x74223))),x74224)) % 19.23/19.04 [7423]~P89(x74231)+E(f341(f341(f89(x74231),f341(f113(x74231),x74232)),f341(f341(f3(x74231),f341(f113(x74231),x74233)),x74234)),f341(f341(f3(x74231),f341(f113(x74231),f341(f341(f89(a1),x74232),x74233))),x74234)) % 19.23/19.04 [7424]~P89(x74241)+E(f341(f341(f90(x74241),f341(f113(x74241),x74242)),f341(f341(f90(x74241),f341(f113(x74241),x74243)),x74244)),f341(f341(f90(x74241),f341(f113(x74241),f341(f341(f90(a1),x74242),x74243))),x74244)) % 19.23/19.04 [7470]~P112(x74701)+E(f341(f160(x74701),f341(f341(f149(x74702,x74701),f341(f18(x74701,x74702),x74703)),x74704)),f341(f341(f90(x74701),f341(f109(x74701),f341(f186(f858(x74702)),x74704))),x74703)) % 19.23/19.04 [7706]E(f341(f274(x77061,f341(f341(f146(f863(a108,x77061)),x77062),x77063)),x77064),f341(f259(a108,x77061),x77062))+~P85(f341(f341(f242(a108),x77064),f341(f249(a108,x77061),x77062))) % 19.23/19.04 [7754]~P89(x77541)+E(f341(f341(f89(x77541),f341(f113(x77541),x77542)),f341(f341(f3(x77541),x77543),f341(f113(x77541),x77544))),f341(f341(f89(x77541),f341(f113(x77541),f341(f341(f89(a1),x77542),f341(f88(a1),x77544)))),x77543)) % 19.23/19.04 [7885]E(f341(f274(x78851,x78852),f341(f341(f3(a108),x78853),f341(f249(a108,x78851),x78854))),f341(f274(x78851,f341(f341(f146(f863(a108,x78851)),x78854),x78852)),x78853))+P85(f341(f341(f242(a108),x78853),f341(f249(a108,x78851),x78854))) % 19.23/19.04 [8314]~P85(f341(f341(f343(x83141),x83142),f341(f163(x83141),f123(x83141,x83144))))+P85(f341(f341(f343(x83141),x83142),f341(f163(x83141),f123(x83141,f341(f341(f132(x83141),x83143),x83144))))) % 19.23/19.04 [8315]~P85(f341(f341(f343(x83151),x83152),f341(f163(x83151),f123(x83151,x83153))))+P85(f341(f341(f343(x83151),x83152),f341(f163(x83151),f123(x83151,f341(f341(f132(x83151),x83153),x83154))))) % 19.23/19.04 [8338]E(f341(f341(f110(f864(x83381,a850)),f341(f341(f111(f864(x83381,a850)),x83382),x83383)),x83384),f341(f341(f111(f864(x83381,a850)),x83382),f341(f341(f110(f864(x83381,a850)),x83383),x83384)))+~P85(f341(f341(f241(f864(x83381,a850)),x83384),x83382)) % 19.23/19.04 [8624]~E(f341(f341(f110(f864(x86241,a850)),f341(f341(f111(f864(x86241,a850)),x86243),x86244)),x86242),f341(f341(f111(f864(x86241,a850)),x86243),f341(f341(f110(f864(x86241,a850)),x86244),x86242)))+P85(f341(f341(f241(f864(x86241,a850)),x86242),x86243)) % 19.23/19.04 [8875]~P85(f341(f341(f241(f864(x88751,a850)),x88752),f341(f341(f110(f864(x88751,a850)),x88753),x88754)))+P85(f341(f341(f241(f864(x88751,a850)),f341(f341(f3(f864(x88751,a850)),x88752),x88753)),x88754)) % 19.23/19.04 [8993]P85(f341(f341(f241(f864(x89931,a850)),x89932),f341(f341(f110(f864(x89931,a850)),x89933),x89934)))+~P85(f341(f341(f241(f864(x89931,a850)),f341(f341(f3(f864(x89931,a850)),x89932),x89933)),x89934)) % 19.23/19.04 [9072]~P79(x90721)+E(f341(f84(x90721),f341(f341(f8(x90722,x90721),f341(f341(f10(x90721,x90721,x90722),f84(x90721)),x90723)),x90724)),f341(f341(f8(x90722,x90721),f341(f341(f10(x90721,x90721,x90722),f84(x90721)),x90723)),x90724)) % 19.23/19.04 [9215]~P79(x92151)+P85(f341(f341(f241(x92151),f2(x92151)),f341(f341(f8(x92152,x92151),f341(f341(f10(x92151,x92151,x92152),f84(x92151)),x92153)),x92154))) % 19.23/19.04 [9218]~P3(x92181)+E(f341(f160(x92181),f341(f341(f149(x92182,x92181),f341(f82(x92181,x92181,x92182,f88(x92181)),x92183)),x92184)),f341(f88(x92181),f341(f160(x92181),f341(f341(f149(x92182,x92181),x92183),x92184)))) % 19.23/19.04 [9355]~P79(x93551)+P85(f341(f341(f241(x93551),f341(f84(x93551),f341(f341(f8(x93552,x93551),x93553),x93554))),f341(f341(f8(x93552,x93551),f341(f341(f10(x93551,x93551,x93552),f84(x93551)),x93553)),x93554))) % 19.23/19.04 [9382]~E(f341(f341(f89(a857),x93821),x93824),f341(f341(f89(a857),x93823),x93822))+P85(f341(f341(f343(f863(f863(a857,a857),f863(a857,a857))),f341(f341(f250(f863(a857,a857),f863(a857,a857)),f341(f341(f250(a857,a857),x93821),x93822)),f341(f341(f250(a857,a857),x93823),x93824))),a118)) % 19.23/19.04 [9383]~P85(f341(f341(f242(a857),x93831),x93833))+P85(f341(f341(f343(f863(f863(a857,a857),f863(a857,a857))),f341(f341(f250(f863(a857,a857),f863(a857,a857)),f341(f341(f250(a857,a857),x93831),x93832)),f341(f341(f250(a857,a857),x93833),x93834))),a47)) % 19.23/19.04 [9384]~P85(f341(f341(f242(a857),x93841),x93843))+P85(f341(f341(f343(f863(f863(a857,a857),f863(a857,a857))),f341(f341(f250(f863(a857,a857),f863(a857,a857)),f341(f341(f250(a857,a857),x93841),x93842)),f341(f341(f250(a857,a857),x93843),x93844))),a79)) % 19.23/19.04 [9525]E(f341(f341(f89(a857),x95251),x95252),f341(f341(f89(a857),x95253),x95254))+~P85(f341(f341(f343(f863(f863(a857,a857),f863(a857,a857))),f341(f341(f250(f863(a857,a857),f863(a857,a857)),f341(f341(f250(a857,a857),x95251),x95254)),f341(f341(f250(a857,a857),x95253),x95252))),a118)) % 19.23/19.04 [9572]~P85(f341(f341(f343(x95722),x95724),f341(f341(f54(x95721,f864(x95722,a850)),f248(f864(x95721,a850))),x95723)))+P85(f341(f341(f341(f54(x95721,f864(x95722,a850)),f248(f864(x95721,a850))),f341(f341(f10(f864(x95722,a850),f864(x95722,a850),x95721),f341(f9(x95722,f864(x95722,a850),a850),f343(x95722))),x95723)),x95724)) % 19.23/19.04 [9573]~P85(f341(f341(f343(x95732),x95734),f341(f341(f55(x95731,f864(x95732,a850)),f248(f864(x95731,a850))),x95733)))+P85(f341(f341(f341(f55(x95731,f864(x95732,a850)),f248(f864(x95731,a850))),f341(f341(f10(f864(x95732,a850),f864(x95732,a850),x95731),f341(f9(x95732,f864(x95732,a850),a850),f343(x95732))),x95733)),x95734)) % 19.23/19.04 [9644]~P85(f341(f64(x96441,x96442),f341(f341(f250(a1,a1),x96444),x96443)))+P85(f341(f64(f341(f88(a1),x96441),x96442),f341(f341(f250(a1,a1),f341(f341(f341(f105(a1),f341(f341(a338,x96443),f2(a1))),f341(f88(a1),x96444)),f341(f341(f3(a1),f341(f88(a1),x96444)),f87(a1)))),f341(f341(f341(f105(a1),f341(f341(a338,x96443),f2(a1))),f2(a1)),f341(f341(f3(a1),x96442),x96443))))) % 19.23/19.04 [9653]P85(f341(f341(f343(x96531),x96532),f341(f341(f54(x96533,f864(x96531,a850)),f248(f864(x96533,a850))),x96534)))+~P85(f341(f341(f341(f54(x96533,f864(x96531,a850)),f248(f864(x96533,a850))),f341(f341(f10(f864(x96531,a850),f864(x96531,a850),x96533),f341(f9(x96531,f864(x96531,a850),a850),f343(x96531))),x96534)),x96532)) % 19.23/19.04 [9654]P85(f341(f341(f343(x96541),x96542),f341(f341(f55(x96543,f864(x96541,a850)),f248(f864(x96543,a850))),x96544)))+~P85(f341(f341(f341(f55(x96543,f864(x96541,a850)),f248(f864(x96543,a850))),f341(f341(f10(f864(x96541,a850),f864(x96541,a850),x96543),f341(f9(x96541,f864(x96541,a850),a850),f343(x96541))),x96544)),x96542)) % 19.23/19.04 [9665]E(f341(f341(f54(a857,f864(x96651,a850)),f248(f864(a857,a850))),x96652),f341(f341(f54(a857,f864(x96651,a850)),f248(f864(a857,a850))),x96653))+~E(f341(f341(f54(a857,f864(x96651,a850)),f341(f303(a857,f2(a857)),f536(x96652,x96654,x96653,x96651))),x96653),f341(f341(f54(a857,f864(x96651,a850)),f341(f303(a857,f2(a857)),f341(f341(f89(a857),f536(x96652,x96654,x96653,x96651)),x96654))),x96652)) % 19.23/19.04 [9996]~P85(f341(f341(f241(f864(f863(x99961,x99962),a850)),x99963),x99964))+P85(f341(f341(f241(f864(x99961,f864(x99962,a850))),f341(f341(f9(x99961,f864(f863(x99961,x99962),a850),f864(x99962,a850)),f341(f341(f10(f864(x99962,f864(f864(f863(x99961,x99962),a850),a850)),f864(f864(f863(x99961,x99962),a850),f864(x99962,a850)),x99961),f9(x99962,f864(f863(x99961,x99962),a850),a850)),f341(f341(f10(f864(x99962,f863(x99961,x99962)),f864(x99962,f864(f864(f863(x99961,x99962),a850),a850)),x99961),f341(f10(f863(x99961,x99962),f864(f864(f863(x99961,x99962),a850),a850),x99962),f343(f863(x99961,x99962)))),f250(x99961,x99962)))),x99963)),f341(f341(f9(x99961,f864(f863(x99961,x99962),a850),f864(x99962,a850)),f341(f341(f10(f864(x99962,f864(f864(f863(x99961,x99962),a850),a850)),f864(f864(f863(x99961,x99962),a850),f864(x99962,a850)),x99961),f9(x99962,f864(f863(x99961,x99962),a850),a850)),f341(f341(f10(f864(x99962,f863(x99961,x99962)),f864(x99962,f864(f864(f863(x99961,x99962),a850),a850)),x99961),f341(f10(f863(x99961,x99962),f864(f864(f863(x99961,x99962),a850),a850),x99962),f343(f863(x99961,x99962)))),f250(x99961,x99962)))),x99964))) % 19.23/19.04 [10011]P85(f341(f341(f241(f864(f863(x100111,x100112),a850)),x100113),x100114))+~P85(f341(f341(f241(f864(x100111,f864(x100112,a850))),f341(f341(f9(x100111,f864(f863(x100111,x100112),a850),f864(x100112,a850)),f341(f341(f10(f864(x100112,f864(f864(f863(x100111,x100112),a850),a850)),f864(f864(f863(x100111,x100112),a850),f864(x100112,a850)),x100111),f9(x100112,f864(f863(x100111,x100112),a850),a850)),f341(f341(f10(f864(x100112,f863(x100111,x100112)),f864(x100112,f864(f864(f863(x100111,x100112),a850),a850)),x100111),f341(f10(f863(x100111,x100112),f864(f864(f863(x100111,x100112),a850),a850),x100112),f343(f863(x100111,x100112)))),f250(x100111,x100112)))),x100113)),f341(f341(f9(x100111,f864(f863(x100111,x100112),a850),f864(x100112,a850)),f341(f341(f10(f864(x100112,f864(f864(f863(x100111,x100112),a850),a850)),f864(f864(f863(x100111,x100112),a850),f864(x100112,a850)),x100111),f9(x100112,f864(f863(x100111,x100112),a850),a850)),f341(f341(f10(f864(x100112,f863(x100111,x100112)),f864(x100112,f864(f864(f863(x100111,x100112),a850),a850)),x100111),f341(f10(f863(x100111,x100112),f864(f864(f863(x100111,x100112),a850),a850),x100112),f343(f863(x100111,x100112)))),f250(x100111,x100112)))),x100114))) % 19.23/19.04 [9116]~P85(f341(f341(f343(f863(x91161,x91161)),x91162),f309(x91161,x91164)))+P85(f341(f341(f343(f863(x91161,x91161)),x91162),f309(x91161,f341(f341(f110(f864(f863(x91161,x91161),a850)),x91163),x91164)))) % 19.23/19.04 [9117]~P85(f341(f341(f343(f863(x91171,x91171)),x91172),f309(x91171,x91173)))+P85(f341(f341(f343(f863(x91171,x91171)),x91172),f309(x91171,f341(f341(f110(f864(f863(x91171,x91171),a850)),x91173),x91174)))) % 19.23/19.04 [9445]~E(f341(f163(x94451),x94454),f174(x94451,x94452,x94453))+E(f171(x94451,x94452,f341(f341(f149(x94451,f863(x94451,x94452)),f341(f341(f20(x94451,x94452,f863(x94451,x94452)),f250(x94451,x94452)),f341(f341(f10(f861(x94452),x94452,x94451),f239(x94452)),x94453))),x94454)),x94453) % 19.23/19.04 [9746]~P85(f341(f341(f242(a857),f341(f341(f89(a857),x97461),x97464)),f341(f341(f89(a857),x97463),x97462)))+P85(f341(f341(f242(a1),f341(a98,f341(f286(f863(a857,a857),f863(a857,a857),a118),f341(f341(f311(f863(a857,a857)),f341(f341(f250(a857,a857),x97461),x97462)),f185(f864(f863(a857,a857),a850)))))),f341(a98,f341(f286(f863(a857,a857),f863(a857,a857),a118),f341(f341(f311(f863(a857,a857)),f341(f341(f250(a857,a857),x97463),x97464)),f185(f864(f863(a857,a857),a850))))))) % 19.23/19.04 [9747]~P85(f341(f341(f241(a857),f341(f341(f89(a857),x97471),x97474)),f341(f341(f89(a857),x97473),x97472)))+P85(f341(f341(f241(a1),f341(a98,f341(f286(f863(a857,a857),f863(a857,a857),a118),f341(f341(f311(f863(a857,a857)),f341(f341(f250(a857,a857),x97471),x97472)),f185(f864(f863(a857,a857),a850)))))),f341(a98,f341(f286(f863(a857,a857),f863(a857,a857),a118),f341(f341(f311(f863(a857,a857)),f341(f341(f250(a857,a857),x97473),x97474)),f185(f864(f863(a857,a857),a850))))))) % 19.23/19.04 [9838]P85(f341(f341(f242(a857),f341(f341(f89(a857),x98381),x98382)),f341(f341(f89(a857),x98383),x98384)))+~P85(f341(f341(f242(a1),f341(a98,f341(f286(f863(a857,a857),f863(a857,a857),a118),f341(f341(f311(f863(a857,a857)),f341(f341(f250(a857,a857),x98381),x98384)),f185(f864(f863(a857,a857),a850)))))),f341(a98,f341(f286(f863(a857,a857),f863(a857,a857),a118),f341(f341(f311(f863(a857,a857)),f341(f341(f250(a857,a857),x98383),x98382)),f185(f864(f863(a857,a857),a850))))))) % 19.23/19.04 [9839]P85(f341(f341(f241(a857),f341(f341(f89(a857),x98391),x98392)),f341(f341(f89(a857),x98393),x98394)))+~P85(f341(f341(f241(a1),f341(a98,f341(f286(f863(a857,a857),f863(a857,a857),a118),f341(f341(f311(f863(a857,a857)),f341(f341(f250(a857,a857),x98391),x98394)),f185(f864(f863(a857,a857),a850)))))),f341(a98,f341(f286(f863(a857,a857),f863(a857,a857),a118),f341(f341(f311(f863(a857,a857)),f341(f341(f250(a857,a857),x98393),x98392)),f185(f864(f863(a857,a857),a850))))))) % 19.23/19.04 [9885]P85(f341(f341(f241(f864(x98851,a850)),f341(f341(f54(a857,f864(x98851,a850)),f248(f864(a857,a850))),x98852)),f341(f341(f54(a857,f864(x98851,a850)),f248(f864(a857,a850))),x98853)))+~P85(f341(f341(f241(f864(x98851,a850)),f341(f341(f54(a857,f864(x98851,a850)),f341(f303(a857,f2(a857)),f537(x98853,x98854,x98852,x98851))),x98852)),f341(f341(f54(a857,f864(x98851,a850)),f341(f303(a857,f2(a857)),f341(f341(f89(a857),f537(x98853,x98854,x98852,x98851)),x98854))),x98853))) % 19.23/19.04 [9936]P85(f341(f341(f241(a108),x99364),f2(a108)))+E(f341(f341(f262(f863(a108,a108),f863(x99361,f864(a860,a849)),f863(a108,a108),f863(f864(a108,f864(a850,f861(f859(x99361)))),f863(a108,a108))),f341(x99362,x99363)),f341(f341(f10(f864(f864(a108,f864(a850,f861(f859(x99361)))),f864(f863(a108,a108),f863(f864(a108,f864(a850,f861(f859(x99361)))),f863(a108,a108)))),f864(f863(a108,a108),f863(f864(a108,f864(a850,f861(f859(x99361)))),f863(a108,a108))),f863(x99361,f864(a860,a849))),f341(f262(f863(a108,a108),f864(a108,f864(a850,f861(f859(x99361)))),f863(a108,a108),f863(f864(a108,f864(a850,f861(f859(x99361)))),f863(a108,a108))),f281(x99361,x99362,f341(f341(f3(a108),x99364),f87(a108)),x99363))),f341(f341(f10(f864(f864(a108,f864(a850,f861(f859(x99361)))),f864(a108,f864(a850,f861(f859(x99361))))),f864(f864(a108,f864(a850,f861(f859(x99361)))),f864(f863(a108,a108),f863(f864(a108,f864(a850,f861(f859(x99361)))),f863(a108,a108)))),f863(x99361,f864(a860,a849))),f341(f10(f864(a108,f864(a850,f861(f859(x99361)))),f864(f863(a108,a108),f863(f864(a108,f864(a850,f861(f859(x99361)))),f863(a108,a108))),f864(a108,f864(a850,f861(f859(x99361))))),f250(f864(a108,f864(a850,f861(f859(x99361)))),f863(a108,a108)))),f341(f341(f10(f864(a108,f864(a850,f861(f859(x99361)))),f864(f864(a108,f864(a850,f861(f859(x99361)))),f864(a108,f864(a850,f861(f859(x99361))))),f863(x99361,f864(a860,a849))),f59(x99361)),f341(f341(f10(x99361,f864(a108,f864(a850,f861(f859(x99361)))),f863(x99361,f864(a860,a849))),f57(x99361)),f249(x99361,f864(a860,a849))))))),f281(x99361,x99362,x99364,x99363)) % 19.23/19.04 [9987]~P85(f341(f341(f343(x99872),x99874),f341(f268(x99871,x99872),x99873)))+P85(f341(f256(x99871,x99872,f341(f341(f9(x99871,f864(f863(x99871,x99872),a850),f864(x99872,a850)),f341(f341(f10(f864(x99872,f864(f864(f863(x99871,x99872),a850),a850)),f864(f864(f863(x99871,x99872),a850),f864(x99872,a850)),x99871),f9(x99872,f864(f863(x99871,x99872),a850),a850)),f341(f341(f10(f864(x99872,f863(x99871,x99872)),f864(x99872,f864(f864(f863(x99871,x99872),a850),a850)),x99871),f341(f10(f863(x99871,x99872),f864(f864(f863(x99871,x99872),a850),a850),x99872),f343(f863(x99871,x99872)))),f250(x99871,x99872)))),x99873)),x99874)) % 19.23/19.04 [9988]~P85(f341(f341(f343(x99881),x99884),f341(f270(x99881,x99882),x99883)))+P85(f341(f255(x99881,x99882,f341(f341(f9(x99881,f864(f863(x99881,x99882),a850),f864(x99882,a850)),f341(f341(f10(f864(x99882,f864(f864(f863(x99881,x99882),a850),a850)),f864(f864(f863(x99881,x99882),a850),f864(x99882,a850)),x99881),f9(x99882,f864(f863(x99881,x99882),a850),a850)),f341(f341(f10(f864(x99882,f863(x99881,x99882)),f864(x99882,f864(f864(f863(x99881,x99882),a850),a850)),x99881),f341(f10(f863(x99881,x99882),f864(f864(f863(x99881,x99882),a850),a850),x99882),f343(f863(x99881,x99882)))),f250(x99881,x99882)))),x99883)),x99884)) % 19.23/19.04 [9999]P85(f341(f341(f343(x99991),x99992),f341(f268(x99993,x99991),x99994)))+~P85(f341(f256(x99993,x99991,f341(f341(f9(x99993,f864(f863(x99993,x99991),a850),f864(x99991,a850)),f341(f341(f10(f864(x99991,f864(f864(f863(x99993,x99991),a850),a850)),f864(f864(f863(x99993,x99991),a850),f864(x99991,a850)),x99993),f9(x99991,f864(f863(x99993,x99991),a850),a850)),f341(f341(f10(f864(x99991,f863(x99993,x99991)),f864(x99991,f864(f864(f863(x99993,x99991),a850),a850)),x99993),f341(f10(f863(x99993,x99991),f864(f864(f863(x99993,x99991),a850),a850),x99991),f343(f863(x99993,x99991)))),f250(x99993,x99991)))),x99994)),x99992)) % 19.23/19.04 [10000]P85(f341(f341(f343(x100001),x100002),f341(f270(x100001,x100003),x100004)))+~P85(f341(f255(x100001,x100003,f341(f341(f9(x100001,f864(f863(x100001,x100003),a850),f864(x100003,a850)),f341(f341(f10(f864(x100003,f864(f864(f863(x100001,x100003),a850),a850)),f864(f864(f863(x100001,x100003),a850),f864(x100003,a850)),x100001),f9(x100003,f864(f863(x100001,x100003),a850),a850)),f341(f341(f10(f864(x100003,f863(x100001,x100003)),f864(x100003,f864(f864(f863(x100001,x100003),a850),a850)),x100001),f341(f10(f863(x100001,x100003),f864(f864(f863(x100001,x100003),a850),a850),x100003),f343(f863(x100001,x100003)))),f250(x100001,x100003)))),x100004)),x100002)) % 19.23/19.04 [9760]~P86(x97601)+E(f341(f341(f90(x97601),f341(f341(f89(x97601),f87(x97601)),f87(x97601))),f341(f341(f8(a857,x97601),f341(f341(f10(x97601,x97601,a857),f341(f89(x97601),x97602)),f341(f341(f9(a857,x97601,x97601),f341(f341(f10(x97601,f864(x97601,x97601),a857),f90(x97601)),f109(x97601))),x97603))),f341(f266(a857),x97604))),f341(f341(f90(x97601),f341(f109(x97601),x97604)),f341(f341(f89(x97601),x97602),f341(f341(f89(x97601),x97602),f341(f341(f90(x97601),f341(f109(x97601),f341(f341(f3(a857),x97604),f87(a857)))),x97603))))) % 19.23/19.04 [9906]P85(f341(x99061,f592(x99062,x99063,x99064,x99061)))+P35(x99062,f341(f265(f863(x99062,x99062)),f341(f260(x99062,x99062,a850),f341(f341(f10(f864(x99062,a850),f864(x99062,a850),x99062),f341(f20(x99062,a850,a850),f341(f341(f10(a850,f864(a850,a850),x99062),a339),x99061))),f341(f341(f9(x99062,f864(x99062,x99062),f864(x99062,a850)),f341(f341(f10(f864(x99062,a850),f864(f864(x99062,x99062),f864(x99062,a850)),x99062),f10(x99062,a850,x99062)),a338)),x99063))))) % 19.23/19.04 [9918]~P85(f341(f341(f242(a857),f341(x99184,f341(x99183,f592(x99181,x99183,x99184,x99182)))),f341(x99184,f592(x99181,x99183,x99184,x99182))))+P35(x99181,f341(f265(f863(x99181,x99181)),f341(f260(x99181,x99181,a850),f341(f341(f10(f864(x99181,a850),f864(x99181,a850),x99181),f341(f20(x99181,a850,a850),f341(f341(f10(a850,f864(a850,a850),x99181),a339),x99182))),f341(f341(f9(x99181,f864(x99181,x99181),f864(x99181,a850)),f341(f341(f10(f864(x99181,a850),f864(f864(x99181,x99181),f864(x99181,a850)),x99181),f10(x99181,a850,x99181)),a338)),x99183))))) % 19.23/19.04 [10023]~P85(f341(f341(f343(f863(x100231,x100231)),f341(f341(f250(x100231,x100231),x100233),x100234)),f341(f341(f110(f864(f863(x100231,x100231),a850)),x100232),f309(x100231,f185(f864(f863(x100231,x100231),a850))))))+P85(f341(f341(f341(f341(f110(f864(x100231,f864(x100231,a850))),f341(f341(f9(x100231,f864(f863(x100231,x100231),a850),f864(x100231,a850)),f341(f341(f10(f864(x100231,f864(f864(f863(x100231,x100231),a850),a850)),f864(f864(f863(x100231,x100231),a850),f864(x100231,a850)),x100231),f9(x100231,f864(f863(x100231,x100231),a850),a850)),f341(f341(f10(f864(x100231,f863(x100231,x100231)),f864(x100231,f864(f864(f863(x100231,x100231),a850),a850)),x100231),f341(f10(f863(x100231,x100231),f864(f864(f863(x100231,x100231),a850),a850),x100231),f343(f863(x100231,x100231)))),f250(x100231,x100231)))),x100232)),a338),x100233),x100234)) % 19.23/19.04 [10031]P85(f341(f341(f343(f863(x100311,x100311)),f341(f341(f250(x100311,x100311),x100312),x100313)),f341(f341(f110(f864(f863(x100311,x100311),a850)),x100314),f309(x100311,f185(f864(f863(x100311,x100311),a850))))))+~P85(f341(f341(f341(f341(f110(f864(x100311,f864(x100311,a850))),f341(f341(f9(x100311,f864(f863(x100311,x100311),a850),f864(x100311,a850)),f341(f341(f10(f864(x100311,f864(f864(f863(x100311,x100311),a850),a850)),f864(f864(f863(x100311,x100311),a850),f864(x100311,a850)),x100311),f9(x100311,f864(f863(x100311,x100311),a850),a850)),f341(f341(f10(f864(x100311,f863(x100311,x100311)),f864(x100311,f864(f864(f863(x100311,x100311),a850),a850)),x100311),f341(f10(f863(x100311,x100311),f864(f864(f863(x100311,x100311),a850),a850),x100311),f343(f863(x100311,x100311)))),f250(x100311,x100311)))),x100314)),a338),x100312),x100313)) % 19.23/19.04 [9984]E(f341(f341(f146(f858(x99841)),f341(f341(f146(x99841),x99842),f341(f138(f858(x99841),f858(x99841),f132(x99841),f122(x99841)),f341(f341(f149(f858(x99841),f858(x99841)),f151(f858(x99841),x99841,f122(x99841),f341(f341(f10(f858(x99841),f864(f858(x99841),f858(x99841)),x99841),f18(f858(x99841),f858(x99841))),f341(f341(f9(x99841,f858(x99841),f858(x99841)),f146(x99841)),f122(x99841))))),x99843)))),f169(x99841,f341(f341(f146(f858(x99841)),x99844),f341(f138(f858(f858(x99841)),f858(f858(x99841)),f132(f858(x99841)),f122(f858(x99841))),f341(f341(f149(f858(x99841),f858(f858(x99841))),f151(f858(f858(x99841)),x99841,f122(f858(x99841)),f341(f18(f864(f858(x99841),f858(f858(x99841))),x99841),f341(f341(f9(f858(x99841),f858(f858(x99841)),f858(f858(x99841))),f146(f858(x99841))),f122(f858(x99841)))))),x99843))))),f169(x99841,f341(f341(f146(f858(x99841)),f341(f341(f146(x99841),x99842),x99844)),x99843)))+~P85(f341(f330(f858(f858(x99841)),f170(x99841)),f341(f341(f146(f858(x99841)),f341(f341(f146(x99841),x99842),x99844)),x99843))) % 19.23/19.04 [10022]~P85(f341(f71(x100222),f341(f265(x100222),x100224)))+P85(f341(f71(x100221),f341(f265(x100221),f341(f341(f10(f864(x100222,a850),a850,x100221),f96(x100222)),f341(f341(f9(x100221,f864(x100222,a850),f864(x100222,a850)),f341(f341(f10(f864(x100222,f864(a850,a850)),f864(f864(x100222,a850),f864(x100222,a850)),x100221),f20(x100222,a850,a850)),f341(f341(f10(f864(x100222,a850),f864(x100222,f864(a850,a850)),x100221),f341(f10(a850,f864(a850,a850),x100222),a339)),f341(f341(f9(x100221,f864(x100222,x100221),f864(x100222,a850)),f341(f341(f10(f864(x100221,a850),f864(f864(x100222,x100221),f864(x100222,a850)),x100221),f10(x100221,a850,x100222)),a338)),x100223)))),x100224))))) % 19.23/19.04 [7177]E(x71771,x71772)+~E(f325(x71773,x71774,x71775,x71771),f325(x71773,x71774,x71775,x71772)) % 19.23/19.04 [7178]E(x71781,x71782)+~E(f326(x71783,x71784,x71785,x71781),f326(x71783,x71784,x71785,x71782)) % 19.23/19.04 [8987]~P38(f38(x89871,x89875),x89872,x89873,x89874)+P38(x89871,x89872,x89873,f838(x89874,x89873,x89872,x89875,x89871)) % 19.23/19.04 [8988]~P38(f38(x89881,x89885),x89882,x89883,x89884)+P38(x89881,x89882,x89883,f845(x89884,x89883,x89882,x89885,x89881)) % 19.23/19.04 [8989]~P38(f38(x89895,x89891),x89894,x89893,x89892)+P38(x89891,f838(x89892,x89893,x89894,x89891,x89895),x89893,x89892) % 19.23/19.04 [8990]~P38(f38(x89905,x89901),x89904,x89903,x89902)+P38(x89901,f845(x89902,x89903,x89904,x89901,x89905),x89903,x89902) % 19.23/19.04 [5532]E(f341(f341(f311(x55321),x55322),f174(x55321,x55323,x55324)),f174(x55321,x55323,x55324))+~E(f341(x55324,x55322),f341(f235(x55323),x55325)) % 19.23/19.04 [5946]P85(f341(f256(x59461,x59462,x59463),x59464))+~P85(f341(f341(x59463,x59465),x59464)) % 19.23/19.04 [5948]P85(f341(f255(x59481,x59482,x59483),x59484))+~P85(f341(f341(x59483,x59484),x59485)) % 19.23/19.04 [5951]~E(f341(x59514,x59512),f341(f235(x59513),x59515))+P85(f341(f341(f343(x59511),x59512),f174(x59511,x59513,x59514))) % 19.23/19.04 [5952]~E(f341(x59524,x59525),f341(f235(x59521),x59522))+P85(f341(f341(f343(x59521),x59522),f176(x59523,x59521,x59524))) % 19.23/19.04 [6434]~E(x64345,f2(a108))+E(f341(f199(x64341,x64342,x64343,x64344),x64345),f131(x64342)) % 19.23/19.04 [6435]~E(x64355,f2(a108))+E(f341(f201(x64351,x64352,x64353,x64354),x64355),f124(x64352)) % 19.23/19.04 [6530]~P38(f30(x65303,x65304),x65302,x65305,x65301)+E(x65301,f341(f341(f341(a194,x65302),x65303),f341(x65304,x65302))) % 19.23/19.04 [6575]~E(x65753,f2(a108))+E(f341(f277(x65751,x65752,x65753,x65754),x65755),f341(f250(x65751,x65752),x65755)) % 19.23/19.04 [6653]~E(f341(x66534,x66535),f188(x66532))+E(f341(f237(f861(x66531),x66532,f188(x66531),x66533),f341(x66534,x66535)),f188(x66531)) % 19.23/19.04 [7300]E(f341(x73001,x73002),f188(x73003))+~E(f341(f175(x73004,x73003,x73005,x73001),x73002),f188(x73003)) % 19.23/19.04 [7301]E(f341(x73011,x73012),f188(x73013))+~E(f341(f175(x73014,x73013,x73011,x73015),x73012),f188(x73013)) % 19.23/19.04 [7341]E(f341(f175(x73411,x73412,x73413,x73414),x73415),f341(x73413,x73415))+P85(f341(f341(f343(x73411),x73415),f174(x73411,x73412,x73414))) % 19.23/19.04 [7342]E(f341(f175(x73421,x73422,x73423,x73424),x73425),f341(x73424,x73425))+P85(f341(f341(f343(x73421),x73425),f174(x73421,x73422,x73423))) % 19.23/19.04 [7667]~P21(x76674,x76671,x76672,x76675)+E(f341(f82(x76671,x76671,x76671,f341(x76672,x76673)),f341(x76672,x76673)),f341(x76672,x76673)) % 19.23/19.04 [7710]E(f341(f175(x77101,x77102,x77103,x77104),x77105),f341(x77104,x77105))+~P85(f341(f341(f343(x77101),x77105),f174(x77101,x77102,x77104))) % 19.23/19.04 [8056]~P17(x80565,x80561,x80562)+E(f341(f82(x80561,x80561,x80561,f341(x80562,x80563)),f341(x80562,x80564)),f341(f82(x80561,x80561,x80561,f341(x80562,x80564)),f341(x80562,x80563))) % 19.23/19.04 [8377]P85(f341(f341(f343(f863(x83771,x83771)),f341(f341(f250(x83771,x83771),x83772),x83773)),f336(x83771,x83774,x83775)))+~P85(f341(f341(f242(a857),f341(x83774,x83772)),f341(x83774,x83773))) % 19.23/19.04 [8475]~P85(f341(f341(f343(x84754),x84753),f300(x84754,x84751,x84752,x84755)))+P85(f341(f341(x84751,x84752),x84753)) % 19.23/19.04 [8476]~P85(f341(f341(f343(x84764),x84763),f291(x84764,x84761,x84762,x84765)))+P85(f341(f341(x84761,x84762),x84763)) % 19.23/19.04 [8477]~P85(f341(f341(f343(x84774),x84772),f300(x84774,x84771,x84775,x84773)))+P85(f341(f341(x84771,x84772),x84773)) % 19.23/19.04 [8478]~P85(f341(f341(f343(x84784),x84782),f291(x84784,x84781,x84785,x84783)))+P85(f341(f341(x84781,x84782),x84783)) % 19.23/19.04 [8601]~P54(x86012,x86011,x86015,x86013,x86014)+E(f341(f312(x86011,x86012,x86013),x86014),f248(f864(x86012,a850))) % 19.23/19.04 [9373]P85(f341(f341(f343(f863(f858(x93731),f858(x93731))),f341(f341(f250(f858(x93731),f858(x93731)),f341(f341(f146(x93731),x93732),x93733)),f341(f341(f146(x93731),x93732),x93734))),f152(x93731,x93735)))+~P85(f341(f341(f343(f863(f858(x93731),f858(x93731))),f341(f341(f250(f858(x93731),f858(x93731)),x93733),x93734)),f152(x93731,x93735))) % 19.23/19.04 [9374]P85(f341(f341(f343(f863(f858(x93741),f858(x93741))),f341(f341(f250(f858(x93741),f858(x93741)),f341(f341(f132(x93741),x93742),x93743)),f341(f341(f132(x93741),x93742),x93744))),f143(x93741,x93745)))+~P85(f341(f341(f343(f863(f858(x93741),f858(x93741))),f341(f341(f250(f858(x93741),f858(x93741)),x93743),x93744)),f143(x93741,x93745))) % 19.23/19.04 [9553]E(f341(f341(f146(x95531),f727(x95532,x95533,x95534,x95535,x95531)),f728(x95532,x95533,x95534,x95535,x95531)),x95535)+~P85(f341(f341(f343(f863(f858(x95531),f858(x95531))),f341(f341(f250(f858(x95531),f858(x95531)),x95535),f341(f341(f146(x95531),x95534),x95533))),f153(x95531,x95532))) % 19.23/19.04 [9582]E(f341(f341(f146(x95821),f729(x95822,x95823,x95824,x95825,x95821)),f730(x95822,x95823,x95824,x95825,x95821)),x95823)+~P85(f341(f341(f343(f863(f858(x95821),f858(x95821))),f341(f341(f250(f858(x95821),f858(x95821)),f341(f341(f146(x95821),x95825),x95824)),x95823)),f153(x95821,x95822))) % 19.23/19.04 [9718]~P85(f341(f341(f343(f863(f858(x97181),f858(x97181))),f341(f341(f250(f858(x97181),f858(x97181)),f341(f341(f146(x97181),x97185),x97182)),x97184)),f153(x97181,x97183)))+P85(f341(f341(f343(f863(f858(x97181),f858(x97181))),f341(f341(f250(f858(x97181),f858(x97181)),x97182),f730(x97183,x97184,x97182,x97185,x97181))),f153(x97181,x97183))) % 19.23/19.04 [9803]~P85(f341(f341(f343(f863(f858(x98031),f858(x98031))),f341(f341(f250(f858(x98031),f858(x98031)),x98035),f341(f341(f146(x98031),x98034),x98033))),f153(x98031,x98032)))+P85(f341(f341(f343(f863(f858(x98031),f858(x98031))),f341(f341(f250(f858(x98031),f858(x98031)),f728(x98032,x98033,x98034,x98035,x98031)),x98033)),f153(x98031,x98032))) % 19.23/19.04 [9978]P85(f341(f341(f343(f863(x99781,x99781)),f341(f341(f250(x99781,x99781),f341(x99782,f341(f341(f89(a857),x99783),x99784))),f341(x99782,x99783))),f309(x99781,x99785)))+~P85(f341(f341(f343(f863(x99781,x99781)),f341(f341(f250(x99781,x99781),f341(x99782,f341(a121,f643(x99784,x99783,x99785,x99782,x99781)))),f341(x99782,f643(x99784,x99783,x99785,x99782,x99781)))),f309(x99781,x99785))) % 19.23/19.04 [10002]E(x100021,f2(a108))+E(f341(f237(f863(f858(x100022),x100023),f863(x100022,x100023),f341(f341(f250(f858(x100022),x100023),f122(x100022)),x100024),f341(f260(x100022,x100023,f863(f858(x100022),x100023)),f341(f341(f9(x100022,f864(x100023,f863(f858(x100022),x100023)),f864(x100023,f863(f858(x100022),x100023))),f341(f341(f10(f864(f863(f858(x100022),x100023),f863(f858(x100022),x100023)),f864(f864(x100023,f863(f858(x100022),x100023)),f864(x100023,f863(f858(x100022),x100023))),x100022),f10(f863(f858(x100022),x100023),f863(f858(x100022),x100023),x100023)),f341(f341(f10(f864(f858(x100022),f864(x100023,f863(f858(x100022),x100023))),f864(f863(f858(x100022),x100023),f863(f858(x100022),x100023)),x100022),f260(f858(x100022),x100023,f863(f858(x100022),x100023))),f341(f341(f10(f864(f858(x100022),f858(x100022)),f864(f858(x100022),f864(x100023,f863(f858(x100022),x100023))),x100022),f341(f10(f858(x100022),f864(x100023,f863(f858(x100022),x100023)),f858(x100022)),f250(f858(x100022),x100023))),f146(x100022))))),f126(x100023,x100022,x100025,f341(f341(f3(a108),x100021),f87(a108)))))),f341(x100025,x100024)),f341(f126(x100023,x100022,x100025,x100021),x100024)) % 19.23/19.04 [5136]E(x51361,x51362)+~E(f341(f341(f146(x51363),x51364),x51361),f341(f341(f146(x51363),x51365),x51362)) % 19.23/19.04 [5137]E(x51371,x51372)+~E(f341(f341(f146(x51373),x51371),x51374),f341(f341(f146(x51373),x51372),x51375)) % 19.23/19.04 [5330]~E(f341(f341(f135(x53301),x53303),x53302),f341(f341(f146(x53301),x53304),x53305))+E(f341(f341(f158(x53301),x53302),x53303),x53304) % 19.23/19.04 [5463]~P16(x54634,x54635,x54631)+E(f341(f341(x54631,x54632),f341(f341(x54631,x54632),x54633)),f341(f341(x54631,x54632),x54633)) % 19.23/19.04 [6078]~P101(x60782)+~E(f341(f341(f144(x60781,x60782,x60783),x60784),x60785),f122(x60781)) % 19.23/19.04 [6476]E(x64761,x64762)+~E(f341(f341(f132(x64763),x64764),f341(f341(f146(x64763),x64761),f122(x64763))),f341(f341(f132(x64763),x64765),f341(f341(f146(x64763),x64762),f122(x64763)))) % 19.23/19.04 [6477]E(x64771,x64772)+~E(f341(f341(f132(x64773),x64771),f341(f341(f146(x64773),x64774),f122(x64773))),f341(f341(f132(x64773),x64772),f341(f341(f146(x64773),x64775),f122(x64773)))) % 19.23/19.04 [6736]E(f341(f178(x67361,x67362,x67363,x67364),x67365),f188(x67362))+P85(f341(f341(f343(x67361),x67365),x67364)) % 19.23/19.04 [6805]E(f341(f341(f311(x68051),f341(x68052,x68053)),f341(f312(x68054,x68051,x68052),x68055)),f341(f312(x68054,x68051,x68052),x68055))+~P85(f341(f341(f343(x68054),x68053),x68055)) % 19.23/19.04 [6814]~P85(f341(x68144,f341(x68143,x68145)))+P85(f341(f341(f314(x68141,x68142,x68143),x68144),x68145)) % 19.23/19.04 [6819]~E(x68194,f2(a108))+E(f341(f126(x68191,x68192,x68193,x68194),x68195),f341(f341(f250(f858(x68192),x68191),f122(x68192)),x68195)) % 19.23/19.04 [6913]~E(f341(f312(x69131,x69132,x69133),x69134),x69135)+E(f341(f312(f864(x69131,a850),f864(x69132,a850),f312(x69131,x69132,x69133)),f341(f310(x69131),x69134)),f341(f310(x69132),x69135)) % 19.23/19.04 [6943]E(f341(f178(x69431,x69432,x69433,x69434),x69435),f341(x69433,x69435))+~P85(f341(f341(f343(x69431),x69435),x69434)) % 19.23/19.04 [7257]P26(x72571,x72572,x72573,x72574)+~P26(x72571,x72572,x72573,f341(f341(f311(x72571),x72575),x72574)) % 19.23/19.04 [7328]P85(f341(x73281,x73282))+~P85(f341(f341(f101(x73283,x73284,x73281),x73285),x73282)) % 19.23/19.04 [7379]~P85(f341(f341(f343(x73794),x73793),x73795))+P85(f341(f341(f343(x73791),f341(x73792,x73793)),f341(f312(x73794,x73791,x73792),x73795))) % 19.23/19.04 [7430]P85(f341(x74301,f341(x74302,x74303)))+~P85(f341(f341(f314(x74304,x74305,x74302),x74301),x74303)) % 19.23/19.04 [7431]P85(f341(f341(x74311,x74312),x74313))+~P85(f341(f341(f101(x74314,x74311,x74315),x74312),x74313)) % 19.23/19.04 [7500]~P85(f341(f341(f343(x75003),f341(x75004,x75002)),x75005))+P85(f341(f341(f343(x75001),x75002),f341(f314(x75001,x75003,x75004),x75005))) % 19.23/19.04 [7899]~P85(f341(f341(f343(x78995),x78993),f341(f314(x78995,x78991,x78992),x78994)))+P85(f341(f341(f343(x78991),f341(x78992,x78993)),x78994)) % 19.23/19.04 [8116]~E(x81163,f341(f341(f341(f81(x81161,f861(x81162)),f341(f18(f861(x81162),x81161),f188(x81162))),x81164),f341(f235(x81162),x81165)))+E(f174(x81161,x81162,x81163),f341(f341(f311(x81161),x81164),f185(f864(x81161,a850)))) % 19.23/19.04 [8210]E(f341(x82101,f365(x82102,x82101,x82103,x82104)),x82104)+~P85(f341(f341(f343(x82105),x82104),f341(f312(x82103,x82105,x82101),x82102))) % 19.23/19.04 [8462]P85(f341(f341(f343(f865(x84621,x84622)),f341(f322(x84622,x84621),x84623)),f323(x84621,x84622,x84624,x84625)))+~P85(f341(f341(f343(x84622),x84623),x84625)) % 19.23/19.04 [8463]P85(f341(f341(f343(f865(x84631,x84632)),f341(f313(x84631,x84632),x84633)),f323(x84631,x84632,x84634,x84635)))+~P85(f341(f341(f343(x84631),x84633),x84634)) % 19.23/19.04 [8519]~E(x85192,f341(f341(f146(x85191),x85194),x85195))+P85(f341(f341(f343(f863(f858(x85191),f858(x85191))),f341(f341(f250(f858(x85191),f858(x85191)),f122(x85191)),x85192)),f143(x85191,x85193))) % 19.23/19.04 [8570]P85(f341(f341(f241(f864(x85701,a850)),f341(f341(f55(x85702,f864(x85701,a850)),x85703),x85704)),f341(x85704,x85705)))+~P85(f341(f341(f343(x85702),x85705),x85703)) % 19.23/19.04 [8617]~P54(x86171,x86172,x86173,x86175,x86174)+E(f341(f312(x86171,x86172,x86173),f248(f864(x86171,a850))),x86174) % 19.23/19.04 [8806]E(f341(f341(f341(f81(x88061,f861(x88062)),f178(x88061,x88062,x88063,x88064)),x88065),f188(x88062)),f178(x88061,x88062,x88063,x88064))+P85(f341(f341(f343(x88061),x88065),x88064)) % 19.23/19.04 [8809]E(f341(x88091,f713(x88092,x88093,x88091,x88094,x88095)),x88092)+~E(f341(f341(f204(x88095,x88094),x88091),x88093),f341(f235(x88094),x88092)) % 19.23/19.04 [8812]E(f341(f235(x88121),f713(x88122,x88123,x88124,x88125,x88121)),x88123)+~E(f341(f341(f204(x88121,x88125),x88124),x88123),f341(f235(x88125),x88122)) % 19.23/19.04 [8898]E(f341(f186(f858(x88981)),x88982),x88983)+~P85(f341(f341(f343(f863(f858(x88981),f858(x88981))),f341(f341(f250(f858(x88981),f858(x88981)),x88984),x88982)),f341(f139(x88981,x88985),x88983))) % 19.23/19.04 [8899]E(f341(f186(f858(x88991)),x88992),x88993)+~P85(f341(f341(f343(f863(f858(x88991),f858(x88991))),f341(f341(f250(f858(x88991),f858(x88991)),x88992),x88994)),f341(f139(x88991,x88995),x88993))) % 19.23/19.04 [8959]P85(f341(f341(f343(x89591),f365(x89592,x89593,x89591,x89594)),x89592))+~P85(f341(f341(f343(x89595),x89594),f341(f312(x89591,x89595,x89593),x89592))) % 19.23/19.04 [9114]E(f341(f312(x91141,x91142,x91143),f366(x91144,x91143,x91141,x91145,x91142)),x91145)+~P85(f341(f341(f241(f864(x91142,a850)),x91145),f341(f312(x91141,x91142,x91143),x91144))) % 19.23/19.04 [9346]E(f341(x93461,f529(x93462,x93461,x93463,x93464,x93465)),f341(f235(x93465),x93464))+~P85(f341(f341(f343(x93465),x93464),f176(x93463,x93465,f178(x93463,x93465,x93461,x93462)))) % 19.23/19.04 [9389]P85(f341(f341(f343(f863(f858(x93891),f858(x93891))),f341(f341(f250(f858(x93891),f858(x93891)),f341(f341(f146(x93891),x93892),x93893)),f341(f341(f146(x93891),x93892),x93894))),f309(f858(x93891),f152(x93891,x93895))))+~P85(f341(f341(f343(f863(f858(x93891),f858(x93891))),f341(f341(f250(f858(x93891),f858(x93891)),x93893),x93894)),f309(f858(x93891),f152(x93891,x93895)))) % 19.23/19.04 [9419]~E(f341(x94193,f714(x94195,x94194,x94193,x94192,x94191)),f341(x94195,f714(x94195,x94194,x94193,x94192,x94191)))+E(f341(f341(f149(x94191,x94192),x94193),x94194),f341(f341(f149(x94191,x94192),x94195),x94194)) % 19.23/19.04 [9498]E(f341(f341(f149(x94981,x94982),x94983),x94984),f341(f341(f149(x94981,x94982),x94985),x94984))+P85(f341(f341(f343(x94981),f714(x94983,x94984,x94985,x94982,x94981)),f341(f163(x94981),x94984))) % 19.23/19.04 [9526]~P85(f341(f341(f343(x95265),x95264),f341(f286(x95261,x95265,x95263),x95262)))+P85(f341(f341(f343(x95261),f368(x95262,x95263,x95261,x95264,x95265)),x95262)) % 19.23/19.04 [9527]~P85(f341(f341(f343(x95275),x95274),f341(f286(x95271,x95275,x95273),x95272)))+P85(f341(f341(f343(x95271),f372(x95272,x95273,x95271,x95274,x95275)),x95272)) % 19.23/19.04 [9551]~P85(f341(f341(f241(f864(x95515,a850)),x95514),f341(f312(x95511,x95515,x95513),x95512)))+P85(f341(f341(f241(f864(x95511,a850)),f366(x95512,x95513,x95511,x95514,x95515)),x95512)) % 19.23/19.04 [9600]~P85(f341(f341(f343(x96005),x96004),f176(x96001,x96005,f178(x96001,x96005,x96003,x96002))))+P85(f341(f341(f343(x96001),f529(x96002,x96003,x96001,x96004,x96005)),x96002)) % 19.23/19.04 [5344]~E(f341(x53443,x53444),x53445)+E(f341(f341(f341(f81(x53441,x53442),x53443),x53444),x53445),x53443) % 19.23/19.04 [5793]E(f341(x57931,x57932),x57933)+~E(f341(f341(f341(f81(x57934,x57935),x57931),x57932),x57933),x57931) % 19.23/19.04 [5828]~P29(x58285,x58281)+E(f341(f341(x58281,f341(f341(x58281,x58282),x58283)),x58284),f341(f341(x58281,x58282),f341(f341(x58281,x58283),x58284))) % 19.23/19.04 [5883]E(x58831,x58832)+~E(f341(f259(x58833,x58834),f341(f341(f250(x58833,x58834),x58835),x58831)),x58832) % 19.23/19.04 [5884]E(x58841,x58842)+~E(f341(f249(x58843,x58844),f341(f341(f250(x58843,x58844),x58841),x58845)),x58842) % 19.23/19.04 [6563]E(f341(f312(x65631,x65632,f341(f18(x65632,x65631),x65633)),x65634),f341(f341(f311(x65632),x65633),f185(f864(x65632,a850))))+~P85(f341(f341(f343(x65631),x65635),x65634)) % 19.23/19.04 [6636]E(f341(f341(f110(f864(x66361,a850)),f341(f163(x66361),x66362)),f341(f163(x66361),x66363)),f341(f163(x66361),x66364))+~E(f161(x66361,x66365,x66364),f341(f341(f250(f858(x66361),f858(x66361)),x66362),x66363)) % 19.23/19.04 [6742]~P101(x67422)+E(f341(f186(f858(x67421)),f341(f341(f144(x67421,x67422,x67423),x67424),x67425)),f341(a121,f341(f186(f858(x67421)),x67425))) % 19.23/19.04 [6756]~P101(x67562)+E(f341(f163(x67561),f341(f341(f144(x67561,x67562,x67563),x67564),x67565)),f341(f341(f311(x67561),x67564),f341(f163(x67561),x67565))) % 19.23/19.04 [7033]~P86(x70331)+E(f341(f341(f89(x70331),f341(f341(f89(x70331),x70332),x70333)),f341(f341(f89(x70331),x70334),x70335)),f341(f341(f89(x70331),f341(f341(f89(x70331),x70332),x70334)),f341(f341(f89(x70331),x70333),x70335))) % 19.23/19.04 [7034]~P86(x70341)+E(f341(f341(f90(x70341),f341(f341(f90(x70341),x70342),x70343)),f341(f341(f90(x70341),x70344),x70345)),f341(f341(f90(x70341),f341(f341(f90(x70341),x70342),x70344)),f341(f341(f90(x70341),x70343),x70345))) % 19.23/19.04 [7035]~P59(x70351)+E(f341(f341(f292(x70351),f341(f341(f90(x70351),x70352),x70353)),f341(f341(f90(x70351),x70354),x70355)),f341(f341(f90(x70351),f341(f341(f292(x70351),x70352),x70354)),f341(f341(f292(x70351),x70353),x70355))) % 19.23/19.04 [7049]~P101(x70491)+E(f307(x70491,f341(f341(f240(x70491),x70492),x70493),f341(f341(f245(x70491),x70494),x70495)),f341(f341(f111(f864(x70491,a850)),f307(x70491,x70492,x70494)),f307(x70491,x70493,x70495))) % 19.23/19.04 [7050]~P101(x70501)+E(f306(x70501,f341(f341(f240(x70501),x70502),x70503),f341(f341(f245(x70501),x70504),x70505)),f341(f341(f111(f864(x70501,a850)),f306(x70501,x70502,x70504)),f306(x70501,x70503,x70505))) % 19.23/19.04 [7051]~P101(x70511)+E(f304(x70511,f341(f341(f240(x70511),x70512),x70513),f341(f341(f245(x70511),x70514),x70515)),f341(f341(f111(f864(x70511,a850)),f304(x70511,x70512,x70514)),f304(x70511,x70513,x70515))) % 19.23/19.04 [7052]~P101(x70521)+E(f341(f341(f111(f864(x70521,a850)),f341(f303(x70521,x70522),x70523)),f341(f303(x70521,x70524),x70525)),f341(f303(x70521,f341(f341(f240(x70521),x70522),x70524)),f341(f341(f245(x70521),x70523),x70525))) % 19.23/19.04 [7169]~P85(f341(x71691,f833(x71693,x71692,x71691)))+P85(f341(x71691,f341(f341(f250(x71692,x71693),x71694),x71695))) % 19.23/19.04 [7269]~E(f341(x72693,x72694),f188(x72692))+E(f176(x72691,x72692,f341(f341(f341(f81(x72691,f861(x72692)),x72693),x72694),f341(f235(x72692),x72695))),f341(f341(f311(x72692),x72695),f176(x72691,x72692,x72693))) % 19.23/19.04 [7292]~E(x72922,f341(x72924,x72925))+P85(f341(f341(f343(x72921),x72922),f341(f312(x72923,x72921,x72924),f248(f864(x72923,a850))))) % 19.23/19.04 [7353]~E(f341(x73533,x73534),f188(x73532))+E(f341(f341(f3(f864(x73531,a850)),f174(x73531,x73532,x73533)),f341(f341(f311(x73531),x73534),x73535)),f341(f341(f3(f864(x73531,a850)),f174(x73531,x73532,x73533)),x73535)) % 19.23/19.04 [7375]~P16(x73753,x73752,x73754)+P16(x73751,x73752,f341(f341(f10(x73753,f864(x73752,x73752),x73751),x73754),x73755)) % 19.23/19.04 [7376]~P17(x73763,x73762,x73764)+P17(x73761,x73762,f341(f341(f10(x73763,f864(x73762,x73762),x73761),x73764),x73765)) % 19.23/19.04 [7516]~P26(x75161,x75162,x75163,x75164)+P26(x75161,x75162,x75163,f341(f341(f3(f864(x75161,a850)),x75164),x75165)) % 19.23/19.04 [7676]~P85(f341(f341(x76763,x76764),x76765))+P85(f341(f341(f260(x76761,x76762,a850),x76763),f341(f341(f250(x76761,x76762),x76764),x76765))) % 19.23/19.04 [7810]P26(x78101,x78102,x78103,x78104)+~P26(x78101,x78102,x78103,f341(f341(f110(f864(x78101,a850)),x78105),x78104)) % 19.23/19.04 [7811]P26(x78111,x78112,x78113,x78114)+~P26(x78111,x78112,x78113,f341(f341(f110(f864(x78111,a850)),x78114),x78115)) % 19.23/19.04 [8170]~P16(x81702,x81701,x81703)+E(f341(f138(x81701,x81702,f341(f9(x81702,x81701,x81701),x81703),x81704),x81705),f341(f341(f74(x81702,x81701,x81703),x81704),f341(f163(x81702),x81705))) % 19.23/19.04 [8220]P85(f341(f341(x82201,x82202),x82203))+~P85(f341(f341(f260(x82204,x82205,a850),x82201),f341(f341(f250(x82204,x82205),x82202),x82203))) % 19.23/19.04 [8292]P38(x82924,f684(x82925,x82924,x82923,x82922),x82922,f793(x82925,x82924,x82923,x82922))+P30(x82921,x82922,f341(f341(f341(f100(x82921),x82923),x82924),x82925)) % 19.23/19.04 [8308]~E(f341(f171(x83081,x83082,x83085),x83083),f341(f235(x83082),x83084))+P85(f341(f341(f343(f863(x83081,x83082)),f341(f341(f250(x83081,x83082),x83083),x83084)),f341(f163(f863(x83081,x83082)),x83085))) % 19.23/19.04 [8670]P85(f341(f341(f241(f864(x86701,a850)),f341(f312(x86702,x86701,x86703),x86704)),f341(f312(x86702,x86701,x86703),x86705)))+~P85(f341(f341(f241(f864(x86702,a850)),x86704),x86705)) % 19.23/19.04 [8671]P85(f341(f341(f241(f864(x86711,a850)),f341(f314(x86711,x86712,x86713),x86714)),f341(f314(x86711,x86712,x86713),x86715)))+~P85(f341(f341(f241(f864(x86712,a850)),x86714),x86715)) % 19.23/19.04 [8742]E(x87421,f2(a108))+E(f341(f341(f262(x87422,x87423,x87422,f863(x87423,x87422)),f341(x87424,x87425)),f277(x87423,x87422,f341(f341(f3(a108),x87421),f87(a108)),x87424)),f341(f277(x87423,x87422,x87421,x87424),x87425)) % 19.23/19.04 [8831]P85(f341(f341(f258(x88311,x88312,a850,x88313),x88314),x88315))+~P85(f341(x88313,f341(f341(f250(x88311,x88312),x88314),x88315))) % 19.23/19.04 [9031]P30(x90311,x90312,f341(f341(f341(f100(x90311),x90313),x90314),x90315))+P85(f341(f341(x90313,f570(x90315,x90314,x90313,x90312)),f684(x90315,x90314,x90313,x90312))) % 19.23/19.04 [9041]~P85(f341(f341(f192(x90413),f341(f341(f341(a194,x90414),f42(x90411)),f341(x90412,x90414))),x90415))+P85(f341(f341(f192(f34(x90411,x90412,x90413)),x90414),f341(f341(f341(a194,x90415),f42(x90411)),f341(f341(a195,x90414),x90411)))) % 19.23/19.04 [9094]~P85(f341(f341(f258(x90942,x90943,a850,x90941),x90944),x90945))+P85(f341(x90941,f341(f341(f250(x90942,x90943),x90944),x90945))) % 19.23/19.04 [9201]E(f341(f235(x92011),f723(x92012,x92013,x92014,x92011,x92015)),f341(f171(x92015,x92011,x92012),x92014))+~P85(f341(f341(f343(f863(x92015,x92011)),f341(f341(f250(x92015,x92011),x92014),x92013)),f341(f163(f863(x92015,x92011)),x92012))) % 19.23/19.04 [9244]P30(x92441,x92442,f341(f341(f341(f100(x92441),x92443),x92444),x92445))+~P85(f341(f341(x92445,f570(x92445,x92444,x92443,x92442)),f793(x92445,x92444,x92443,x92442))) % 19.23/19.04 [9338]~P85(f341(f71(x93383),f341(f312(x93382,x93383,x93385),f248(f864(x93382,a850)))))+P85(f341(f71(x93381),f341(f312(x93382,x93381,f341(f341(f10(x93383,x93381,x93382),x93384),x93385)),f248(f864(x93382,a850))))) % 19.23/19.04 [9359]P85(f341(f341(f241(f864(f864(x93591,a850),a850)),f341(f312(f864(x93592,a850),f864(x93591,a850),f312(x93592,x93591,x93593)),f341(f310(x93592),x93594))),f341(f310(x93591),x93595)))+~P85(f341(f341(f241(f864(x93591,a850)),f341(f312(x93592,x93591,x93593),x93594)),x93595)) % 19.23/19.04 [9369]~P85(f341(f71(f861(x93691)),f341(f312(x93692,f861(x93691),x93693),f248(f864(x93692,a850)))))+P85(f341(f71(f861(x93691)),f341(f312(x93692,f861(x93691),f341(f341(f341(f81(x93692,f861(x93691)),x93693),x93694),f341(f235(x93691),x93695))),f248(f864(x93692,a850))))) % 19.23/19.04 [9400]P85(f341(f341(f192(x94001),f341(f341(f341(a194,x94002),f42(x94003)),f341(x94004,x94002))),f472(x94005,x94002,x94001,x94004,x94003)))+~P85(f341(f341(f192(f34(x94003,x94004,x94001)),x94002),x94005)) % 19.23/19.04 [9427]E(x94271,x94272)+~P85(f341(f76(x94273,x94274,x94275,x94271,f185(f864(x94273,a850))),x94272)) % 19.23/19.04 [9440]E(f341(f341(f250(x94401,x94402),f563(x94403,x94404,x94405,x94402,x94401)),f564(x94403,x94404,x94405,x94402,x94401)),x94405)+~P85(f341(f341(f343(f863(x94401,x94402)),x94405),f341(f341(f257(x94401,x94402),x94404),x94403))) % 19.23/19.04 [9451]P85(f341(f341(f192(x94511),f341(f341(f341(a194,x94512),f42(x94513)),f341(x94514,x94512))),f405(x94515,x94512,x94511,x94514,x94513)))+~P85(f341(f341(f192(f34(x94513,x94514,x94511)),x94512),f341(f341(f341(a194,x94515),f42(x94513)),f341(f341(a195,x94512),x94513)))) % 19.23/19.04 [9457]~P85(f341(f341(f192(f341(a29,x94572)),f341(f341(f341(a194,f341(f341(a196,x94574),a197)),f42(a28)),f341(x94573,x94574))),x94575))+P85(f341(f341(f192(f33(x94571,x94572,x94573)),x94574),f341(f341(f341(a194,f341(f341(a196,x94575),f341(a195,x94574))),x94571),f341(f341(a195,x94575),a27)))) % 19.23/19.04 [9491]P85(f341(f341(f192(f341(a29,x94911)),f341(f341(f341(a194,f341(f341(a196,x94912),a197)),f42(a28)),f341(x94913,x94912))),f525(x94914,x94912,x94913,x94911,x94915)))+~P85(f341(f341(f192(f33(x94915,x94911,x94913)),x94912),x94914)) % 19.23/19.04 [9531]P85(f341(f341(f343(x95311),f563(x95312,x95313,x95314,x95315,x95311)),x95313))+~P85(f341(f341(f343(f863(x95311,x95315)),x95314),f341(f341(f257(x95311,x95315),x95313),x95312))) % 19.23/19.04 [9557]E(f341(f341(f341(a194,f472(x95571,x95572,x95573,x95574,x95575)),f42(x95575)),f341(f341(a195,x95572),x95575)),x95571)+~P85(f341(f341(f192(f34(x95575,x95574,x95573)),x95572),x95571)) % 19.23/19.04 [9583]E(f341(f341(f341(a194,f405(x95831,x95832,x95833,x95834,x95835)),f42(x95835)),f341(f341(a195,x95832),x95835)),f341(f341(f341(a194,x95831),f42(x95835)),f341(f341(a195,x95832),x95835)))+~P85(f341(f341(f192(f34(x95835,x95834,x95833)),x95832),f341(f341(f341(a194,x95831),f42(x95835)),f341(f341(a195,x95832),x95835)))) % 19.23/19.04 [9609]P85(f341(f341(f192(f341(a29,x96091)),f341(f341(f341(a194,f341(f341(a196,x96092),a197)),f42(a28)),f341(x96093,x96092))),f514(x96094,x96092,x96093,x96091,x96095)))+~P85(f341(f341(f192(f33(x96095,x96091,x96093)),x96092),f341(f341(f341(a194,f341(f341(a196,x96094),f341(a195,x96092))),x96095),f341(f341(a195,x96094),a27)))) % 19.23/19.04 [9676]P85(f341(f341(f343(x96761),f564(x96762,x96763,x96764,x96761,x96765)),f341(x96762,f563(x96762,x96763,x96764,x96761,x96765))))+~P85(f341(f341(f343(f863(x96765,x96761)),x96764),f341(f341(f257(x96765,x96761),x96763),x96762))) % 19.23/19.04 [9695]P85(f341(f341(f343(f863(x96951,x96951)),f341(f341(f250(x96951,x96951),x96952),f665(x96953,x96954,x96955,x96952,x96951))),x96953))+~P85(f341(f341(f343(f863(x96951,x96951)),f341(f341(f250(x96951,x96951),x96952),x96955)),f341(f341(f179(f863(x96951,x96951),a850),f341(a121,x96954)),x96953))) % 19.23/19.04 [9696]P85(f341(f341(f343(f863(x96961,x96961)),f341(f341(f250(x96961,x96961),x96962),f666(x96963,x96964,x96965,x96962,x96961))),x96963))+~P85(f341(f341(f343(f863(x96961,x96961)),f341(f341(f250(x96961,x96961),x96962),x96965)),f341(f341(f179(f863(x96961,x96961),a850),f341(a121,x96964)),x96963))) % 19.23/19.04 [9714]~P85(f341(f341(f343(f863(f858(x97141),f858(x97141))),f341(f341(f250(f858(x97141),f858(x97141)),f341(f341(f146(x97141),x97142),x97145)),x97144)),f153(x97141,x97143)))+P85(f341(f341(f343(f863(x97141,x97141)),f341(f341(f250(x97141,x97141),x97142),f729(x97143,x97144,x97145,x97142,x97141))),x97143)) % 19.23/19.04 [9716]~P25(x97161,x97162,f341(f341(f311(f856(x97161)),f341(f341(f341(f100(x97161),f101(x97161,x97163,x97164)),x97165),x97163)),f185(f864(f856(x97161),a850))))+P25(x97161,x97162,f341(f341(f311(f856(x97161)),f341(f341(f341(f100(x97161),x97163),f37(x97164,x97165)),f101(x97161,x97163,f341(f82(a850,a850,a855,a337),x97164)))),f185(f864(f856(x97161),a850)))) % 19.23/19.04 [9835]E(f341(f341(f341(a194,f341(f341(a196,f525(x98351,x98352,x98353,x98354,x98355)),f341(a195,x98352))),x98355),f341(f341(a195,f525(x98351,x98352,x98353,x98354,x98355)),a27)),x98351)+~P85(f341(f341(f192(f33(x98355,x98354,x98353)),x98352),x98351)) % 19.23/19.04 [9847]E(f341(f341(f341(a194,f341(f341(a196,f514(x98471,x98472,x98473,x98474,x98475)),f341(a195,x98472))),x98475),f341(f341(a195,f514(x98471,x98472,x98473,x98474,x98475)),a27)),f341(f341(f341(a194,f341(f341(a196,x98471),f341(a195,x98472))),x98475),f341(f341(a195,x98471),a27)))+~P85(f341(f341(f192(f33(x98475,x98474,x98473)),x98472),f341(f341(f341(a194,f341(f341(a196,x98471),f341(a195,x98472))),x98475),f341(f341(a195,x98471),a27)))) % 19.23/19.04 [6278]~P72(x62782)+E(f341(f341(f341(f3(f864(x62781,x62782)),x62783),x62784),x62785),f341(f341(f3(x62782),f341(x62783,x62785)),f341(x62784,x62785))) % 19.23/19.04 [6280]~P95(x62802)+E(f341(f341(f341(f110(f864(x62801,x62802)),x62803),x62804),x62805),f341(f341(f110(x62802),f341(x62803,x62805)),f341(x62804,x62805))) % 19.23/19.04 [6282]~P95(x62822)+E(f341(f341(f341(f111(f864(x62821,x62822)),x62823),x62824),x62825),f341(f341(f111(x62822),f341(x62823,x62825)),f341(x62824,x62825))) % 19.23/19.04 [6304]E(x63041,x63042)+E(f341(f341(f158(x63043),f341(f341(f154(x63043,x63044),x63041),x63045)),x63042),f341(f341(f158(x63043),x63044),x63042)) % 19.23/19.04 [6580]~E(x65804,f185(f864(x65803,a850)))+E(f341(f341(f3(f864(x65801,a850)),x65802),f341(f341(f54(x65803,f864(x65801,a850)),x65804),x65805)),x65802) % 19.23/19.04 [6581]~E(x65814,f185(f864(x65813,a850)))+E(f341(f341(f110(f864(x65811,a850)),x65812),f341(f341(f54(x65813,f864(x65811,a850)),x65814),x65815)),x65812) % 19.23/19.04 [6582]~E(x65824,f185(f864(x65823,a850)))+E(f341(f341(f111(f864(x65821,a850)),x65822),f341(f341(f55(x65823,f864(x65821,a850)),x65824),x65825)),x65822) % 19.23/19.04 [6595]~E(x65954,f185(f864(x65953,a850)))+E(f341(f341(f311(x65951),x65952),f341(f341(f54(x65953,f864(x65951,a850)),x65954),x65955)),f341(f341(f311(x65951),x65952),f185(f864(x65951,a850)))) % 19.23/19.04 [7420]E(f341(f341(f158(x74201),f341(f341(f149(x74202,x74201),x74203),x74204)),x74205),f341(x74203,f341(f341(f158(x74202),x74204),x74205)))+~P85(f341(f341(f242(a857),x74205),f341(f186(f858(x74202)),x74204))) % 19.23/19.04 [7488]E(f341(f341(f110(f864(x74881,a850)),f341(x74882,x74883)),f341(f341(f54(x74884,f864(x74881,a850)),x74885),x74882)),f341(f341(f54(x74884,f864(x74881,a850)),x74885),x74882))+~P85(f341(f341(f343(x74884),x74883),x74885)) % 19.23/19.04 [7489]E(f341(f341(f111(f864(x74891,a850)),f341(x74892,x74893)),f341(f341(f55(x74894,f864(x74891,a850)),x74895),x74892)),f341(f341(f55(x74894,f864(x74891,a850)),x74895),x74892))+~P85(f341(f341(f343(x74894),x74893),x74895)) % 19.23/19.04 [8091]~E(x80913,f185(f864(x80911,a850)))+E(f341(f341(f54(x80911,f864(x80912,a850)),x80913),f341(f341(f10(f864(x80912,a850),f864(x80912,a850),x80911),f341(f311(x80912),x80914)),x80915)),f185(f864(x80912,a850))) % 19.23/19.04 [8097]~P85(f341(f341(f343(x80974),x80973),x80975))+P85(f341(f341(f241(f864(x80971,a850)),f341(x80972,x80973)),f341(f341(f54(x80974,f864(x80971,a850)),x80975),x80972))) % 19.23/19.04 [8219]~E(f341(x82194,x82192),x82195)+P85(f341(f341(f343(x82191),x82192),f341(f314(x82191,x82193,x82194),f341(f341(f311(x82193),x82195),f185(f864(x82193,a850)))))) % 19.23/19.04 [8266]~P52(x82661,x82662,f341(f287(x82662,x82661),x82663))+E(f341(f341(f111(f864(x82661,a850)),f341(f286(x82662,x82661,x82663),x82664)),f341(f286(x82662,x82661,x82663),x82665)),f341(f286(x82662,x82661,x82663),f341(f341(f111(f864(x82662,a850)),x82664),x82665))) % 19.23/19.04 [8291]E(x82911,f2(a108))+E(f125(x82912,x82913,f341(x82914,f341(f341(f3(a108),x82911),f87(a108))),f341(f341(f9(x82912,a108,f859(x82913)),x82915),x82911)),f341(f201(x82912,x82913,x82914,x82915),x82911)) % 19.23/19.04 [8387]E(x83871,f185(f864(x83872,a850)))+E(f341(f341(f54(x83872,f864(x83873,a850)),x83871),f341(f341(f10(f864(x83873,a850),f864(x83873,a850),x83872),f341(f311(x83873),x83874)),x83875)),f341(f341(f311(x83873),x83874),f341(f341(f54(x83872,f864(x83873,a850)),x83871),x83875))) % 19.23/19.04 [8440]~P26(x84402,x84401,x84403,f248(f864(x84402,a850)))+E(f341(f341(f3(f864(x84401,a850)),f341(f312(x84402,x84401,x84403),x84404)),f341(f312(x84402,x84401,x84403),x84405)),f341(f312(x84402,x84401,x84403),f341(f341(f3(f864(x84402,a850)),x84404),x84405))) % 19.23/19.04 [8441]~P26(x84412,x84411,x84413,f248(f864(x84412,a850)))+E(f341(f341(f111(f864(x84411,a850)),f341(f312(x84412,x84411,x84413),x84414)),f341(f312(x84412,x84411,x84413),x84415)),f341(f312(x84412,x84411,x84413),f341(f341(f111(f864(x84412,a850)),x84414),x84415))) % 19.23/19.04 [8507]~P85(f341(f341(f77(x85071,x85072,x85075),x85073),x85074))+P85(f341(f341(f343(f863(x85071,x85072)),f341(f341(f250(x85071,x85072),x85073),x85074)),x85075)) % 19.23/19.04 [8535]P85(f341(f341(f343(x85351),x85352),f341(f268(x85353,x85351),x85354)))+~P85(f341(f341(f343(f863(x85353,x85351)),f341(f341(f250(x85353,x85351),x85355),x85352)),x85354)) % 19.23/19.04 [8537]P85(f341(f341(f343(x85371),x85372),f341(f270(x85371,x85373),x85374)))+~P85(f341(f341(f343(f863(x85371,x85373)),f341(f341(f250(x85371,x85373),x85372),x85375)),x85374)) % 19.23/19.04 [8659]P85(f341(f341(f77(x86591,x86592,x86593),x86594),x86595))+~P85(f341(f341(f343(f863(x86591,x86592)),f341(f341(f250(x86591,x86592),x86594),x86595)),x86593)) % 19.23/19.04 [8692]E(f341(x86921,x86922),x86923)+~P85(f341(f341(f343(x86924),x86922),f341(f314(x86924,x86925,x86921),f341(f341(f311(x86925),x86923),f185(f864(x86925,a850)))))) % 19.23/19.04 [8895]P85(f341(f341(f343(f863(x88951,x88952)),f341(f341(f250(x88951,x88952),x88953),x88954)),f341(f287(x88952,x88951),x88955)))+~P85(f341(f341(f343(f863(x88952,x88951)),f341(f341(f250(x88952,x88951),x88954),x88953)),x88955)) % 19.23/19.04 [8913]~P85(f341(f341(x89131,x89135),x89134))+P85(f341(f341(x89131,f341(f259(x89132,x89133),f341(f341(f250(x89132,x89133),x89134),x89135))),f341(f249(x89132,x89133),f341(f341(f250(x89132,x89133),x89134),x89135)))) % 19.23/19.04 [8940]~P85(f341(f341(f343(f863(x89402,x89401)),f341(f341(f250(x89402,x89401),x89404),x89403)),f341(f287(x89401,x89402),x89405)))+P85(f341(f341(f343(f863(x89401,x89402)),f341(f341(f250(x89401,x89402),x89403),x89404)),x89405)) % 19.23/19.04 [8967]~P85(f341(f341(f343(f863(x89673,x89671)),f341(f341(f250(x89673,x89671),x89675),x89672)),x89674))+P85(f341(f341(f343(x89671),x89672),f341(f286(x89673,x89671,x89674),f341(f341(f311(x89673),x89675),f185(f864(x89673,a850)))))) % 19.23/19.04 [9014]P85(f341(f341(f343(f863(x90141,x90142)),f341(f341(f250(x90141,x90142),x90143),x90144)),x90145))+~P85(f341(f341(f343(x90142),x90144),f341(f286(x90141,x90142,x90145),f341(f341(f311(x90141),x90143),f185(f864(x90141,a850)))))) % 19.23/19.04 [9034]E(f341(f341(f341(f81(x90341,f861(x90342)),f178(x90341,x90342,x90343,x90344)),x90345),f188(x90342)),f178(x90341,x90342,x90343,f341(f341(f3(f864(x90341,a850)),x90344),f341(f341(f311(x90341),x90345),f185(f864(x90341,a850))))))+~P85(f341(f341(f343(x90341),x90345),x90344)) % 19.23/19.04 [9100]~P68(x91001)+E(f341(f341(f8(a857,x91001),x91002),f304(a857,f341(f341(f89(a857),x91003),x91004),f341(f341(f89(a857),x91005),x91004))),f341(f341(f8(a857,x91001),f341(f341(f10(a857,x91001,a857),x91002),f341(f341(f9(a857,a857,a857),f89(a857)),x91004))),f304(a857,x91003,x91005))) % 19.23/19.04 [9118]~P68(x91181)+E(f341(f341(f8(a857,x91181),x91182),f341(f303(a857,f341(f341(f89(a857),x91183),x91184)),f341(f341(f89(a857),x91185),x91184))),f341(f341(f8(a857,x91181),f341(f341(f10(a857,x91181,a857),x91182),f341(f341(f9(a857,a857,a857),f89(a857)),x91184))),f341(f303(a857,x91183),x91185))) % 19.23/19.04 [9326]P85(f341(f341(f343(f863(f858(x93261),f858(x93261))),f341(f341(f250(f858(x93261),f858(x93261)),f341(f341(f146(x93261),x93262),x93263)),f341(f341(f146(x93261),x93264),x93263))),f152(x93261,x93265)))+~P85(f341(f341(f343(f863(x93261,x93261)),f341(f341(f250(x93261,x93261),x93262),x93264)),x93265)) % 19.23/19.04 [9436]E(f341(f341(f311(x94361),f546(x94362,x94363,x94364,x94365,x94361)),f547(x94362,x94363,x94364,x94365,x94361)),f341(f341(f311(x94361),x94364),x94363))+~P85(f341(f72(x94361,x94365,f341(f341(f311(x94361),x94364),x94363)),x94362)) % 19.23/19.04 [9437]E(f341(f341(f311(x94371),f548(x94372,x94373,x94374,x94375,x94371)),f549(x94372,x94373,x94374,x94375,x94371)),f341(f341(f311(x94371),x94374),x94373))+~P85(f341(f72(x94371,x94375,f341(f341(f311(x94371),x94374),x94373)),x94372)) % 19.23/19.04 [9517]P85(f341(f341(f343(x95171),f677(x95172,x95173,x95174,x95175,x95171)),x95174))+P85(f341(f341(f341(f55(x95171,f864(x95175,a850)),x95174),x95173),x95172)) % 19.23/19.04 [9522]P85(f341(f341(f343(x95221),f676(x95222,x95223,x95221,x95224,x95225)),x95223))+P85(f341(f341(f343(x95225),x95224),f341(f341(f55(x95221,f864(x95225,a850)),x95223),x95222))) % 19.23/19.04 [9530]P85(f341(f341(f343(x95301),f678(x95302,x95303,x95301,x95304,x95305)),x95303))+P85(f341(f341(f241(f864(x95305,a850)),x95304),f341(f341(f55(x95301,f864(x95305,a850)),x95303),x95302))) % 19.23/19.04 [9533]P85(f341(f341(x95331,f416(x95332,x95331,x95333,x95334,x95335)),x95332))+~P85(f341(f341(f341(f54(x95335,f864(x95334,a850)),x95333),x95331),x95332)) % 19.23/19.04 [9535]P85(f341(f341(f343(x95351),f416(x95352,x95353,x95354,x95355,x95351)),x95354))+~P85(f341(f341(f341(f54(x95351,f864(x95355,a850)),x95354),x95353),x95352)) % 19.23/19.04 [9545]P85(f341(f341(f343(x95451),f422(x95452,x95453,x95451,x95454,x95455)),x95453))+~P85(f341(f341(f343(x95455),x95454),f341(f341(f54(x95451,f864(x95455,a850)),x95453),x95452))) % 19.23/19.04 [9550]P85(f341(f341(f343(x95501),x95502),f341(x95503,f422(x95503,x95504,x95505,x95502,x95501))))+~P85(f341(f341(f343(x95501),x95502),f341(f341(f54(x95505,f864(x95501,a850)),x95504),x95503))) % 19.23/19.04 [9639]~P85(f341(f341(x96394,f677(x96395,x96394,x96393,x96392,x96391)),x96395))+P85(f341(f341(f341(f55(x96391,f864(x96392,a850)),x96393),x96394),x96395)) % 19.23/19.04 [9642]~P85(f341(f341(f343(x96421),x96422),f341(x96425,f676(x96425,x96424,x96423,x96422,x96421))))+P85(f341(f341(f343(x96421),x96422),f341(f341(f55(x96423,f864(x96421,a850)),x96424),x96425))) % 19.23/19.04 [9645]~P85(f341(f341(f241(f864(x96451,a850)),x96452),f341(x96455,f678(x96455,x96454,x96453,x96452,x96451))))+P85(f341(f341(f241(f864(x96451,a850)),x96452),f341(f341(f55(x96453,f864(x96451,a850)),x96454),x96455))) % 19.23/19.04 [9699]~P85(f341(f341(f343(x96991),f546(x96995,x96994,x96993,x96992,x96991)),f547(x96995,x96994,x96993,x96992,x96991)))+~P85(f341(f72(x96991,x96992,f341(f341(f311(x96991),x96993),x96994)),x96995)) % 19.23/19.04 [9700]~P85(f341(f341(f343(x97001),f548(x97005,x97004,x97003,x97002,x97001)),f549(x97005,x97004,x97003,x97002,x97001)))+~P85(f341(f72(x97001,x97002,f341(f341(f311(x97001),x97003),x97004)),x97005)) % 19.23/19.04 [9701]~P85(f341(f341(f343(f863(x97011,x97011)),f341(f341(f250(x97011,x97011),x97012),x97015)),f341(f341(f179(f863(x97011,x97011),a850),f341(a121,x97014)),x97013)))+P85(f341(f341(f343(f863(x97011,x97011)),f341(f341(f250(x97011,x97011),x97012),f667(x97013,x97014,x97015,x97012,x97011))),f341(f341(f179(f863(x97011,x97011),a850),x97014),x97013))) % 19.23/19.04 [9708]P85(f341(f76(x97081,x97081,x97082,f546(x97083,x97084,x97085,x97082,x97081),f547(x97083,x97084,x97085,x97082,x97081)),x97083))+~P85(f341(f72(x97081,x97082,f341(f341(f311(x97081),x97085),x97084)),x97083)) % 19.23/19.04 [9709]P85(f341(f76(x97091,x97091,x97092,f548(x97093,x97094,x97095,x97092,x97091),f549(x97093,x97094,x97095,x97092,x97091)),x97093))+~P85(f341(f72(x97091,x97092,f341(f341(f311(x97091),x97095),x97094)),x97093)) % 19.23/19.04 [9720]~P101(x97201)+P15(x97201,f341(f341(f149(x97202,x97201),x97203),f341(f133(x97202,f341(f341(f9(x97202,x97201,a850),f341(f341(f10(x97201,f864(x97201,a850),x97202),a338),x97203)),f341(x97204,x97205))),x97205))) % 19.23/19.04 [9775]~P85(f341(f341(f343(x97752),x97755),f341(f286(x97751,x97752,x97754),x97753)))+P85(f341(f341(f343(f863(x97751,x97752)),f341(f341(f250(x97751,x97752),f368(x97753,x97754,x97751,x97755,x97752)),x97755)),x97754)) % 19.23/19.04 [9776]~P85(f341(f341(f343(x97762),x97765),f341(f286(x97761,x97762,x97764),x97763)))+P85(f341(f341(f343(f863(x97761,x97762)),f341(f341(f250(x97761,x97762),f372(x97763,x97764,x97761,x97765,x97762)),x97765)),x97764)) % 19.23/19.04 [9796]~P85(f341(f341(f343(f863(x97961,x97961)),f341(f341(f250(x97961,x97961),x97965),x97964)),f341(f341(f179(f863(x97961,x97961),a850),f341(a121,x97963)),x97962)))+P85(f341(f341(f343(f863(x97961,x97961)),f341(f341(f250(x97961,x97961),f667(x97962,x97963,x97964,x97965,x97961)),x97964)),x97962)) % 19.23/19.04 [9799]~P85(f341(f341(f343(f863(x97991,x97991)),f341(f341(f250(x97991,x97991),x97995),x97994)),f341(f341(f179(f863(x97991,x97991),a850),f341(a121,x97993)),x97992)))+P85(f341(f341(f343(f863(x97991,x97991)),f341(f341(f250(x97991,x97991),f665(x97992,x97993,x97994,x97995,x97991)),x97994)),f341(f341(f179(f863(x97991,x97991),a850),x97993),x97992))) % 19.23/19.04 [9800]~P85(f341(f341(f343(f863(x98001,x98001)),f341(f341(f250(x98001,x98001),x98005),x98004)),f341(f341(f179(f863(x98001,x98001),a850),f341(a121,x98003)),x98002)))+P85(f341(f341(f343(f863(x98001,x98001)),f341(f341(f250(x98001,x98001),f666(x98002,x98003,x98004,x98005,x98001)),x98004)),f341(f341(f179(f863(x98001,x98001),a850),x98003),x98002))) % 19.23/19.04 [9801]~P85(f341(f341(f343(f863(f858(x98011),f858(x98011))),f341(f341(f250(f858(x98011),f858(x98011)),x98015),f341(f341(f146(x98011),x98014),x98013))),f153(x98011,x98012)))+P85(f341(f341(f343(f863(x98011,x98011)),f341(f341(f250(x98011,x98011),f727(x98012,x98013,x98014,x98015,x98011)),x98014)),x98012)) % 19.23/19.04 [6992]E(x69921,f188(x69922))+E(f174(x69923,x69922,f341(f341(f341(f81(x69923,f861(x69922)),x69924),x69925),x69921)),f341(f341(f311(x69923),x69925),f174(x69923,x69922,x69924))) % 19.23/19.04 [7509]~E(x75093,f185(f864(x75092,a850)))+E(f341(f341(f110(f864(x75091,a850)),f341(f341(f54(x75092,f864(x75091,a850)),x75093),x75094)),x75095),x75095) % 19.23/19.04 [7510]~E(x75103,f185(f864(x75102,a850)))+E(f341(f341(f111(f864(x75101,a850)),f341(f341(f55(x75102,f864(x75101,a850)),x75103),x75104)),x75105),x75105) % 19.23/19.04 [7872]~E(x78725,f188(x78722))+E(f174(x78721,x78722,f341(f341(f341(f81(x78721,f861(x78722)),x78723),x78724),x78725)),f341(f341(f3(f864(x78721,a850)),f174(x78721,x78722,x78723)),f341(f341(f311(x78721),x78724),f185(f864(x78721,a850))))) % 19.23/19.04 [7942]~E(x79423,f185(f864(x79422,a850)))+E(f341(f341(f3(f864(x79421,a850)),f341(f341(f55(x79422,f864(x79421,a850)),x79423),x79424)),x79425),f341(f341(f3(f864(x79421,a850)),f248(f864(x79421,a850))),x79425)) % 19.23/19.04 [8069]E(f341(f341(f154(x80691,f341(f341(f132(x80691),x80692),x80693)),x80694),x80695),f341(f341(f132(x80691),f341(f341(f154(x80691,x80692),x80694),x80695)),x80693))+~P85(f341(f341(f242(a857),x80694),f341(f186(f858(x80691)),x80692))) % 19.23/19.04 [8197]P85(f341(f341(f343(x81971),x81975),f341(f163(x81971),x81973)))+E(f341(f171(x81971,x81972,f341(f341(f172(x81971,x81972),x81973),f341(f341(f149(x81971,x81972),x81974),x81973))),x81975),f188(x81972)) % 19.23/19.04 [8306]~P85(f341(f341(f343(x83061),x83065),f341(f163(x83061),x83063)))+E(f341(f171(x83061,x83062,f341(f341(f172(x83061,x83062),x83063),f341(f341(f149(x83061,x83062),x83064),x83063))),x83065),f341(f235(x83062),f341(x83064,x83065))) % 19.23/19.04 [8337]E(f341(f341(f158(x83371),f341(f341(f149(a857,x83371),x83372),f136(a857,f341(f303(a857,x83373),x83374)))),x83375),f341(x83372,f341(f341(f89(a857),x83373),x83375)))+~P85(f341(f341(f242(a857),x83375),f341(f341(f3(a857),x83374),x83373))) % 19.23/19.04 [8350]E(x83501,f2(a108))+E(f128(x83502,x83503,f341(x83504,f341(f341(f3(a108),x83501),f87(a108))),f341(f341(f9(x83502,a108,f859(f861(x83503))),x83505),x83501)),f341(f199(x83502,x83503,x83504,x83505),x83501)) % 19.23/19.04 [8374]~E(x83743,f185(f864(x83741,a850)))+E(f341(f341(f54(x83741,f864(x83742,a850)),x83743),f341(f341(f10(f864(x83742,a850),f864(x83742,a850),x83741),f341(f110(f864(x83742,a850)),x83744)),x83745)),f185(f864(x83742,a850))) % 19.23/19.04 [8375]~E(x83753,f185(f864(x83751,a850)))+E(f341(f341(f55(x83751,f864(x83752,a850)),x83753),f341(f341(f10(f864(x83752,a850),f864(x83752,a850),x83751),f341(f3(f864(x83752,a850)),x83754)),x83755)),f248(f864(x83752,a850))) % 19.23/19.04 [8376]~E(x83763,f185(f864(x83761,a850)))+E(f341(f341(f55(x83761,f864(x83762,a850)),x83763),f341(f341(f10(f864(x83762,a850),f864(x83762,a850),x83761),f341(f111(f864(x83762,a850)),x83764)),x83765)),f248(f864(x83762,a850))) % 19.23/19.04 [8381]~P139(x83812)+E(f341(f341(f8(x83811,x83812),f341(f341(f10(x83812,x83812,x83811),f341(f90(x83812),x83813)),x83814)),x83815),f341(f341(f90(x83812),x83813),f341(f341(f8(x83811,x83812),x83814),x83815))) % 19.23/19.04 [8644]E(x86441,f185(f864(x86442,a850)))+E(f341(f341(f54(x86442,f864(x86443,a850)),x86441),f341(f341(f10(f864(x86443,a850),f864(x86443,a850),x86442),f341(f110(f864(x86443,a850)),x86444)),x86445)),f341(f341(f110(f864(x86443,a850)),x86444),f341(f341(f54(x86442,f864(x86443,a850)),x86441),x86445))) % 19.23/19.04 [8645]E(x86451,f185(f864(x86452,a850)))+E(f341(f341(f55(x86452,f864(x86453,a850)),x86451),f341(f341(f10(f864(x86453,a850),f864(x86453,a850),x86452),f341(f3(f864(x86453,a850)),x86454)),x86455)),f341(f341(f3(f864(x86453,a850)),x86454),f341(f341(f54(x86452,f864(x86453,a850)),x86451),x86455))) % 19.23/19.04 [8646]E(x86461,f185(f864(x86462,a850)))+E(f341(f341(f55(x86462,f864(x86463,a850)),x86461),f341(f341(f10(f864(x86463,a850),f864(x86463,a850),x86462),f341(f111(f864(x86463,a850)),x86464)),x86465)),f341(f341(f111(f864(x86463,a850)),x86464),f341(f341(f55(x86462,f864(x86463,a850)),x86461),x86465))) % 19.23/19.04 [9068]~P26(x90682,x90681,x90683,f341(f341(f110(f864(x90682,a850)),x90684),x90685))+E(f341(f341(f111(f864(x90681,a850)),f341(f312(x90682,x90681,x90683),f341(f341(f3(f864(x90682,a850)),x90684),x90685))),f341(f312(x90682,x90681,x90683),f341(f341(f3(f864(x90682,a850)),x90685),x90684))),f185(f864(x90681,a850))) % 19.23/19.04 [9322]~P85(f341(f341(f241(f864(x93223,a850)),f341(f286(x93221,x93223,x93224),x93222)),x93225))+P85(f341(f341(f241(f864(x93221,a850)),x93222),f341(f88(f864(x93221,a850)),f341(f286(x93223,x93221,f341(f287(x93221,x93223),x93224)),f341(f88(f864(x93223,a850)),x93225))))) % 19.23/19.04 [9345]~P26(x93451,x93452,x93453,f341(f341(f311(x93451),x93454),x93455))+~P85(f341(f341(f343(x93452),f341(x93453,x93454)),f341(f312(x93451,x93452,x93453),f341(f341(f3(f864(x93451,a850)),x93455),f341(f341(f311(x93451),x93454),f185(f864(x93451,a850))))))) % 19.23/19.04 [9393]P85(f341(f341(f241(f864(x93931,a850)),f341(f286(x93932,x93931,x93933),x93934)),x93935))+~P85(f341(f341(f241(f864(x93932,a850)),x93934),f341(f88(f864(x93932,a850)),f341(f286(x93931,x93932,f341(f287(x93932,x93931),x93933)),f341(f88(f864(x93931,a850)),x93935))))) % 19.23/19.04 [9467]~P79(x94671)+P85(f341(f341(f241(x94671),f341(f84(x94671),f341(f341(f3(x94671),f341(f341(f89(x94671),x94672),x94673)),f341(f341(f89(x94671),x94674),x94675)))),f341(f341(f89(x94671),f341(f84(x94671),f341(f341(f3(x94671),x94672),x94674))),f341(f84(x94671),f341(f341(f3(x94671),x94673),x94675))))) % 19.23/19.04 [9563]P85(f341(f341(f343(x95631),f425(x95632,x95633,x95634,x95631,x95635)),x95634))+P85(f341(f341(f241(f864(x95635,a850)),f341(f341(f54(x95631,f864(x95635,a850)),x95634),x95633)),x95632)) % 19.23/19.04 [9740]~P85(f341(f341(f241(f864(x97401,a850)),f341(x97404,f425(x97405,x97404,x97403,x97402,x97401))),x97405))+P85(f341(f341(f241(f864(x97401,a850)),f341(f341(f54(x97402,f864(x97401,a850)),x97403),x97404)),x97405)) % 19.23/19.04 [8488]E(f341(f341(f132(x84881),x84882),f341(f341(f154(x84881,x84883),f341(f341(f3(a857),x84884),f341(f186(f858(x84881)),x84882))),x84885)),f341(f341(f154(x84881,f341(f341(f132(x84881),x84882),x84883)),x84884),x84885))+P85(f341(f341(f242(a857),x84884),f341(f186(f858(x84881)),x84882))) % 19.23/19.04 [8513]~P138(x85131)+E(f341(f341(f89(x85131),f341(f341(f90(x85131),x85132),x85133)),f341(f341(f89(x85131),f341(f341(f90(x85131),x85134),x85133)),x85135)),f341(f341(f89(x85131),f341(f341(f90(x85131),f341(f341(f89(x85131),x85132),x85134)),x85133)),x85135)) % 19.23/19.04 [9024]~P139(x90241)+E(f341(f160(x90241),f341(f341(f149(x90242,x90241),f341(f341(f10(x90241,x90241,x90242),f341(f90(x90241),x90243)),x90244)),x90245)),f341(f341(f90(x90241),x90243),f341(f160(x90241),f341(f341(f149(x90242,x90241),x90244),x90245)))) % 19.23/19.04 [9401]~P139(x94012)+E(f341(f341(f8(x94011,x94012),f341(f341(f9(x94011,x94012,x94012),f341(f341(f10(x94012,f864(x94012,x94012),x94011),f90(x94012)),x94013)),x94014)),x94015),f341(f341(f90(x94012),f341(f341(f8(x94011,x94012),x94013),x94015)),x94014)) % 19.23/19.04 [9402]~P60(x94022)+E(f341(f341(f8(x94021,x94022),f341(f341(f9(x94021,x94022,x94022),f341(f341(f10(x94022,f864(x94022,x94022),x94021),f292(x94022)),x94023)),x94024)),x94025),f341(f341(f292(x94022),f341(f341(f8(x94021,x94022),x94023),x94025)),x94024)) % 19.23/19.04 [9409]~P71(x94092)+E(f341(f341(f11(x94091,x94092),f341(f341(f20(x94091,x94092,x94092),f341(f341(f10(x94092,f864(x94092,x94092),x94091),f90(x94092)),x94093)),x94094)),x94095),f341(f341(f90(x94092),f341(f341(f11(x94091,x94092),x94093),x94095)),f341(f341(f11(x94091,x94092),x94094),x94095))) % 19.23/19.04 [9410]~P68(x94102)+E(f341(f341(f8(x94101,x94102),f341(f341(f20(x94101,x94102,x94102),f341(f341(f10(x94102,f864(x94102,x94102),x94101),f89(x94102)),x94103)),x94104)),x94105),f341(f341(f89(x94102),f341(f341(f8(x94101,x94102),x94103),x94105)),f341(f341(f8(x94101,x94102),x94104),x94105))) % 19.23/19.04 [9411]~P3(x94112)+E(f341(f341(f8(x94111,x94112),f341(f341(f20(x94111,x94112,x94112),f341(f341(f10(x94112,f864(x94112,x94112),x94111),f3(x94112)),x94113)),x94114)),x94115),f341(f341(f3(x94112),f341(f341(f8(x94111,x94112),x94113),x94115)),f341(f341(f8(x94111,x94112),x94114),x94115))) % 19.23/19.04 [9448]~E(x94483,f185(f864(x94481,a850)))+E(f341(f341(f54(x94481,f864(x94482,a850)),x94483),f341(f341(f9(x94481,f864(x94482,a850),f864(x94482,a850)),f341(f341(f10(f864(x94482,a850),f864(f864(x94482,a850),f864(x94482,a850)),x94481),f110(f864(x94482,a850))),x94484)),x94485)),f185(f864(x94482,a850))) % 19.23/19.04 [9449]~E(x94493,f185(f864(x94491,a850)))+E(f341(f341(f55(x94491,f864(x94492,a850)),x94493),f341(f341(f9(x94491,f864(x94492,a850),f864(x94492,a850)),f341(f341(f10(f864(x94492,a850),f864(f864(x94492,a850),f864(x94492,a850)),x94491),f3(f864(x94492,a850))),x94494)),x94495)),f248(f864(x94492,a850))) % 19.23/19.04 [9450]~E(x94503,f185(f864(x94501,a850)))+E(f341(f341(f55(x94501,f864(x94502,a850)),x94503),f341(f341(f9(x94501,f864(x94502,a850),f864(x94502,a850)),f341(f341(f10(f864(x94502,a850),f864(f864(x94502,a850),f864(x94502,a850)),x94501),f111(f864(x94502,a850))),x94504)),x94505)),f248(f864(x94502,a850))) % 19.23/19.04 [9477]E(x94771,f185(f864(x94772,a850)))+E(f341(f341(f54(x94772,f864(x94773,a850)),x94771),f341(f341(f9(x94772,f864(x94773,a850),f864(x94773,a850)),f341(f341(f10(f864(x94773,a850),f864(f864(x94773,a850),f864(x94773,a850)),x94772),f110(f864(x94773,a850))),x94774)),x94775)),f341(f341(f110(f864(x94773,a850)),f341(f341(f54(x94772,f864(x94773,a850)),x94771),x94774)),x94775)) % 19.23/19.04 [9478]E(x94781,f185(f864(x94782,a850)))+E(f341(f341(f55(x94782,f864(x94783,a850)),x94781),f341(f341(f9(x94782,f864(x94783,a850),f864(x94783,a850)),f341(f341(f10(f864(x94783,a850),f864(f864(x94783,a850),f864(x94783,a850)),x94782),f3(f864(x94783,a850))),x94784)),x94785)),f341(f341(f3(f864(x94783,a850)),f341(f341(f55(x94782,f864(x94783,a850)),x94781),x94784)),x94785)) % 19.23/19.04 [9479]E(x94791,f185(f864(x94792,a850)))+E(f341(f341(f55(x94792,f864(x94793,a850)),x94791),f341(f341(f9(x94792,f864(x94793,a850),f864(x94793,a850)),f341(f341(f10(f864(x94793,a850),f864(f864(x94793,a850),f864(x94793,a850)),x94792),f111(f864(x94793,a850))),x94794)),x94795)),f341(f341(f111(f864(x94793,a850)),f341(f341(f55(x94792,f864(x94793,a850)),x94791),x94794)),x94795)) % 19.23/19.04 [9073]~P85(f341(f341(f241(a857),x90731),x90734))+E(f341(f341(f3(a857),f341(f341(f89(a857),f341(f341(f90(a857),x90731),x90732)),x90733)),f341(f341(f89(a857),f341(f341(f90(a857),x90734),x90732)),x90735)),f341(f341(f3(a857),x90733),f341(f341(f89(a857),f341(f341(f90(a857),f341(f341(f3(a857),x90734),x90731)),x90732)),x90735))) % 19.23/19.04 [9622]~P139(x96221)+E(f341(f160(x96221),f341(f341(f149(x96222,x96221),f341(f341(f9(x96222,x96221,x96221),f341(f341(f10(x96221,f864(x96221,x96221),x96222),f90(x96221)),x96223)),x96224)),x96225)),f341(f341(f90(x96221),f341(f160(x96221),f341(f341(f149(x96222,x96221),x96223),x96225))),x96224)) % 19.23/19.04 [9628]~P68(x96281)+E(f341(f160(x96281),f341(f341(f149(x96282,x96281),f341(f341(f20(x96282,x96281,x96281),f341(f341(f10(x96281,f864(x96281,x96281),x96282),f89(x96281)),x96283)),x96284)),x96285)),f341(f341(f89(x96281),f341(f160(x96281),f341(f341(f149(x96282,x96281),x96283),x96285))),f341(f160(x96281),f341(f341(f149(x96282,x96281),x96284),x96285)))) % 19.23/19.04 [9629]~P3(x96291)+E(f341(f160(x96291),f341(f341(f149(x96292,x96291),f341(f341(f20(x96292,x96291,x96291),f341(f341(f10(x96291,f864(x96291,x96291),x96292),f3(x96291)),x96293)),x96294)),x96295)),f341(f341(f3(x96291),f341(f160(x96291),f341(f341(f149(x96292,x96291),x96293),x96295))),f341(f160(x96291),f341(f341(f149(x96292,x96291),x96294),x96295)))) % 19.23/19.04 [9289]~P85(f341(f341(f241(a857),x92894),x92891))+E(f341(f341(f3(a857),f341(f341(f89(a857),f341(f341(f90(a857),x92891),x92892)),x92893)),f341(f341(f89(a857),f341(f341(f90(a857),x92894),x92892)),x92895)),f341(f341(f3(a857),f341(f341(f89(a857),f341(f341(f90(a857),f341(f341(f3(a857),x92891),x92894)),x92892)),x92893)),x92895)) % 19.23/19.04 [10026]P25(x100261,x100262,f341(f312(a853,f856(x100261),f341(f341(f20(a853,f864(x100261,f864(a855,a850)),f856(x100261)),f341(f341(f20(a853,a851,f864(f864(x100261,f864(a855,a850)),f856(x100261))),f341(f341(f10(f864(x100261,f864(a855,a850)),f864(a851,f864(f864(x100261,f864(a855,a850)),f856(x100261))),a853),f100(x100261)),x100263)),a29)),x100264)),x100265))+~P25(x100261,f341(f341(f110(f864(f856(x100261),a850)),x100262),f341(f312(a853,f856(x100261),f341(f341(f20(a853,f864(x100261,f864(a855,a850)),f856(x100261)),f341(f341(f20(a853,a851,f864(f864(x100261,f864(a855,a850)),f856(x100261))),f341(f341(f10(f864(x100261,f864(a855,a850)),f864(a851,f864(f864(x100261,f864(a855,a850)),f856(x100261))),a853),f100(x100261)),x100263)),a29)),x100264)),x100265)),f341(f312(a853,f856(x100261),f341(f341(f20(a853,f864(x100261,f864(a855,a850)),f856(x100261)),f341(f341(f20(a853,a851,f864(f864(x100261,f864(a855,a850)),f856(x100261))),f341(f341(f10(f864(x100261,f864(a855,a850)),f864(a851,f864(f864(x100261,f864(a855,a850)),f856(x100261))),a853),f100(x100261)),x100263)),f341(f341(f10(f861(a851),a851,a853),f239(a851)),a32))),x100264)),x100265)) % 19.23/19.04 [5161]E(x51611,x51612)+~E(f33(x51613,x51614,x51611),f33(x51615,x51616,x51612)) % 19.23/19.04 [5162]E(x51621,x51622)+~E(f33(x51623,x51621,x51624),f33(x51625,x51622,x51626)) % 19.23/19.04 [5163]E(x51631,x51632)+~E(f33(x51631,x51633,x51634),f33(x51632,x51635,x51636)) % 19.23/19.04 [5164]E(x51641,x51642)+~E(f35(x51643,x51644,x51641),f35(x51645,x51646,x51642)) % 19.23/19.04 [5165]E(x51651,x51652)+~E(f35(x51653,x51651,x51654),f35(x51655,x51652,x51656)) % 19.23/19.04 [5166]E(x51661,x51662)+~E(f35(x51661,x51663,x51664),f35(x51662,x51665,x51666)) % 19.23/19.04 [5167]E(x51671,x51672)+~E(f34(x51673,x51674,x51671),f34(x51675,x51676,x51672)) % 19.23/19.04 [5168]E(x51681,x51682)+~E(f34(x51683,x51681,x51684),f34(x51685,x51682,x51686)) % 19.23/19.04 [5169]E(x51691,x51692)+~E(f34(x51691,x51693,x51694),f34(x51692,x51695,x51696)) % 19.23/19.04 [7179]E(x71791,x71792)+~E(f223(x71793,x71794,x71795,x71791),f223(x71793,x71794,x71796,x71792)) % 19.23/19.04 [7180]E(x71801,x71802)+~E(f223(x71803,x71804,x71801,x71805),f223(x71803,x71804,x71802,x71806)) % 19.23/19.04 [6626]E(f341(f175(x66261,x66262,x66263,x66264),x66265),f341(f235(x66262),x66266))+~E(f341(x66264,x66265),f341(f235(x66262),x66266)) % 19.23/19.04 [6776]E(f341(f237(f861(x67761),x67762,f188(x67761),x67763),f341(x67764,x67765)),f341(x67763,x67766))+~E(f341(x67764,x67765),f341(f235(x67762),x67766)) % 19.23/19.04 [8317]~P20(x83175,x83171,x83172,x83176)+E(f341(f82(x83171,x83171,x83171,f341(x83172,x83173)),f341(x83172,x83174)),f341(f82(x83171,x83171,x83171,f341(x83172,x83174)),f341(x83172,x83173))) % 19.23/19.04 [8548]~P54(x85484,x85485,x85482,x85481,x85486)+E(f341(x85481,f341(x85482,x85483)),x85483) % 19.23/19.04 [8690]P26(x86901,x86902,x86903,x86904)+~P26(x86901,x86905,f341(f82(x86902,x86905,x86901,x86906),x86903),x86904) % 19.23/19.04 [8767]~P26(x87674,x87672,f341(f82(x87671,x87672,x87674,x87673),x87675),x87676)+P26(x87671,x87672,x87673,f341(f312(x87674,x87671,x87675),x87676)) % 19.23/19.04 [9412]P85(f341(f71(x94121),x94122))+~P85(f341(f76(x94121,x94123,x94124,x94125,x94122),x94126)) % 19.23/19.04 [9422]~P85(f341(f341(f343(x94224),x94223),f301(x94224,x94225,x94221,x94222,x94226)))+P85(f341(f341(x94221,x94222),x94223)) % 19.23/19.04 [9423]~P85(f341(f341(f343(x94234),x94233),f298(x94234,x94231,x94235,x94232,x94236)))+P85(f341(f341(x94231,x94232),x94233)) % 19.23/19.04 [9424]~P85(f341(f341(f343(x94244),x94242),f301(x94244,x94241,x94245,x94246,x94243)))+P85(f341(f341(x94241,x94242),x94243)) % 19.23/19.04 [9425]~P85(f341(f341(f343(x94254),x94252),f298(x94254,x94255,x94251,x94256,x94253)))+P85(f341(f341(x94251,x94252),x94253)) % 19.23/19.04 [9594]~P38(f34(x95943,x95944,x95941),x95942,x95945,x95946)+P38(x95941,f341(f341(f341(a194,x95942),f42(x95943)),f341(x95944,x95942)),x95945,f482(x95946,x95945,x95942,x95941,x95944,x95943)) % 19.23/19.04 [9607]~P38(f33(x96076,x96071,x96073),x96072,x96074,x96075)+P38(f341(a29,x96071),f341(f341(f341(a194,f341(f341(a196,x96072),a197)),f42(a28)),f341(x96073,x96072)),x96074,f535(x96075,x96074,x96072,x96073,x96071,x96076)) % 19.23/19.04 [5647]E(x56471,x56472)+~E(f341(f341(f250(x56473,x56474),x56475),x56471),f341(f341(f250(x56473,x56474),x56476),x56472)) % 19.23/19.04 [5649]E(x56491,x56492)+~E(f341(f341(f250(x56493,x56494),x56491),x56495),f341(f341(f250(x56493,x56494),x56492),x56496)) % 19.23/19.04 [5788]~P17(x57885,x57886,x57881)+E(f341(f341(x57881,x57882),f341(f341(x57881,x57883),x57884)),f341(f341(x57881,x57883),f341(f341(x57881,x57882),x57884))) % 19.23/19.04 [7250]~P33(x72504,x72501,f341(f341(f146(x72504),x72502),x72505),f341(f341(f146(x72504),x72503),x72506))+P85(f341(f341(x72501,x72502),x72503)) % 19.23/19.04 [7628]P33(x76281,x76282,x76283,x76284)+~P33(x76281,x76282,f341(f341(f146(x76281),x76285),x76283),f341(f341(f146(x76281),x76286),x76284)) % 19.23/19.04 [8252]~P38(x82523,f341(f341(f341(a194,x82524),f42(x82521)),f341(x82522,x82524)),x82525,x82526)+P38(f34(x82521,x82522,x82523),x82524,x82525,f341(f341(f341(a194,x82526),f42(x82521)),f341(f341(a195,x82524),x82521))) % 19.23/19.04 [8635]~P54(x86355,x86351,x86352,x86356,x86354)+P85(f341(f341(f343(x86351),f341(x86352,x86353)),x86354)) % 19.23/19.04 [8789]E(f341(f85(x87891,x87892,x87893,x87894,x87895),x87896),f341(x87893,x87896))+P85(f341(f341(f343(x87891),x87896),x87895)) % 19.23/19.04 [8807]~E(x88073,f341(f341(f146(x88071),x88075),x88076))+P85(f341(f341(f343(f863(f858(x88071),f858(x88071))),f341(f341(f250(f858(x88071),f858(x88071)),x88072),f341(f341(f132(x88071),x88072),x88073))),f143(x88071,x88074))) % 19.23/19.04 [8811]E(f341(f85(x88111,x88112,x88113,x88114,x88115),x88116),f341(x88114,x88116))+~P85(f341(f341(f343(x88111),x88116),x88115)) % 19.23/19.04 [8815]E(f341(f177(x88151,x88152,x88153,x88154,x88155),x88156),f341(x88153,x88156))+P85(f341(f341(f343(x88151),x88156),f341(f163(x88151),x88154))) % 19.23/19.04 [9015]~P38(f341(a29,x90152),f341(f341(f341(a194,f341(f341(a196,x90154),a197)),f42(a28)),f341(x90153,x90154)),x90155,x90156)+P38(f33(x90151,x90152,x90153),x90154,x90155,f341(f341(f341(a194,f341(f341(a196,x90156),f341(a195,x90154))),x90151),f341(f341(a195,x90156),a27))) % 19.23/19.04 [9489]~P24(x94894,x94892,x94895,x94893,x94896,x94891)+E(f341(x94891,f185(f864(x94892,a850))),x94893) % 19.23/19.04 [9605]P38(x96051,f341(f341(f341(a194,x96052),f42(x96053)),f341(x96054,x96052)),x96055,f417(x96056,x96055,x96052,x96051,x96054,x96053))+~P38(f34(x96053,x96054,x96051),x96052,x96055,f341(f341(f341(a194,x96056),f42(x96053)),f341(f341(a195,x96052),x96053))) % 19.23/19.04 [9633]P38(f341(a29,x96331),f341(f341(f341(a194,f341(f341(a196,x96332),a197)),f42(a28)),f341(x96333,x96332)),x96334,f506(x96335,x96334,x96332,x96333,x96331,x96336))+~P38(f33(x96336,x96331,x96333),x96332,x96334,f341(f341(f341(a194,f341(f341(a196,x96335),f341(a195,x96332))),x96336),f341(f341(a195,x96335),a27))) % 19.23/19.04 [9702]~E(f341(x97024,f341(f249(x97021,x97023),x97025)),f341(x97026,f341(f249(x97021,x97023),x97025)))+E(f341(f261(x97021,x97022,x97023,x97023,x97024,f41(x97023)),x97025),f341(f261(x97021,x97022,x97023,x97023,x97026,f41(x97023)),x97025)) % 19.23/19.04 [9703]~E(f341(x97034,f341(f259(x97031,x97032),x97035)),f341(x97036,f341(f259(x97031,x97032),x97035)))+E(f341(f261(x97031,x97031,x97032,x97033,f41(x97031),x97034),x97035),f341(f261(x97031,x97031,x97032,x97033,f41(x97031),x97036),x97035)) % 19.23/19.04 [9763]~E(f341(f261(x97632,x97636,x97633,x97633,x97631,f41(x97633)),x97634),f341(f261(x97632,x97636,x97633,x97633,x97635,f41(x97633)),x97634))+E(f341(x97631,f341(f249(x97632,x97633),x97634)),f341(x97635,f341(f249(x97632,x97633),x97634))) % 19.23/19.04 [9764]~E(f341(f261(x97642,x97642,x97643,x97646,f41(x97642),x97641),x97644),f341(f261(x97642,x97642,x97643,x97646,f41(x97642),x97645),x97644))+E(f341(x97641,f341(f259(x97642,x97643),x97644)),f341(x97645,f341(f259(x97642,x97643),x97644))) % 19.23/19.04 [9825]~P38(f34(x98256,x98255,x98254),x98253,x98252,x98251)+E(f341(f341(f341(a194,f482(x98251,x98252,x98253,x98254,x98255,x98256)),f42(x98256)),f341(f341(a195,x98253),x98256)),x98251) % 19.23/19.04 [9832]~P38(f34(x98326,x98325,x98324),x98323,x98322,f341(f341(f341(a194,x98321),f42(x98326)),f341(f341(a195,x98323),x98326)))+E(f341(f341(f341(a194,f417(x98321,x98322,x98323,x98324,x98325,x98326)),f42(x98326)),f341(f341(a195,x98323),x98326)),f341(f341(f341(a194,x98321),f42(x98326)),f341(f341(a195,x98323),x98326))) % 19.23/19.04 [8724]P85(f341(f341(f343(x87241),x87242),x87243))+~P85(f341(f341(f343(f863(x87241,x87244)),f341(f341(f250(x87241,x87244),x87242),x87245)),f341(f341(f257(x87241,x87244),x87243),x87246))) % 19.23/19.04 [8739]P85(f341(f341(f343(x87391),x87392),f341(x87393,x87394)))+~P85(f341(f341(f343(f863(x87395,x87391)),f341(f341(f250(x87395,x87391),x87394),x87392)),f341(f341(f257(x87395,x87391),x87396),x87393))) % 19.23/19.04 [8813]~E(f341(f186(f858(x88131)),x88134),f341(f186(f858(x88132)),x88135))+E(f177(x88131,x88132,x88133,x88134,f341(f341(f132(x88132),x88135),x88136)),f177(x88131,x88132,x88133,x88134,x88135)) % 19.23/19.04 [8814]~E(f341(f186(f858(x88141)),x88144),f341(f186(f858(x88142)),x88146))+E(f177(x88141,x88142,x88143,f341(f341(f132(x88141),x88144),x88145),x88146),f177(x88141,x88142,x88143,x88144,x88146)) % 19.23/19.04 [9048]P85(f341(f341(f343(x90481),x90484),f174(x90481,x90482,x90486)))+E(f175(x90481,x90482,f341(f341(f341(f81(x90481,f861(x90482)),x90483),x90484),f341(f235(x90482),x90485)),x90486),f341(f341(f341(f81(x90481,f861(x90482)),f175(x90481,x90482,x90483,x90486)),x90484),f341(f235(x90482),x90485))) % 19.23/19.04 [9139]P85(f341(f341(f343(f863(x91391,x91391)),f341(f341(f250(x91391,x91391),f341(x91392,x91393)),f341(x91392,x91394))),x91395))+~P85(f341(f341(f343(f863(x91396,x91396)),f341(f341(f250(x91396,x91396),x91393),x91394)),f341(f341(f289(x91391,x91396),x91395),x91392))) % 19.23/19.04 [9152]~P85(f341(f341(f343(f863(x91524,x91524)),f341(f341(f250(x91524,x91524),f341(x91526,x91522)),f341(x91526,x91523))),x91525))+P85(f341(f341(f343(f863(x91521,x91521)),f341(f341(f250(x91521,x91521),x91522),x91523)),f341(f341(f289(x91524,x91521),x91525),x91526))) % 19.23/19.04 [9766]E(f341(f341(f250(x97661,x97662),f711(x97663,x97664,x97665,x97666,x97662,x97661)),f717(x97663,x97664,x97665,x97666,x97662,x97661)),x97666)+~P85(f341(f341(f343(f863(x97661,x97662)),x97666),f341(f341(f290(x97661,x97665,x97662),x97664),x97663))) % 19.23/19.04 [9960]~P38(f33(x99606,x99605,x99604),x99603,x99602,x99601)+E(f341(f341(f341(a194,f341(f341(a196,f535(x99601,x99602,x99603,x99604,x99605,x99606)),f341(a195,x99603))),x99606),f341(f341(a195,f535(x99601,x99602,x99603,x99604,x99605,x99606)),a27)),x99601) % 19.23/19.04 [9965]~P38(f33(x99656,x99655,x99654),x99653,x99652,f341(f341(f341(a194,f341(f341(a196,x99651),f341(a195,x99653))),x99656),f341(f341(a195,x99651),a27)))+E(f341(f341(f341(a194,f341(f341(a196,f506(x99651,x99652,x99653,x99654,x99655,x99656)),f341(a195,x99653))),x99656),f341(f341(a195,f506(x99651,x99652,x99653,x99654,x99655,x99656)),a27)),f341(f341(f341(a194,f341(f341(a196,x99651),f341(a195,x99653))),x99656),f341(f341(a195,x99651),a27))) % 19.23/19.04 [9976]~P85(f341(f341(f343(f863(x99761,x99766)),x99765),f341(f341(f290(x99761,x99762,x99766),x99764),x99763)))+P85(f341(f341(f343(f863(x99761,x99762)),f341(f341(f250(x99761,x99762),f711(x99763,x99764,x99762,x99765,x99766,x99761)),f718(x99763,x99764,x99762,x99765,x99766,x99761))),x99764)) % 19.23/19.04 [9977]~P85(f341(f341(f343(f863(x99776,x99772)),x99775),f341(f341(f290(x99776,x99771,x99772),x99774),x99773)))+P85(f341(f341(f343(f863(x99771,x99772)),f341(f341(f250(x99771,x99772),f718(x99773,x99774,x99771,x99775,x99772,x99776)),f717(x99773,x99774,x99771,x99775,x99772,x99776))),x99773)) % 19.23/19.04 [6065]~E(x60656,x60654)+E(f341(f341(f341(f341(f81(x60651,x60652),x60653),x60654),x60655),x60656),x60655) % 19.23/19.04 [6114]E(x61141,x61142)+E(f341(f341(f341(f341(f81(x61143,x61144),x61145),x61142),x61146),x61141),f341(x61145,x61141)) % 19.23/19.04 [7694]~P6(x76942)+E(f341(f341(f54(x76941,x76942),x76943),f341(f341(f9(x76941,x76944,x76942),x76945),x76946)),f341(f341(f341(f54(x76941,f864(x76944,x76942)),x76943),x76945),x76946)) % 19.23/19.04 [7695]~P6(x76952)+E(f341(f341(f55(x76951,x76952),x76953),f341(f341(f9(x76951,x76954,x76952),x76955),x76956)),f341(f341(f341(f55(x76951,f864(x76954,x76952)),x76953),x76955),x76956)) % 19.23/19.04 [8470]E(f341(f341(f54(x84701,f864(x84702,a850)),x84703),f341(f341(f10(f864(x84702,a850),f864(x84702,a850),x84701),f341(f311(x84702),x84704)),x84705)),f341(f341(f311(x84702),x84704),f341(f341(f54(x84701,f864(x84702,a850)),x84703),x84705)))+~P85(f341(f341(f343(x84701),x84706),x84703)) % 19.23/19.04 [8853]~P6(x88532)+E(f341(f341(f54(x88531,x88532),x88533),f341(f341(f10(f864(x88534,x88532),x88532,x88531),f341(f54(x88534,x88532),x88535)),f341(f9(x88534,x88531,x88532),x88536))),f341(f341(f54(x88534,x88532),x88535),f341(f341(f10(f864(x88531,x88532),x88532,x88534),f341(f54(x88531,x88532),x88533)),x88536))) % 19.23/19.04 [8854]~P6(x88542)+E(f341(f341(f55(x88541,x88542),x88543),f341(f341(f10(f864(x88544,x88542),x88542,x88541),f341(f55(x88544,x88542),x88545)),f341(f9(x88544,x88541,x88542),x88546))),f341(f341(f55(x88544,x88542),x88545),f341(f341(f10(f864(x88541,x88542),x88542,x88544),f341(f55(x88541,x88542),x88543)),x88546))) % 19.23/19.04 [9056]P85(f341(f341(f343(x90561),x90562),f341(f163(x90561),x90563)))+~P85(f341(f341(f343(f863(x90564,x90561)),f341(f341(f250(x90564,x90561),x90565),x90562)),f341(f163(f863(x90564,x90561)),f341(f341(f172(x90564,x90561),x90566),x90563)))) % 19.23/19.04 [9057]P85(f341(f341(f343(x90571),x90572),f341(f163(x90571),x90573)))+~P85(f341(f341(f343(f863(x90571,x90574)),f341(f341(f250(x90571,x90574),x90572),x90575)),f341(f163(f863(x90571,x90574)),f341(f341(f172(x90571,x90574),x90573),x90576)))) % 19.23/19.04 [9150]P85(f341(f341(f241(f864(x91501,a850)),f341(f286(x91502,x91501,x91503),x91504)),x91505))+~P85(f341(f341(f241(f864(f863(x91502,x91501),a850)),x91503),f341(f341(f257(x91502,x91501),x91506),f341(f18(f864(x91501,a850),x91502),x91505)))) % 19.23/19.04 [9325]P85(f341(f341(f343(f863(f858(x93251),f858(x93251))),f341(f341(f250(f858(x93251),f858(x93251)),f341(f341(f146(x93251),x93252),x93253)),f341(f341(f146(x93251),x93254),x93255))),f143(x93251,x93256)))+~P85(f341(f341(f343(f863(x93251,x93251)),f341(f341(f250(x93251,x93251),x93252),x93254)),x93256)) % 19.23/19.04 [9762]E(f341(f341(f250(x97621,x97622),f618(x97623,x97624,x97625,x97622,x97621,x97626)),f619(x97623,x97624,x97625,x97622,x97621,x97626)),x97626)+P85(f341(f341(f343(x97625),x97624),f341(f341(f260(x97621,x97622,f864(x97625,a850)),x97623),x97626))) % 19.23/19.04 [9767]E(f341(f341(f250(x97671,x97672),f620(x97673,x97674,x97672,x97671,x97675,x97676)),f621(x97673,x97674,x97672,x97671,x97675,x97676)),x97673)+~P85(f341(f341(f343(x97676),x97675),f341(f341(f260(x97671,x97672,f864(x97676,a850)),x97674),x97673))) % 19.23/19.04 [9929]P85(f341(f341(f343(x99291),x99292),f341(f341(x99293,f620(x99294,x99293,x99295,x99296,x99292,x99291)),f621(x99294,x99293,x99295,x99296,x99292,x99291))))+~P85(f341(f341(f343(x99291),x99292),f341(f341(f260(x99296,x99295,f864(x99291,a850)),x99293),x99294))) % 19.23/19.04 [9953]~P85(f341(f341(f343(x99531),x99532),f341(f341(x99535,f618(x99535,x99532,x99531,x99534,x99533,x99536)),f619(x99535,x99532,x99531,x99534,x99533,x99536))))+P85(f341(f341(f343(x99531),x99532),f341(f341(f260(x99533,x99534,f864(x99531,a850)),x99535),x99536))) % 19.23/19.04 [7819]P85(f341(f341(f343(x78191),x78194),x78196))+E(f178(x78191,x78192,f341(f341(f341(f81(x78191,f861(x78192)),x78193),x78194),x78195),x78196),f178(x78191,x78192,x78193,x78196)) % 19.23/19.04 [7894]P85(f341(f341(f343(x78941),x78944),x78946))+E(f341(f312(x78941,x78942,f341(f341(f341(f81(x78941,x78942),x78943),x78944),x78945)),x78946),f341(f312(x78941,x78942,x78943),x78946)) % 19.23/19.04 [7922]P85(f341(f341(f343(x79221),x79224),f341(f163(x79221),x79226)))+E(f341(f341(f149(x79221,x79222),f341(f341(f341(f81(x79221,x79222),x79223),x79224),x79225)),x79226),f341(f341(f149(x79221,x79222),x79223),x79226)) % 19.23/19.04 [8367]E(x83671,x83672)+E(f341(f341(f154(x83673,f341(f341(f154(x83673,x83674),x83671),x83675)),x83672),x83676),f341(f341(f154(x83673,f341(f341(f154(x83673,x83674),x83672),x83676)),x83671),x83675)) % 19.23/19.04 [8859]~P85(f341(f341(f343(x88593),x88596),x88595))+E(f341(f341(f311(x88591),x88592),f341(f312(x88593,x88591,x88594),f341(f341(f3(f864(x88593,a850)),x88595),f341(f341(f311(x88593),x88596),f185(f864(x88593,a850)))))),f341(f312(x88593,x88591,f341(f341(f341(f81(x88593,x88591),x88594),x88596),x88592)),x88595)) % 19.23/19.04 [9587]E(f177(x95871,x95872,x95873,f341(f341(f132(x95871),x95874),f341(f341(f146(x95871),x95875),f122(x95871))),x95876),f341(f341(f341(f81(x95871,f861(x95872)),f177(x95871,x95872,x95873,x95874,x95876)),x95875),f341(f235(x95872),f341(f341(f158(x95872),x95876),f341(f186(f858(x95871)),x95874)))))+~P85(f341(f341(f242(a857),f341(f186(f858(x95871)),x95874)),f341(f186(f858(x95872)),x95876))) % 19.23/19.04 [8685]~E(x86853,x86856)+E(f341(f171(x86851,x86852,f341(f341(f146(f863(x86851,x86852)),f341(f341(f250(x86851,x86852),x86853),x86854)),x86855)),x86856),f341(f235(x86852),x86854)) % 19.23/19.04 [8726]E(x87261,x87262)+E(f341(f171(x87263,x87264,f341(f341(f146(f863(x87263,x87264)),f341(f341(f250(x87263,x87264),x87261),x87265)),x87266)),x87262),f341(f171(x87263,x87264,x87266),x87262)) % 19.23/19.04 [8934]~P85(f341(f341(x89344,x89345),x89346))+P85(f341(f341(f341(f341(f110(f864(x89341,f864(x89342,a850))),x89343),x89344),x89345),x89346)) % 19.23/19.04 [8936]~P85(f341(f341(x89363,x89365),x89366))+P85(f341(f341(f341(f341(f110(f864(x89361,f864(x89362,a850))),x89363),x89364),x89365),x89366)) % 19.23/19.04 [9189]P85(f341(f341(x91891,x91892),x91893))+~P85(f341(f341(f341(f341(f111(f864(x91894,f864(x91895,a850))),x91896),x91891),x91892),x91893)) % 19.23/19.04 [9190]P85(f341(f341(x91901,x91902),x91903))+~P85(f341(f341(f341(f341(f111(f864(x91904,f864(x91905,a850))),x91901),x91906),x91902),x91903)) % 19.23/19.04 [9612]~P71(x96122)+E(f341(f341(f11(x96121,x96122),f341(f341(f9(x96121,f864(x96123,a850),x96122),f341(f341(f10(f864(x96123,x96122),f864(f864(x96123,a850),x96122),x96121),f11(x96123,x96122)),x96124)),x96125)),x96126),f341(f341(f11(f863(x96121,x96123),x96122),f341(f260(x96121,x96123,x96122),x96124)),f341(f341(f257(x96121,x96123),x96126),f341(f18(f864(x96123,a850),x96121),x96125)))) % 19.23/19.04 [9613]~P68(x96132)+E(f341(f341(f8(x96131,x96132),f341(f341(f9(x96131,f864(x96133,a850),x96132),f341(f341(f10(f864(x96133,x96132),f864(f864(x96133,a850),x96132),x96131),f8(x96133,x96132)),x96134)),x96135)),x96136),f341(f341(f8(f863(x96131,x96133),x96132),f341(f260(x96131,x96133,x96132),x96134)),f341(f341(f257(x96131,x96133),x96136),f341(f18(f864(x96133,a850),x96131),x96135)))) % 19.23/19.04 [9729]~P68(x97292)+E(f341(f341(f8(x97291,x97292),f341(f341(f9(x97291,f864(x97293,a850),x97292),f341(f341(f10(f864(x97293,x97292),f864(f864(x97293,a850),x97292),x97291),f8(x97293,x97292)),f341(f9(x97293,x97291,x97292),x97294))),x97295)),x97296),f341(f341(f8(x97293,x97292),f341(f341(f9(x97293,f864(x97291,a850),x97292),f341(f341(f10(f864(x97291,x97292),f864(f864(x97291,a850),x97292),x97293),f8(x97291,x97292)),x97294)),x97296)),x97295)) % 19.23/19.04 [9453]~P85(f341(f341(f343(x94531),x94535),x94534))+E(f341(f341(f341(f81(x94531,f861(x94532)),f178(x94531,x94532,x94533,f341(f341(f3(f864(x94531,a850)),x94534),f341(f341(f311(x94531),x94535),f185(f864(x94531,a850)))))),x94535),x94536),f178(x94531,x94532,f341(f341(f341(f81(x94531,f861(x94532)),x94533),x94535),x94536),x94534)) % 19.23/19.04 [10029]~P85(f341(f341(f343(f863(x100291,x100292)),f341(f341(f250(x100291,x100292),x100295),x100296)),f341(f341(f110(f864(f863(x100291,x100292),a850)),x100293),x100294)))+P85(f341(f341(f341(f341(f110(f864(x100291,f864(x100292,a850))),f341(f341(f9(x100291,f864(f863(x100291,x100292),a850),f864(x100292,a850)),f341(f341(f10(f864(x100292,f864(f864(f863(x100291,x100292),a850),a850)),f864(f864(f863(x100291,x100292),a850),f864(x100292,a850)),x100291),f9(x100292,f864(f863(x100291,x100292),a850),a850)),f341(f341(f10(f864(x100292,f863(x100291,x100292)),f864(x100292,f864(f864(f863(x100291,x100292),a850),a850)),x100291),f341(f10(f863(x100291,x100292),f864(f864(f863(x100291,x100292),a850),a850),x100292),f343(f863(x100291,x100292)))),f250(x100291,x100292)))),x100293)),f341(f341(f9(x100291,f864(f863(x100291,x100292),a850),f864(x100292,a850)),f341(f341(f10(f864(x100292,f864(f864(f863(x100291,x100292),a850),a850)),f864(f864(f863(x100291,x100292),a850),f864(x100292,a850)),x100291),f9(x100292,f864(f863(x100291,x100292),a850),a850)),f341(f341(f10(f864(x100292,f863(x100291,x100292)),f864(x100292,f864(f864(f863(x100291,x100292),a850),a850)),x100291),f341(f10(f863(x100291,x100292),f864(f864(f863(x100291,x100292),a850),a850),x100292),f343(f863(x100291,x100292)))),f250(x100291,x100292)))),x100294)),x100295),x100296)) % 19.23/19.04 [10030]~P85(f341(f341(f343(f863(x100301,x100302)),f341(f341(f250(x100301,x100302),x100305),x100306)),f341(f341(f111(f864(f863(x100301,x100302),a850)),x100303),x100304)))+P85(f341(f341(f341(f341(f111(f864(x100301,f864(x100302,a850))),f341(f341(f9(x100301,f864(f863(x100301,x100302),a850),f864(x100302,a850)),f341(f341(f10(f864(x100302,f864(f864(f863(x100301,x100302),a850),a850)),f864(f864(f863(x100301,x100302),a850),f864(x100302,a850)),x100301),f9(x100302,f864(f863(x100301,x100302),a850),a850)),f341(f341(f10(f864(x100302,f863(x100301,x100302)),f864(x100302,f864(f864(f863(x100301,x100302),a850),a850)),x100301),f341(f10(f863(x100301,x100302),f864(f864(f863(x100301,x100302),a850),a850),x100302),f343(f863(x100301,x100302)))),f250(x100301,x100302)))),x100303)),f341(f341(f9(x100301,f864(f863(x100301,x100302),a850),f864(x100302,a850)),f341(f341(f10(f864(x100302,f864(f864(f863(x100301,x100302),a850),a850)),f864(f864(f863(x100301,x100302),a850),f864(x100302,a850)),x100301),f9(x100302,f864(f863(x100301,x100302),a850),a850)),f341(f341(f10(f864(x100302,f863(x100301,x100302)),f864(x100302,f864(f864(f863(x100301,x100302),a850),a850)),x100301),f341(f10(f863(x100301,x100302),f864(f864(f863(x100301,x100302),a850),a850),x100302),f343(f863(x100301,x100302)))),f250(x100301,x100302)))),x100304)),x100305),x100306)) % 19.23/19.04 [10034]P85(f341(f341(f343(f863(x100341,x100342)),f341(f341(f250(x100341,x100342),x100343),x100344)),f341(f341(f110(f864(f863(x100341,x100342),a850)),x100345),x100346)))+~P85(f341(f341(f341(f341(f110(f864(x100341,f864(x100342,a850))),f341(f341(f9(x100341,f864(f863(x100341,x100342),a850),f864(x100342,a850)),f341(f341(f10(f864(x100342,f864(f864(f863(x100341,x100342),a850),a850)),f864(f864(f863(x100341,x100342),a850),f864(x100342,a850)),x100341),f9(x100342,f864(f863(x100341,x100342),a850),a850)),f341(f341(f10(f864(x100342,f863(x100341,x100342)),f864(x100342,f864(f864(f863(x100341,x100342),a850),a850)),x100341),f341(f10(f863(x100341,x100342),f864(f864(f863(x100341,x100342),a850),a850),x100342),f343(f863(x100341,x100342)))),f250(x100341,x100342)))),x100345)),f341(f341(f9(x100341,f864(f863(x100341,x100342),a850),f864(x100342,a850)),f341(f341(f10(f864(x100342,f864(f864(f863(x100341,x100342),a850),a850)),f864(f864(f863(x100341,x100342),a850),f864(x100342,a850)),x100341),f9(x100342,f864(f863(x100341,x100342),a850),a850)),f341(f341(f10(f864(x100342,f863(x100341,x100342)),f864(x100342,f864(f864(f863(x100341,x100342),a850),a850)),x100341),f341(f10(f863(x100341,x100342),f864(f864(f863(x100341,x100342),a850),a850),x100342),f343(f863(x100341,x100342)))),f250(x100341,x100342)))),x100346)),x100343),x100344)) % 19.23/19.04 [10035]P85(f341(f341(f343(f863(x100351,x100352)),f341(f341(f250(x100351,x100352),x100353),x100354)),f341(f341(f111(f864(f863(x100351,x100352),a850)),x100355),x100356)))+~P85(f341(f341(f341(f341(f111(f864(x100351,f864(x100352,a850))),f341(f341(f9(x100351,f864(f863(x100351,x100352),a850),f864(x100352,a850)),f341(f341(f10(f864(x100352,f864(f864(f863(x100351,x100352),a850),a850)),f864(f864(f863(x100351,x100352),a850),f864(x100352,a850)),x100351),f9(x100352,f864(f863(x100351,x100352),a850),a850)),f341(f341(f10(f864(x100352,f863(x100351,x100352)),f864(x100352,f864(f864(f863(x100351,x100352),a850),a850)),x100351),f341(f10(f863(x100351,x100352),f864(f864(f863(x100351,x100352),a850),a850),x100352),f343(f863(x100351,x100352)))),f250(x100351,x100352)))),x100355)),f341(f341(f9(x100351,f864(f863(x100351,x100352),a850),f864(x100352,a850)),f341(f341(f10(f864(x100352,f864(f864(f863(x100351,x100352),a850),a850)),f864(f864(f863(x100351,x100352),a850),f864(x100352,a850)),x100351),f9(x100352,f864(f863(x100351,x100352),a850),a850)),f341(f341(f10(f864(x100352,f863(x100351,x100352)),f864(x100352,f864(f864(f863(x100351,x100352),a850),a850)),x100351),f341(f10(f863(x100351,x100352),f864(f864(f863(x100351,x100352),a850),a850),x100352),f343(f863(x100351,x100352)))),f250(x100351,x100352)))),x100356)),x100353),x100354)) % 19.23/19.04 [10024]~P85(f341(f341(f343(f863(x100242,x100243)),f341(f341(f250(x100242,x100243),x100245),x100246)),f341(f341(f54(x100241,f864(f863(x100242,x100243),a850)),f248(f864(x100241,a850))),x100244)))+P85(f341(f341(f341(f341(f54(x100241,f864(x100242,f864(x100243,a850))),f248(f864(x100241,a850))),f341(f341(f10(f864(f863(x100242,x100243),a850),f864(x100242,f864(x100243,a850)),x100241),f341(f9(x100242,f864(f863(x100242,x100243),a850),f864(x100243,a850)),f341(f341(f10(f864(x100243,f864(f864(f863(x100242,x100243),a850),a850)),f864(f864(f863(x100242,x100243),a850),f864(x100243,a850)),x100242),f9(x100243,f864(f863(x100242,x100243),a850),a850)),f341(f341(f10(f864(x100243,f863(x100242,x100243)),f864(x100243,f864(f864(f863(x100242,x100243),a850),a850)),x100242),f341(f10(f863(x100242,x100243),f864(f864(f863(x100242,x100243),a850),a850),x100243),f343(f863(x100242,x100243)))),f250(x100242,x100243))))),x100244)),x100245),x100246)) % 19.23/19.04 [10025]~P85(f341(f341(f343(f863(x100252,x100253)),f341(f341(f250(x100252,x100253),x100255),x100256)),f341(f341(f55(x100251,f864(f863(x100252,x100253),a850)),f248(f864(x100251,a850))),x100254)))+P85(f341(f341(f341(f341(f55(x100251,f864(x100252,f864(x100253,a850))),f248(f864(x100251,a850))),f341(f341(f10(f864(f863(x100252,x100253),a850),f864(x100252,f864(x100253,a850)),x100251),f341(f9(x100252,f864(f863(x100252,x100253),a850),f864(x100253,a850)),f341(f341(f10(f864(x100253,f864(f864(f863(x100252,x100253),a850),a850)),f864(f864(f863(x100252,x100253),a850),f864(x100253,a850)),x100252),f9(x100253,f864(f863(x100252,x100253),a850),a850)),f341(f341(f10(f864(x100253,f863(x100252,x100253)),f864(x100253,f864(f864(f863(x100252,x100253),a850),a850)),x100252),f341(f10(f863(x100252,x100253),f864(f864(f863(x100252,x100253),a850),a850),x100253),f343(f863(x100252,x100253)))),f250(x100252,x100253))))),x100254)),x100255),x100256)) % 19.23/19.04 [10032]P85(f341(f341(f343(f863(x100321,x100322)),f341(f341(f250(x100321,x100322),x100323),x100324)),f341(f341(f54(x100325,f864(f863(x100321,x100322),a850)),f248(f864(x100325,a850))),x100326)))+~P85(f341(f341(f341(f341(f54(x100325,f864(x100321,f864(x100322,a850))),f248(f864(x100325,a850))),f341(f341(f10(f864(f863(x100321,x100322),a850),f864(x100321,f864(x100322,a850)),x100325),f341(f9(x100321,f864(f863(x100321,x100322),a850),f864(x100322,a850)),f341(f341(f10(f864(x100322,f864(f864(f863(x100321,x100322),a850),a850)),f864(f864(f863(x100321,x100322),a850),f864(x100322,a850)),x100321),f9(x100322,f864(f863(x100321,x100322),a850),a850)),f341(f341(f10(f864(x100322,f863(x100321,x100322)),f864(x100322,f864(f864(f863(x100321,x100322),a850),a850)),x100321),f341(f10(f863(x100321,x100322),f864(f864(f863(x100321,x100322),a850),a850),x100322),f343(f863(x100321,x100322)))),f250(x100321,x100322))))),x100326)),x100323),x100324)) % 19.23/19.04 [10033]P85(f341(f341(f343(f863(x100331,x100332)),f341(f341(f250(x100331,x100332),x100333),x100334)),f341(f341(f55(x100335,f864(f863(x100331,x100332),a850)),f248(f864(x100335,a850))),x100336)))+~P85(f341(f341(f341(f341(f55(x100335,f864(x100331,f864(x100332,a850))),f248(f864(x100335,a850))),f341(f341(f10(f864(f863(x100331,x100332),a850),f864(x100331,f864(x100332,a850)),x100335),f341(f9(x100331,f864(f863(x100331,x100332),a850),f864(x100332,a850)),f341(f341(f10(f864(x100332,f864(f864(f863(x100331,x100332),a850),a850)),f864(f864(f863(x100331,x100332),a850),f864(x100332,a850)),x100331),f9(x100332,f864(f863(x100331,x100332),a850),a850)),f341(f341(f10(f864(x100332,f863(x100331,x100332)),f864(x100332,f864(f864(f863(x100331,x100332),a850),a850)),x100331),f341(f10(f863(x100331,x100332),f864(f864(f863(x100331,x100332),a850),a850),x100332),f343(f863(x100331,x100332)))),f250(x100331,x100332))))),x100336)),x100333),x100334)) % 19.23/19.04 [9124]E(x91241,x91242)+~E(f328(x91243,x91244,x91245,x91246,x91241),f328(x91243,x91244,x91245,x91247,x91242)) % 19.23/19.04 [9125]E(x91251,x91252)+~E(f328(x91253,x91254,x91255,x91251,x91256),f328(x91253,x91254,x91255,x91252,x91257)) % 19.23/19.04 [7368]E(f341(x73681,f341(x73682,x73683)),f341(x73684,x73683))+~E(f341(f82(x73685,x73686,x73687,x73681),x73682),x73684) % 19.23/19.04 [9488]~P23(x94883,x94884,x94881,x94885,x94886,x94887)+E(f341(f341(x94881,x94882),x94882),x94882) % 19.23/19.04 [9822]~P50(x98225,x98226,x98227,x98221,x98224,x98222,x98223)+P85(f341(f341(x98221,x98222),f591(x98223,x98222,x98224,x98221))) % 19.23/19.04 [9851]~E(f341(f237(f861(x98517),x98511,f188(x98517),x98515),f341(x98514,x98513)),f341(f235(x98517),x98512))+E(f341(f235(x98511),f721(x98512,x98513,x98514,x98515,x98516,x98517,x98511)),f341(x98514,x98513)) % 19.23/19.04 [9852]~E(f341(f237(f861(x98526),x98527,f188(x98526),x98521),f341(x98524,x98523)),f341(f235(x98526),x98522))+E(f341(x98521,f721(x98522,x98523,x98524,x98521,x98525,x98526,x98527)),f341(f235(x98526),x98522)) % 19.23/19.04 [5885]~E(f341(f341(f149(x58851,x58855),x58856),x58852),f341(f341(f149(x58853,x58855),x58857),x58854))+E(f341(f186(f858(x58851)),x58852),f341(f186(f858(x58853)),x58854)) % 19.23/19.04 [7443]E(x74431,x74432)+~E(f341(f341(f341(f81(x74433,f861(x74434)),x74435),x74436),f341(f235(x74434),x74431)),f341(f341(f341(f81(x74433,f861(x74434)),x74437),x74436),f341(f235(x74434),x74432))) % 19.23/19.04 [8402]E(f341(x84021,f341(x84022,x84023)),f341(x84024,x84023))+~E(f341(f82(x84025,x84026,x84027,x84021),x84022),f341(f82(x84026,x84026,x84027,f41(x84026)),x84024)) % 19.23/19.04 [9828]~P50(x98285,x98286,x98287,x98284,x98281,x98283,x98282)+P85(f341(f341(x98281,f591(x98282,x98283,x98281,x98284)),x98282)) % 19.23/19.04 [5931]E(x59311,x59312)+~E(f341(f341(f341(f100(x59313),x59314),x59315),x59311),f341(f341(f341(f100(x59313),x59316),x59317),x59312)) % 19.23/19.04 [5932]E(x59321,x59322)+~E(f341(f341(f341(f100(x59323),x59324),x59321),x59325),f341(f341(f341(f100(x59323),x59326),x59322),x59327)) % 19.23/19.04 [5933]E(x59331,x59332)+~E(f341(f341(f341(f100(x59333),x59331),x59334),x59335),f341(f341(f341(f100(x59333),x59332),x59336),x59337)) % 19.23/19.04 [8817]~P21(x88176,x88171,x88173,x88177)+E(f341(f82(x88171,x88171,x88172,f341(x88173,x88174)),f341(f82(x88171,x88171,x88172,f341(x88173,x88174)),x88175)),f341(f82(x88171,x88171,x88172,f341(x88173,x88174)),x88175)) % 19.23/19.04 [9569]E(f177(x95691,x95692,f341(f341(f341(f81(x95691,f861(x95692)),x95693),x95694),f341(f235(x95692),x95695)),x95696,x95697),f341(f341(f341(f81(x95691,f861(x95692)),f177(x95691,x95692,x95693,x95696,x95697)),x95694),f341(f235(x95692),x95695)))+P85(f341(f341(f343(x95691),x95694),f341(f163(x95691),x95696))) % 19.23/19.04 [8816]~P85(f341(f341(f343(x88161),x88162),f341(f341(x88165,x88166),x88167)))+P85(f341(f341(f343(x88161),x88162),f341(f341(f260(x88163,x88164,f864(x88161,a850)),x88165),f341(f341(f250(x88163,x88164),x88166),x88167)))) % 19.23/19.04 [9084]P85(f341(f341(f341(x90841,x90842),x90843),x90844))+~P85(f341(f341(f341(f260(x90845,x90846,f864(x90847,a850)),x90841),f341(f341(f250(x90845,x90846),x90842),x90843)),x90844)) % 19.23/19.04 [9202]P85(f341(f341(f343(x92021),f341(f341(x92022,x92023),x92024)),f341(f312(f863(x92025,x92026),x92021,f341(f260(x92025,x92026,x92021),x92022)),x92027)))+~P85(f341(f341(f343(f863(x92025,x92026)),f341(f341(f250(x92025,x92026),x92023),x92024)),x92027)) % 19.23/19.04 [9528]P85(f341(f341(f343(f863(f858(x95281),f858(x95281))),f341(f341(f250(f858(x95281),f858(x95281)),f341(f341(f132(x95281),x95282),f341(f341(f146(x95281),x95283),x95284))),f341(f341(f132(x95281),x95282),f341(f341(f146(x95281),x95285),x95286)))),f143(x95281,x95287)))+~P85(f341(f341(f343(f863(x95281,x95281)),f341(f341(f250(x95281,x95281),x95283),x95285)),x95287)) % 19.23/19.04 [9952]P50(x99521,x99522,x99523,f341(f341(f9(x99521,f864(f863(x99521,x99522),a850),f864(x99522,a850)),f341(f341(f10(f864(x99522,f864(f864(f863(x99521,x99522),a850),a850)),f864(f864(f863(x99521,x99522),a850),f864(x99522,a850)),x99521),f9(x99522,f864(f863(x99521,x99522),a850),a850)),f341(f341(f10(f864(x99522,f863(x99521,x99522)),f864(x99522,f864(f864(f863(x99521,x99522),a850),a850)),x99521),f341(f10(f863(x99521,x99522),f864(f864(f863(x99521,x99522),a850),a850),x99522),f343(f863(x99521,x99522)))),f250(x99521,x99522)))),x99524),f341(f341(f9(x99522,f864(f863(x99522,x99523),a850),f864(x99523,a850)),f341(f341(f10(f864(x99523,f864(f864(f863(x99522,x99523),a850),a850)),f864(f864(f863(x99522,x99523),a850),f864(x99523,a850)),x99522),f9(x99523,f864(f863(x99522,x99523),a850),a850)),f341(f341(f10(f864(x99523,f863(x99522,x99523)),f864(x99523,f864(f864(f863(x99522,x99523),a850),a850)),x99522),f341(f10(f863(x99522,x99523),f864(f864(f863(x99522,x99523),a850),a850),x99523),f343(f863(x99522,x99523)))),f250(x99522,x99523)))),x99525),x99526,x99527)+~P85(f341(f341(f343(f863(x99521,x99523)),f341(f341(f250(x99521,x99523),x99526),x99527)),f341(f341(f290(x99521,x99522,x99523),x99524),x99525))) % 19.23/19.04 [9983]~P50(x99831,x99835,x99832,f341(f341(f9(x99831,f864(f863(x99831,x99835),a850),f864(x99835,a850)),f341(f341(f10(f864(x99835,f864(f864(f863(x99831,x99835),a850),a850)),f864(f864(f863(x99831,x99835),a850),f864(x99835,a850)),x99831),f9(x99835,f864(f863(x99831,x99835),a850),a850)),f341(f341(f10(f864(x99835,f863(x99831,x99835)),f864(x99835,f864(f864(f863(x99831,x99835),a850),a850)),x99831),f341(f10(f863(x99831,x99835),f864(f864(f863(x99831,x99835),a850),a850),x99835),f343(f863(x99831,x99835)))),f250(x99831,x99835)))),x99836),f341(f341(f9(x99835,f864(f863(x99835,x99832),a850),f864(x99832,a850)),f341(f341(f10(f864(x99832,f864(f864(f863(x99835,x99832),a850),a850)),f864(f864(f863(x99835,x99832),a850),f864(x99832,a850)),x99835),f9(x99832,f864(f863(x99835,x99832),a850),a850)),f341(f341(f10(f864(x99832,f863(x99835,x99832)),f864(x99832,f864(f864(f863(x99835,x99832),a850),a850)),x99835),f341(f10(f863(x99835,x99832),f864(f864(f863(x99835,x99832),a850),a850),x99832),f343(f863(x99835,x99832)))),f250(x99835,x99832)))),x99837),x99833,x99834)+P85(f341(f341(f343(f863(x99831,x99832)),f341(f341(f250(x99831,x99832),x99833),x99834)),f341(f341(f290(x99831,x99835,x99832),x99836),x99837))) % 19.23/19.04 [9079]E(x90791,x90792)+E(f341(f341(f341(f81(x90793,x90794),f341(f341(f341(f81(x90793,x90794),x90795),x90791),x90796)),x90792),x90797),f341(f341(f341(f81(x90793,x90794),f341(f341(f341(f81(x90793,x90794),x90795),x90792),x90797)),x90791),x90796)) % 19.23/19.04 [9299]E(f177(x92991,x92992,f341(f341(f341(f81(x92991,f861(x92992)),x92993),x92994),f341(f235(x92992),x92995)),x92996,x92997),f177(x92991,x92992,x92993,x92996,x92997))+~P85(f341(f341(f343(x92991),x92994),f341(f163(x92991),f341(f341(f164(x92991),f341(f186(f858(x92992)),x92997)),x92996)))) % 19.23/19.04 [9597]E(f177(x95971,x95972,f341(f341(f341(f81(x95971,f861(x95972)),x95973),x95974),f341(f235(x95972),x95975)),x95976,x95977),f341(f341(f341(f81(x95971,f861(x95972)),f177(x95971,x95972,x95973,x95976,x95977)),x95974),f341(f235(x95972),x95975)))+P85(f341(f341(f343(x95971),x95974),f341(f163(x95971),f341(f341(f164(x95971),f341(f186(f858(x95972)),x95977)),x95976)))) % 19.23/19.04 [9964]P85(f341(f341(f343(x99641),f679(x99642,x99643,x99644,x99645,x99646,x99647,x99641)),x99645))+P85(f341(f341(f341(f341(f55(x99641,f864(x99647,f864(x99646,a850))),x99645),x99644),x99643),x99642)) % 19.23/19.04 [9966]P85(f341(f341(f343(x99661),f432(x99662,x99663,x99664,x99665,x99666,x99667,x99661)),x99665))+~P85(f341(f341(f341(f341(f54(x99661,f864(x99667,f864(x99666,a850))),x99665),x99664),x99663),x99662)) % 19.23/19.04 [9993]P85(f341(f341(f341(x99931,f432(x99932,x99933,x99931,x99934,x99935,x99936,x99937)),x99933),x99932))+~P85(f341(f341(f341(f341(f54(x99937,f864(x99936,f864(x99935,a850))),x99934),x99931),x99933),x99932)) % 19.23/19.04 [10009]~P85(f341(f341(f341(x100095,f679(x100097,x100096,x100095,x100094,x100093,x100092,x100091)),x100096),x100097))+P85(f341(f341(f341(f341(f55(x100091,f864(x100092,f864(x100093,a850))),x100094),x100095),x100096),x100097)) % 19.23/19.04 [9975]~P139(x99752)+E(f341(f341(f8(x99751,x99752),f341(f341(f9(x99751,f864(x99753,a850),x99752),f341(f341(f10(f864(x99753,x99752),f864(f864(x99753,a850),x99752),x99751),f8(x99753,x99752)),f341(f341(f9(x99751,f864(x99753,x99752),f864(x99753,x99752)),f341(f341(f10(f864(x99752,x99752),f864(f864(x99753,x99752),f864(x99753,x99752)),x99751),f10(x99752,x99752,x99753)),f341(f341(f10(x99752,f864(x99752,x99752),x99751),f90(x99752)),x99754))),x99755))),x99756)),x99757),f341(f341(f90(x99752),f341(f341(f8(x99751,x99752),x99754),x99757)),f341(f341(f8(x99753,x99752),x99755),x99756))) % 19.23/19.04 [9115]~P20(x91157,x91151,x91153,x91158)+E(f341(f82(x91151,x91151,x91152,f341(x91153,x91154)),f341(f82(x91151,x91151,x91152,f341(x91153,x91155)),x91156)),f341(f82(x91151,x91151,x91152,f341(x91153,x91155)),f341(f82(x91151,x91151,x91152,f341(x91153,x91154)),x91156))) % 19.23/19.04 [10020]P25(x100201,x100202,f341(f341(f311(f856(x100201)),f341(f341(f341(f100(x100201),f341(f341(f10(f864(a855,a850),f864(a855,a850),x100201),f341(f20(a855,a850,a850),f341(f341(f10(a850,f864(a850,a850),a855),a339),f341(a338,x100203)))),f341(f341(f9(x100201,f864(a855,a855),f864(a855,a850)),f341(f341(f10(f864(a855,a850),f864(f864(a855,a855),f864(a855,a850)),x100201),f10(a855,a850,a855)),x100204)),f341(f341(f20(a855,a857,a855),f341(f341(f9(a855,a852,f864(a857,a855)),a194),f42(x100205))),x100206)))),f34(x100205,x100206,x100207)),x100208)),f185(f864(f856(x100201),a850))))+~P25(x100201,x100202,f341(f341(f311(f856(x100201)),f341(f341(f341(f100(x100201),x100204),x100207),f341(f341(f9(x100201,f864(a855,a855),f864(a855,a850)),f341(f341(f10(f864(a855,a850),f864(f864(a855,a855),f864(a855,a850)),x100201),f10(a855,a850,a855)),x100208)),f341(f341(f9(a855,a857,a855),f341(f341(f9(a855,a852,f864(a857,a855)),a194),f42(x100205))),f341(f341(a195,x100203),x100205))))),f185(f864(f856(x100201),a850)))) % 19.23/19.04 [10027]E(f341(f341(f250(x100271,x100272),f341(x100273,f565(x100274,x100275,x100273,x100276,x100277,x100278,x100272,x100271))),f341(x100275,f572(x100274,x100275,x100273,x100276,x100277,x100278,x100272,x100271))),x100278)+~P85(f341(f341(f343(f863(x100271,x100272)),x100278),f341(f312(f863(x100277,x100276),f863(x100271,x100272),f261(x100277,x100271,x100276,x100272,x100273,x100275)),x100274))) % 19.23/19.04 [10039]P25(x100391,x100392,f341(f341(f311(f856(x100391)),f341(f341(f341(f100(x100391),f341(f341(f10(f864(a855,a850),f864(a855,a850),x100391),f341(f20(a855,a850,a850),f341(f341(f10(a850,f864(a850,a850),a855),a339),f341(a338,x100393)))),f341(f341(f9(x100391,f864(a855,a855),f864(a855,a850)),f341(f341(f10(f864(a855,a850),f864(f864(a855,a855),f864(a855,a850)),x100391),f10(a855,a850,a855)),x100394)),f341(f341(f20(a855,a857,a855),f341(f341(f9(a855,a852,f864(a857,a855)),f341(f341(f10(a855,f864(a852,f864(a857,a855)),a855),a194),f341(f341(f9(a855,f864(a854,a857),a855),a196),a197))),f42(a28))),x100395)))),f33(x100396,x100397,x100395)),x100398)),f185(f864(f856(x100391),a850))))+~P25(x100391,x100392,f341(f341(f311(f856(x100391)),f341(f341(f341(f100(x100391),x100394),f341(a29,x100397)),f341(f341(f9(x100391,f864(a855,a855),f864(a855,a850)),f341(f341(f10(f864(a855,a850),f864(f864(a855,a855),f864(a855,a850)),x100391),f10(a855,a850,a855)),x100398)),f341(f341(f20(a855,a857,a855),f341(f341(f9(a855,a852,f864(a857,a855)),f341(f341(f10(a855,f864(a852,f864(a857,a855)),a855),a194),f341(f341(f9(a855,f864(a854,a857),a855),a196),f341(a195,x100393)))),x100396)),f341(f341(f9(a855,a854,a857),a195),a27))))),f185(f864(f856(x100391),a850)))) % 19.23/19.04 [10040]~P85(f341(f341(f343(f863(x100408,x100407)),x100406),f341(f312(f863(x100401,x100402),f863(x100408,x100407),f261(x100401,x100408,x100402,x100407,x100405,x100404)),x100403)))+P85(f341(f341(f343(f863(x100401,x100402)),f341(f341(f250(x100401,x100402),f565(x100403,x100404,x100405,x100402,x100401,x100406,x100407,x100408)),f572(x100403,x100404,x100405,x100402,x100401,x100406,x100407,x100408))),x100403)) % 19.23/19.04 [9518]P85(f341(f341(f343(f863(f863(x95181,x95182),f863(x95181,x95182))),f341(f341(f250(f863(x95181,x95182),f863(x95181,x95182)),f341(f341(f250(x95181,x95182),x95183),x95184)),f341(f341(f250(x95181,x95182),x95185),x95186))),f335(x95181,x95182,x95187,x95188)))+~P85(f341(f341(f343(f863(x95181,x95181)),f341(f341(f250(x95181,x95181),x95183),x95185)),x95187)) % 19.23/19.04 [8408]E(f341(x84081,f341(x84082,x84083)),f341(x84084,f341(x84085,x84083)))+~E(f341(f82(x84086,x84087,x84088,x84081),x84082),f341(f82(x84089,x84087,x84088,x84084),x84085)) % 19.23/19.04 [9900]P85(f341(f341(f343(f863(x99001,x99002)),f341(f341(f250(x99001,x99002),f341(x99003,x99004)),f341(x99005,x99006))),f341(f312(f863(x99007,x99008),f863(x99001,x99002),f261(x99007,x99001,x99008,x99002,x99003,x99005)),x99009)))+~P85(f341(f341(f343(f863(x99007,x99008)),f341(f341(f250(x99007,x99008),x99004),x99006)),x99009)) % 19.23/19.04 [8666]~E(f341(x86664,f341(x86665,x86666)),f341(x86669,f341(x866610,x866611)))+E(f341(f341(f82(x86661,x86662,x86663,x86664),x86665),x86666),f341(f341(f82(x86667,x86662,x86668,x86669),x866610),x866611)) % 19.23/19.04 [4509]~P101(x45091)+~P98(x45091)+E(f240(x45091),f110(x45091)) % 19.23/19.04 [4510]~P101(x45101)+~P99(x45101)+E(f245(x45101),f111(x45101)) % 19.23/19.04 [4743]~P113(x47431)+~P89(x47431)+E(f341(f84(x47431),f341(f113(x47431),a106)),f87(x47431)) % 19.23/19.04 [5019]E(x50191,f2(a1))+E(f91(a1,x50191),f341(f88(a1),f87(a1)))+P85(f341(f341(f242(a1),f2(a1)),x50191)) % 19.23/19.04 [5218]E(x52181,f2(a1))+E(f91(a1,x52181),f87(a1))+~P85(f341(f341(f242(a1),f2(a1)),x52181)) % 19.23/19.04 [7255]~P37(x72551)+P85(f341(f71(a1),x72551))+~P85(f341(f71(a857),f341(f312(a1,a857,a114),x72551))) % 19.23/19.04 [8512]~P10(a5000)+~P85(f341(f341(f343(f863(a853,a851)),x85121),f341(f163(f863(a853,a851)),a31)))+P85(f341(f341(f260(a853,a851,a850),f341(f18(f864(a851,a850),a853),a26)),x85121)) % 19.23/19.04 [9487]E(x94871,f185(f864(f863(a857,a857),a850)))+~P85(f341(f71(f863(a857,a857)),x94871))+P85(f341(f341(f343(f863(f864(f863(a857,a857),a850),f864(f863(a857,a857),a850))),f341(f341(f250(f864(f863(a857,a857),a850),f864(f863(a857,a857),a850)),f185(f864(f863(a857,a857),a850))),x94871)),a49)) % 19.23/19.04 [9643]E(x96431,f2(a857))+E(x96431,f341(a121,f2(a857)))+~P85(f341(f341(f242(a857),x96431),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106))))) % 19.23/19.04 [9924]E(x99241,f2(a108))+E(f341(f341(f89(a1),f341(f341(f90(a1),f341(f113(a1),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),f341(a23,f341(f341(f51(a108),x99241),f341(f113(a108),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106))))))),f87(a1)),f341(a23,x99241))+E(f60(a108,x99241,f341(f113(a108),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),f2(a108)) % 19.23/19.04 [9771]E(x97711,f2(a108))+~E(f60(a108,x97711,f341(f113(a108),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),f2(a108))+E(f341(f341(f90(a1),f341(f113(a1),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),f341(a23,f341(f341(f51(a108),x97711),f341(f113(a108),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))))),f341(a23,x97711)) % 19.23/19.04 [4580]~P55(x45801,x45802)+P41(x45801,x45802)+~P42(a850) % 19.23/19.04 [4520]~P112(x45201)+P32(x45201,x45202)+~E(x45202,f2(x45201)) % 19.23/19.04 [4529]~P113(x45291)+~E(x45292,f2(x45291))+E(f91(x45291,x45292),f2(x45291)) % 19.23/19.04 [4530]~P82(x45301)+~E(x45302,f2(x45301))+E(f91(x45301,x45302),f2(x45301)) % 19.23/19.04 [4536]~P112(x45362)+~P32(x45362,x45361)+E(x45361,f2(x45362)) % 19.23/19.04 [4570]~P113(x45702)+~E(f91(x45702,x45701),f2(x45702))+E(x45701,f2(x45702)) % 19.23/19.04 [4587]~P7(x45872)+~P7(x45871)+P7(f193(x45871,x45872)) % 19.23/19.04 [4588]~P58(x45882)+~P58(x45881)+P58(f865(x45881,x45882)) % 19.23/19.04 [4589]~P58(x45892)+~P58(x45891)+P58(f864(x45891,x45892)) % 19.23/19.04 [4590]~P58(x45902)+~P58(x45901)+P58(f863(x45901,x45902)) % 19.23/19.04 [4591]~P141(x45912)+~P141(x45911)+P141(f863(x45911,x45912)) % 19.23/19.04 [4946]~P7(x49462)+~P7(x49461)+P7(f60(a1,x49461,x49462)) % 19.23/19.04 [4538]~P69(x45381)+~E(x45382,f2(x45381))+E(f341(f88(x45381),x45382),x45382) % 19.23/19.04 [4542]~P136(x45421)+~E(x45422,f2(a1))+E(f341(f112(x45421),x45422),f2(x45421)) % 19.23/19.04 [4543]~P88(x45431)+~E(x45432,f2(a1))+E(f341(f112(x45431),x45432),f2(x45431)) % 19.23/19.04 [4567]~P70(x45671)+~E(f2(x45671),x45672)+E(f341(f88(x45671),x45672),f2(x45671)) % 19.23/19.04 [4568]~P70(x45681)+~E(x45682,f2(x45681))+E(f341(f88(x45681),x45682),f2(x45681)) % 19.23/19.04 [4569]~P79(x45691)+~E(x45692,f2(x45691))+E(f341(f84(x45691),x45692),f2(x45691)) % 19.23/19.04 [4593]~P69(x45932)+E(x45931,f2(x45932))+~E(f341(f88(x45932),x45931),x45931) % 19.23/19.04 [4601]E(x46011,f341(a114,x46012))+~E(x46011,f2(a857))+~E(x46012,f341(f109(a1),x46011)) % 19.23/19.04 [4602]E(f341(a114,x46021),x46022)+~E(x46022,f2(a857))+~E(x46021,f341(f109(a1),x46022)) % 19.23/19.04 [4606]~P88(x46062)+E(x46061,f2(a1))+~E(f341(f112(x46062),x46061),f2(x46062)) % 19.23/19.04 [4611]~P70(x46112)+E(x46111,f2(x46112))+~E(f341(f88(x46112),x46111),f2(x46112)) % 19.23/19.04 [4612]~P79(x46122)+E(x46121,f2(x46122))+~E(f341(f84(x46122),x46121),f2(x46122)) % 19.23/19.04 [4613]~P70(x46131)+E(f2(x46131),x46132)+~E(f341(f88(x46131),x46132),f2(x46131)) % 19.23/19.04 [4747]~P10(a5000)+~E(f341(a32,x47472),f341(f235(a851),x47471))+P85(f341(a26,x47471)) % 19.23/19.04 [4786]~P101(x47861)+~P15(x47861,x47862)+P15(x47861,f341(f162(x47861),x47862)) % 19.23/19.04 [4812]~P85(x48122)+~P85(x48121)+P85(f341(f341(a339,x48121),x48122)) % 19.23/19.04 [4846]~E(f87(a857),f2(a857))+E(f341(f50(x48461),x48462),f2(a857))+~P85(f341(f71(x48461),x48462)) % 19.23/19.04 [4877]~P106(x48771)+~P139(x48771)+E(f341(f341(f251(x48771),f2(x48771)),f341(a121,x48772)),f2(x48771)) % 19.23/19.04 [4917]~P101(x49171)+P15(x49171,f136(x49171,x49172))+~P85(f341(f71(x49171),x49172)) % 19.23/19.04 [4937]~P101(x49371)+E(f341(f163(x49371),f136(x49371,x49372)),x49372)+~P85(f341(f71(x49371),x49372)) % 19.23/19.04 [4972]P85(x49721)+P85(x49722)+~P85(f341(f341(a340,x49722),x49721)) % 19.23/19.04 [4984]E(x49841,f185(f864(x49842,a850)))+~E(f341(f50(x49842),x49841),f2(a857))+~P85(f341(f71(x49842),x49841)) % 19.23/19.04 [4989]P85(x49891)+~P85(x49892)+~P85(f341(f341(a344,x49892),x49891)) % 19.23/19.04 [5037]~P66(x50371)+E(f341(f84(x50371),x50372),x50372)+P85(f341(f341(f242(x50371),x50372),f2(x50371))) % 19.23/19.04 [5132]~P85(f341(a26,x51322))+~P85(f341(a26,x51321))+P85(f341(a26,f38(x51321,x51322))) % 19.23/19.04 [5139]E(x51391,f122(x51392))+P85(f341(f134(x51392),f123(x51392,x51391)))+~P85(f341(f134(x51392),x51391)) % 19.23/19.04 [5144]~P101(x51441)+~P85(f341(f71(x51441),x51442))+P85(f341(f134(x51441),f136(x51441,x51442))) % 19.23/19.04 [5150]~P136(x51501)+E(f341(f109(x51501),f341(a114,x51502)),f341(f112(x51501),x51502))+P85(f341(f341(f242(a1),x51502),f2(a1))) % 19.23/19.04 [5176]P8(x51762,x51761)+E(f341(x51761,f490(x51761)),f341(x51761,f538(x51761)))+P85(f341(f341(x51761,f490(x51761)),f538(x51761))) % 19.23/19.04 [5188]E(f341(f109(a1),f738(x51881,x51882)),x51881)+P85(f341(x51882,f341(a114,x51881)))+~P85(f341(x51882,f2(a857))) % 19.23/19.04 [5228]~P113(x52281)+~E(f91(x52281,x52282),f341(f88(x52281),f87(x52281)))+P85(f341(f341(f242(x52281),x52282),f2(x52281))) % 19.23/19.04 [5300]~E(x53002,f2(a1))+E(f218(x53001,x53002),f341(f341(f250(a1,a1),f2(a1)),f87(a1)))+P85(f341(f341(f242(a1),x53002),f2(a1))) % 19.23/19.04 [5301]~E(x53011,f2(a1))+E(f218(x53011,x53012),f341(f341(f250(a1,a1),f2(a1)),f87(a1)))+P85(f341(f341(f242(a1),x53012),f2(a1))) % 19.23/19.04 [5324]~P85(f341(x53241,x53242))+~P85(f341(x53241,f626(x53242,x53241)))+P85(f341(x53241,f2(a857))) % 19.23/19.04 [5353]E(f341(f109(a1),f738(x53531,x53532)),x53531)+P85(f341(x53532,f341(a114,x53531)))+P85(f341(f341(f242(a1),x53531),f2(a1))) % 19.23/19.04 [5419]~P113(x54191)+E(f91(x54191,x54192),f341(f88(x54191),f87(x54191)))+~P85(f341(f341(f242(x54191),x54192),f2(x54191))) % 19.23/19.04 [5420]~P79(x54201)+E(f341(f84(x54201),x54202),f341(f88(x54201),x54202))+~P85(f341(f341(f242(x54201),x54202),f2(x54201))) % 19.23/19.04 [5421]~P79(x54211)+E(f341(f84(x54211),x54212),f341(f88(x54211),x54212))+~P85(f341(f341(f241(x54211),x54212),f2(x54211))) % 19.23/19.04 [5422]~P66(x54221)+E(f341(f84(x54221),x54222),f341(f88(x54221),x54222))+~P85(f341(f341(f242(x54221),x54222),f2(x54221))) % 19.23/19.04 [5513]~P85(f341(x55131,f738(x55132,x55131)))+P85(f341(x55131,f341(a114,x55132)))+~P85(f341(x55131,f2(a857))) % 19.23/19.04 [5520]E(x55201,f2(a857))+E(f341(a121,f651(x55202,x55201)),x55201)+~P85(f341(f341(f242(a857),x55201),f341(a121,x55202))) % 19.23/19.04 [5524]P8(x55241,x55242)+~E(f341(x55242,f490(x55242)),f341(x55242,f538(x55242)))+~P85(f341(f341(x55242,f490(x55242)),f538(x55242))) % 19.23/19.04 [5543]~P101(x55431)+P15(x55431,x55432)+P85(f341(f341(f241(a857),f775(x55432,x55431)),f776(x55432,x55431))) % 19.23/19.04 [5629]~P79(x56291)+~E(x56292,f2(x56291))+P85(f341(f341(f241(x56291),f341(f84(x56291),x56292)),f2(x56291))) % 19.23/19.04 [5718]~P85(f341(x57181,f738(x57182,x57181)))+P85(f341(x57181,f341(a114,x57182)))+P85(f341(f341(f242(a1),x57182),f2(a1))) % 19.23/19.04 [5744]~P85(f341(x57441,f341(a114,x57442)))+P85(f341(x57441,f2(a857)))+~P85(f341(f341(f242(a1),x57442),f2(a1))) % 19.23/19.04 [6087]~P113(x60871)+~P85(f341(f341(f242(x60871),x60872),f2(x60871)))+P85(f341(f341(f242(x60871),f91(x60871,x60872)),f2(x60871))) % 19.23/19.04 [6204]~P113(x62041)+P85(f341(f341(f242(x62041),f341(f112(x62041),x62042)),f2(x62041)))+~P85(f341(f341(f242(a1),x62042),f2(a1))) % 19.23/19.04 [6205]~P113(x62051)+P85(f341(f341(f241(x62051),f341(f112(x62051),x62052)),f2(x62051)))+~P85(f341(f341(f241(a1),x62052),f2(a1))) % 19.23/19.04 [6210]~P79(x62102)+E(x62101,f2(x62102))+~P85(f341(f341(f241(x62102),f341(f84(x62102),x62101)),f2(x62102))) % 19.23/19.04 [6294]~P136(x62941)+~P85(f341(f341(f343(x62941),x62942),f119(x62941)))+P85(f341(f341(f343(x62941),f341(f88(x62941),x62942)),f119(x62941))) % 19.23/19.04 [6326]~P113(x63261)+~P85(f341(f341(f242(x63261),f91(x63261,x63262)),f2(x63261)))+P85(f341(f341(f242(x63261),x63262),f2(x63261))) % 19.23/19.04 [6407]~P100(x64071)+P49(a857,x64071,f288(a857),x64072)+P85(f341(f341(f288(a857),f349(x64072,x64071)),f354(x64072,x64071))) % 19.23/19.04 [6504]~P113(x65042)+~P85(f341(f341(f242(x65042),f341(f112(x65042),x65041)),f2(x65042)))+P85(f341(f341(f242(a1),x65041),f2(a1))) % 19.23/19.04 [6505]~P113(x65052)+~P85(f341(f341(f241(x65052),f341(f112(x65052),x65051)),f2(x65052)))+P85(f341(f341(f241(a1),x65051),f2(a1))) % 19.23/19.04 [7025]~P69(x70251)+~P85(f341(f341(f242(x70251),x70252),f2(x70251)))+P85(f341(f341(f242(x70251),f341(f341(f89(x70251),x70252),x70252)),f2(x70251))) % 19.23/19.04 [7026]~P113(x70261)+~P85(f341(f341(f242(x70261),x70262),f2(x70261)))+P85(f341(f341(f242(x70261),f341(f341(f89(x70261),x70262),x70262)),f2(x70261))) % 19.23/19.04 [7027]~P69(x70271)+~P85(f341(f341(f241(x70271),x70272),f2(x70271)))+P85(f341(f341(f241(x70271),f341(f341(f89(x70271),x70272),x70272)),f2(x70271))) % 19.23/19.04 [7621]~P69(x76211)+~P85(f341(f341(f242(x76211),f341(f341(f89(x76211),x76212),x76212)),f2(x76211)))+P85(f341(f341(f242(x76211),x76212),f2(x76211))) % 19.23/19.04 [7622]~P113(x76221)+~P85(f341(f341(f242(x76221),f341(f341(f89(x76221),x76222),x76222)),f2(x76221)))+P85(f341(f341(f242(x76221),x76222),f2(x76221))) % 19.23/19.04 [7623]~P69(x76231)+~P85(f341(f341(f241(x76231),f341(f341(f89(x76231),x76232),x76232)),f2(x76231)))+P85(f341(f341(f241(x76231),x76232),f2(x76231))) % 19.23/19.04 [4650]~E(x46502,f2(a857))+~E(x46501,f2(a857))+E(f341(f341(f89(a857),x46501),x46502),f2(a857)) % 19.23/19.04 [4651]~E(x46512,f87(a857))+~E(x46511,f87(a857))+E(f341(f341(f90(a857),x46511),x46512),f87(a857)) % 19.23/19.04 [4652]~E(x46522,f87(a1))+~E(x46521,f87(a1))+E(f341(f341(f90(a1),x46521),x46522),f87(a1)) % 19.23/19.04 [4702]~P4(x47022)+E(x47021,f2(x47022))+E(f341(f341(f51(x47022),x47021),x47021),f87(x47022)) % 19.23/19.04 [4703]~P116(x47032)+E(x47031,f2(x47032))+E(f341(f341(f292(x47032),x47031),x47031),f87(x47032)) % 19.23/19.04 [4704]~P117(x47042)+E(x47041,f2(x47042))+E(f341(f341(f292(x47042),x47041),x47041),f87(x47042)) % 19.23/19.04 [4719]~P69(x47191)+~E(x47192,f2(x47191))+E(f341(f341(f89(x47191),x47192),x47192),f2(x47191)) % 19.23/19.04 [4722]~P135(x47221)+~E(x47222,f87(x47221))+E(f341(f341(f90(x47221),x47222),x47222),f87(x47221)) % 19.23/19.04 [4723]~P117(x47231)+~E(x47232,f2(x47231))+E(f341(f341(f292(x47231),x47232),x47232),f2(x47231)) % 19.23/19.04 [4767]~E(x47672,f2(a857))+~E(x47671,f2(a857))+E(f341(f88(a1),f341(f109(a1),x47671)),f341(f109(a1),x47672)) % 19.23/19.04 [4785]E(x47851,f87(a857))+E(x47852,f2(a857))+~E(f341(f341(f90(a857),x47852),x47851),x47852) % 19.23/19.04 [4793]E(x47931,f2(a857))+E(x47932,f2(a857))+~E(f341(f341(f90(a857),x47932),x47931),f2(a857)) % 19.23/19.04 [4821]~E(x48212,f2(a857))+~E(x48211,f341(a121,f2(a857)))+E(f341(f341(f89(a857),x48211),x48212),f341(a121,f2(a857))) % 19.23/19.04 [4822]~E(x48221,f2(a857))+~E(x48222,f341(a121,f2(a857)))+E(f341(f341(f89(a857),x48221),x48222),f341(a121,f2(a857))) % 19.23/19.04 [4827]E(x48271,f87(a1))+E(x48272,f341(f113(a1),a106))+~E(f341(f341(f90(a1),x48271),x48272),f87(a1)) % 19.23/19.04 [4828]E(x48281,f87(a1))+E(x48282,f341(f113(a1),a106))+~E(f341(f341(f90(a1),x48282),x48281),f87(a1)) % 19.23/19.04 [4829]E(x48291,f87(a1))+E(x48291,f341(f113(a1),a106))+~E(f341(f341(f90(a1),x48292),x48291),f87(a1)) % 19.23/19.04 [4831]E(x48311,f87(a1))+E(x48311,f341(f113(a1),a106))+~E(f341(f341(f90(a1),x48311),x48312),f87(a1)) % 19.23/19.04 [4850]~P69(x48502)+E(x48501,f2(x48502))+~E(f341(f341(f89(x48502),x48501),x48501),f2(x48502)) % 19.23/19.04 [4856]~E(x48561,f341(f113(a1),a106))+~E(x48562,f341(f113(a1),a106))+E(f341(f341(f90(a1),x48561),x48562),f87(a1)) % 19.23/19.04 [4868]E(x48681,f2(a857))+E(x48682,f2(a857))+~E(f341(f341(f89(a857),x48682),x48681),f341(a121,f2(a857))) % 19.23/19.04 [4876]~P89(x48761)+~P59(x48761)+E(f341(f341(f292(x48761),x48762),f341(f113(x48761),a92)),f2(x48761)) % 19.23/19.04 [4883]~P135(x48831)+~E(x48832,f341(f88(x48831),f87(x48831)))+E(f341(f341(f90(x48831),x48832),x48832),f87(x48831)) % 19.23/19.04 [4888]~P7(x48882)+~P7(x48881)+P7(f341(f341(f89(a1),x48881),x48882)) % 19.23/19.04 [4889]~P7(x48892)+~P7(x48891)+P7(f341(f341(f90(a1),x48891),x48892)) % 19.23/19.04 [4890]~P7(x48902)+~P7(x48901)+P7(f341(f341(f51(a1),x48901),x48902)) % 19.23/19.04 [4892]~E(x48922,f2(a1))+E(x48921,f2(a1))+E(f61(x48921,x48922),f341(f341(f250(a1,a1),f2(a1)),x48921)) % 19.23/19.04 [4915]~E(x49152,f341(a121,f2(a857)))+~E(x49151,f341(a121,f2(a857)))+E(f341(f341(f90(a857),x49151),x49152),f341(a121,f2(a857))) % 19.23/19.04 [4928]E(x49281,f2(a857))+E(x49282,f341(a121,f2(a857)))+~E(f341(f341(f251(a857),x49282),x49281),f341(a121,f2(a857))) % 19.23/19.04 [4929]E(x49291,f2(a857))+E(x49291,f341(a121,f2(a857)))+~E(f341(f341(f89(a857),x49292),x49291),f341(a121,f2(a857))) % 19.23/19.04 [4930]E(x49301,f2(a857))+E(x49301,f341(a121,f2(a857)))+~E(f341(f341(f89(a857),x49301),x49302),f341(a121,f2(a857))) % 19.23/19.04 [4938]~P89(x49381)+~P59(x49381)+E(f341(f341(f292(x49381),x49382),f341(f113(x49381),a106)),f341(f88(x49381),x49382)) % 19.23/19.04 [4959]E(x49591,f341(a114,x49592))+~E(x49591,f2(a857))+P85(f341(f341(f241(a1),f2(a1)),x49592)) % 19.23/19.04 [4960]E(f341(a114,x49601),x49602)+~E(x49602,f2(a857))+P85(f341(f341(f241(a1),f2(a1)),x49601)) % 19.23/19.04 [4980]E(x49801,f341(a121,f2(a857)))+E(x49802,f341(a121,f2(a857)))+~E(f341(f341(f89(a857),x49801),x49802),f341(a121,f2(a857))) % 19.23/19.04 [4991]~E(x49911,f341(a114,x49912))+E(x49911,f2(a857))+P85(f341(f341(f241(a1),f2(a1)),x49912)) % 19.23/19.04 [4992]~E(f341(a114,x49922),x49921)+E(x49921,f2(a857))+P85(f341(f341(f241(a1),f2(a1)),x49922)) % 19.23/19.04 [5015]~P95(x50151)+E(f341(f73(x50151,f110(x50151)),x50152),f15(x50151,x50152))+~P85(f341(f71(x50151),x50152)) % 19.23/19.04 [5016]~P95(x50161)+E(f341(f73(x50161,f111(x50161)),x50162),f12(x50161,x50162))+~P85(f341(f71(x50161),x50162)) % 19.23/19.04 [5017]~P101(x50171)+E(f341(f73(x50171,f240(x50171)),x50172),f16(x50171,x50172))+~P85(f341(f71(x50171),x50172)) % 19.23/19.04 [5018]~P101(x50181)+E(f341(f73(x50181,f245(x50181)),x50182),f17(x50181,x50182))+~P85(f341(f71(x50181),x50182)) % 19.23/19.04 [5100]E(x51001,x51002)+~E(f341(f341(f3(a857),x51002),x51001),f2(a857))+~E(f341(f341(f3(a857),x51001),x51002),f2(a857)) % 19.23/19.04 [5110]P7(x51101)+~P37(x51102)+~P85(f341(f341(f343(a1),x51101),x51102)) % 19.23/19.04 [5140]~P113(x51401)+~E(f91(x51401,x51402),f87(x51401))+P85(f341(f341(f242(x51401),f2(x51401)),x51402)) % 19.23/19.04 [5151]~P89(x51511)+E(f341(f109(x51511),f341(f113(a857),x51512)),f341(f113(x51511),x51512))+P85(f341(a191,f341(f113(a1),x51512))) % 19.23/19.04 [5156]~P41(x51561,x51562)+P42(a850)+P85(f341(f71(f863(x51561,x51561)),x51562)) % 19.23/19.04 [5220]~P101(x52201)+E(f341(f73(x52201,f240(x52201)),x52202),f13(x52201,f240(x52201),x52202))+~P85(f341(f71(x52201),x52202)) % 19.23/19.04 [5221]~P101(x52211)+E(f341(f73(x52211,f245(x52211)),x52212),f14(x52211,f245(x52211),x52212))+~P85(f341(f71(x52211),x52212)) % 19.23/19.04 [5234]E(x52341,x52342)+P85(f341(f341(f242(a857),x52342),x52341))+P85(f341(f341(f242(a857),x52341),x52342)) % 19.23/19.04 [5235]E(x52351,x52352)+P85(f341(f341(f242(a1),x52352),x52351))+P85(f341(f341(f242(a1),x52351),x52352)) % 19.23/19.04 [5287]~P89(x52871)+E(f341(f109(x52871),f341(f113(a857),x52872)),f2(x52871))+~P85(f341(a191,f341(f113(a1),x52872))) % 19.23/19.04 [5290]~E(x52902,f341(a114,x52901))+E(x52901,f341(f109(a1),x52902))+~P85(f341(f341(f241(a1),f2(a1)),x52901)) % 19.23/19.04 [5291]~E(f341(a114,x52911),x52912)+E(x52911,f341(f109(a1),x52912))+~P85(f341(f341(f241(a1),f2(a1)),x52911)) % 19.23/19.04 [5292]~E(x52921,f341(a114,x52922))+E(f341(f109(a1),x52921),x52922)+~P85(f341(f341(f241(a1),f2(a1)),x52922)) % 19.23/19.04 [5302]E(x53021,f341(a114,x53022))+~E(x53022,f341(f109(a1),x53021))+~P85(f341(f341(f241(a1),f2(a1)),x53022)) % 19.23/19.04 [5303]E(f341(a114,x53031),x53032)+~E(x53031,f341(f109(a1),x53032))+~P85(f341(f341(f241(a1),f2(a1)),x53031)) % 19.23/19.04 [5333]~P86(x53332)+E(x53331,f2(x53332))+~P85(f341(f341(f288(x53332),f2(x53332)),x53331)) % 19.23/19.04 [5342]~P79(x53422)+E(x53421,f2(x53422))+P85(f341(f341(f242(x53422),f2(x53422)),f341(f84(x53422),x53421))) % 19.23/19.04 [5410]~P113(x54101)+E(f91(x54101,x54102),f87(x54101))+~P85(f341(f341(f242(x54101),f2(x54101)),x54102)) % 19.23/19.04 [5416]~P89(x54161)+E(f341(f109(x54161),f341(f113(a857),x54162)),f2(x54161))+P85(f341(f341(f241(a1),f2(a1)),f341(f113(a1),x54162))) % 19.23/19.04 [5423]~P79(x54231)+E(f341(f84(x54231),x54232),x54232)+~P85(f341(f341(f242(x54231),f2(x54231)),x54232)) % 19.23/19.04 [5424]~P79(x54241)+E(f341(f84(x54241),x54242),x54242)+~P85(f341(f341(f241(x54241),f2(x54241)),x54242)) % 19.23/19.04 [5431]E(x54311,f2(a857))+~E(f136(a857,f341(f303(a857,x54312),x54311)),f122(a857))+P85(f341(f341(f241(a857),x54311),x54312)) % 19.23/19.04 [5441]~P68(x54411)+E(f341(f341(f8(x54411,x54411),f7(x54411)),f341(f163(x54411),x54412)),f341(f160(x54411),x54412))+~P85(f341(f134(x54411),x54412)) % 19.23/19.04 [5444]~P136(x54441)+E(f341(f109(x54441),f341(a114,x54442)),f341(f112(x54441),x54442))+~P85(f341(f341(f241(a1),f2(a1)),x54442)) % 19.23/19.04 [5467]E(x54671,x54672)+P85(f341(f341(f242(a857),x54671),x54672))+~P85(f341(f341(f241(a857),x54671),x54672)) % 19.23/19.04 [5468]E(x54681,x54682)+P85(f341(f341(f242(a1),x54681),x54682))+~P85(f341(f341(f241(a1),x54681),x54682)) % 19.23/19.04 [5471]E(x54711,f87(a1))+~E(f341(f341(f90(a1),x54712),x54711),f87(a1))+~P85(f341(f341(f242(a1),f2(a1)),x54712)) % 19.23/19.04 [5472]E(x54721,f87(a1))+~E(f341(f341(f90(a1),x54721),x54722),f87(a1))+~P85(f341(f341(f242(a1),f2(a1)),x54721)) % 19.23/19.04 [5510]~P37(x55102)+P85(f341(f341(f241(a1),f2(a1)),x55101))+~P85(f341(f341(f343(a1),x55101),x55102)) % 19.23/19.04 [5521]~P85(f341(x55211,x55212))+P85(f341(x55211,f2(a857)))+P85(f341(x55211,f341(a121,f626(x55212,x55211)))) % 19.23/19.04 [5529]~P55(x55291,x55292)+P35(x55291,x55292)+~P85(f341(f71(f863(x55291,x55291)),x55292)) % 19.23/19.04 [5531]~P55(x55311,x55312)+P41(x55311,x55312)+~P85(f341(f71(f863(x55311,x55311)),x55312)) % 19.23/19.04 [5571]E(x55711,f185(f864(x55712,a850)))+~P85(f341(f71(x55712),x55711))+P85(f341(f341(f242(a857),f2(a857)),f341(f50(x55712),x55711))) % 19.23/19.04 [5597]~P85(f341(x55971,x55972))+P85(f341(x55971,f2(a857)))+P85(f341(f341(f242(a857),f803(x55972,x55971)),x55972)) % 19.23/19.04 [5622]E(x56221,f2(a857))+~E(f341(f160(a857),x56222),f2(a857))+~P85(f341(f341(f343(a857),x56221),f341(f163(a857),x56222))) % 19.23/19.04 [5684]~E(x56842,f2(a857))+P85(f341(f341(f241(a1),f2(a1)),x56841))+P85(f341(f341(f288(a857),f341(a114,x56841)),x56842)) % 19.23/19.04 [5687]E(x56871,x56872)+~P85(f341(f341(f241(a857),x56872),x56871))+~P85(f341(f341(f241(a857),x56871),x56872)) % 19.23/19.04 [5688]E(x56881,x56882)+~P85(f341(f341(f241(a1),x56882),x56881))+~P85(f341(f341(f241(a1),x56881),x56882)) % 19.23/19.04 [5697]E(x56971,x56972)+~P85(f341(f341(f288(a857),x56972),x56971))+~P85(f341(f341(f288(a857),x56971),x56972)) % 19.23/19.04 [5698]E(f341(f50(x56981),x56982),f2(a857))+~P85(f341(f71(x56981),x56982))+P85(f341(f341(f343(x56981),f627(x56982,x56981)),x56982)) % 19.23/19.04 [5704]E(f65(x57041,x57042),f61(x57041,x57042))+P85(f341(f341(f241(a1),f2(a1)),x57041))+~P85(f341(f341(f242(a1),f2(a1)),x57042)) % 19.23/19.04 [5733]~P85(f341(x57331,f800(x57331)))+P85(f341(x57331,f341(a114,x57332)))+~P85(f341(f341(f241(a1),f2(a1)),x57332)) % 19.23/19.04 [5735]P85(f341(f341(f242(a857),x57351),f379(x57352)))+~P85(f341(f71(a857),x57352))+~P85(f341(f341(f343(a857),x57351),x57352)) % 19.23/19.04 [5736]P85(f341(f341(f241(a857),x57361),f376(x57362)))+~P85(f341(f71(a857),x57362))+~P85(f341(f341(f343(a857),x57361),x57362)) % 19.23/19.04 [5765]E(x57651,x57652)+~P85(f341(f341(f242(a857),x57651),f341(a121,x57652)))+P85(f341(f341(f242(a857),x57651),x57652)) % 19.23/19.04 [5803]E(x58031,f341(a121,x58032))+~P85(f341(f341(f241(a857),x58031),f341(a121,x58032)))+P85(f341(f341(f241(a857),x58031),x58032)) % 19.23/19.04 [5813]P85(f341(x58131,f801(x58131)))+~P85(f341(x58131,f341(a114,x58132)))+~P85(f341(f341(f241(a1),f2(a1)),x58132)) % 19.23/19.04 [5815]E(f341(f84(a1),x58151),f341(f84(a1),x58152))+~P85(f341(f341(f288(a1),x58152),x58151))+~P85(f341(f341(f288(a1),x58151),x58152)) % 19.23/19.04 [5827]~P85(f341(x58271,x58272))+~P85(f341(f341(f241(a1),f2(a1)),x58272))+P85(f341(x58271,f341(f109(a1),f791(x58271)))) % 19.23/19.04 [5840]~P79(x58402)+~E(x58401,f2(x58402))+~P85(f341(f341(f242(x58402),f2(x58402)),f341(f84(x58402),x58401))) % 19.23/19.04 [5865]~P55(x58651,x58652)+P35(x58651,f341(f287(x58651,x58651),x58652))+~P85(f341(f71(f863(x58651,x58651)),x58652)) % 19.23/19.04 [5873]~P89(x58731)+E(f341(f109(x58731),f341(f113(a857),x58732)),f341(f113(x58731),x58732))+~P85(f341(f341(f241(a1),f2(a1)),f341(f113(a1),x58732))) % 19.23/19.04 [5877]E(f341(a121,x58771),x58772)+~P85(f341(f341(f242(a857),x58771),x58772))+P85(f341(f341(f242(a857),f341(a121,x58771)),x58772)) % 19.23/19.04 [5890]E(f341(f341(f51(a1),x58901),x58902),f2(a1))+~P85(f341(f341(f241(a1),x58901),f2(a1)))+~P85(f341(f341(f242(a1),x58902),x58901)) % 19.23/19.04 [5903]E(f60(a1,x59031,x59032),x59031)+~P85(f341(f341(f241(a1),x59031),f2(a1)))+~P85(f341(f341(f242(a1),x59032),x59031)) % 19.23/19.04 [5915]E(f62(x59151,x59152),f61(x59151,x59152))+~P85(f341(f341(f241(a1),f2(a1)),x59151))+~P85(f341(f341(f241(a1),f2(a1)),x59152)) % 19.23/19.04 [5923]E(f341(f341(f51(a1),x59231),x59232),f2(a1))+~P85(f341(f341(f241(a1),f2(a1)),x59231))+~P85(f341(f341(f242(a1),x59231),x59232)) % 19.23/19.04 [5937]E(f60(a857,f341(f113(a857),x59371),f341(f113(a857),x59372)),f341(f113(a857),x59371))+P85(f341(a191,f341(f113(a1),x59371)))+~P85(f341(a191,f341(f113(a1),x59372))) % 19.23/19.04 [5939]E(f60(a1,x59391,x59392),x59391)+~P85(f341(f341(f241(a1),f2(a1)),x59391))+~P85(f341(f341(f242(a1),x59391),x59392)) % 19.23/19.04 [5941]E(x59411,x59412)+~P85(f341(f341(f242(a857),x59411),f341(a121,x59412)))+~P85(f341(f341(f241(a857),x59412),x59411)) % 19.23/19.04 [5957]~P113(x59571)+~P85(f341(f341(f242(x59571),x59572),f2(x59571)))+P85(f341(f341(f242(x59571),x59572),f341(f88(x59571),x59572))) % 19.23/19.04 [5958]~P69(x59581)+~P85(f341(f341(f241(x59581),x59582),f2(x59581)))+P85(f341(f341(f241(x59581),x59582),f341(f88(x59581),x59582))) % 19.23/19.04 [5966]~P6(x59661)+E(f341(f341(f74(x59661,x59661,f111(x59661)),f248(x59661)),x59662),f53(x59661,x59662))+~P85(f341(f71(x59661),x59662)) % 19.23/19.04 [5967]~P6(x59671)+E(f341(f341(f74(x59671,x59671,f110(x59671)),f185(x59671)),x59672),f52(x59671,x59672))+~P85(f341(f71(x59671),x59672)) % 19.23/19.04 [5981]~P120(x59811)+~P85(f341(f341(f242(a857),f2(a857)),x59812))+P85(f341(f341(f242(x59811),f2(x59811)),f341(f109(x59811),x59812))) % 19.23/19.04 [5982]~P113(x59821)+~P85(f341(f341(f242(a1),f2(a1)),x59822))+P85(f341(f341(f242(x59821),f2(x59821)),f341(f112(x59821),x59822))) % 19.23/19.04 [5983]~P113(x59831)+~P85(f341(f341(f241(a1),f2(a1)),x59832))+P85(f341(f341(f241(x59831),f2(x59831)),f341(f112(x59831),x59832))) % 19.23/19.04 [5986]~P7(x59862)+~P7(x59861)+E(f341(f312(a857,a1,f109(a1)),f304(a857,f341(a114,x59861),f341(a114,x59862))),f304(a1,x59861,x59862)) % 19.23/19.04 [5992]P85(f341(x59921,x59922))+~P85(f341(f341(f241(a1),f2(a1)),x59922))+~P85(f341(x59921,f341(f109(a1),f798(x59921)))) % 19.23/19.04 [6019]E(f341(f341(f89(a857),f341(f113(a857),x60191)),f341(f113(a857),x60192)),f341(f113(a857),x60191))+P85(f341(f341(f242(a1),x60191),a92))+~P85(f341(f341(f242(a1),x60192),a92)) % 19.23/19.04 [6023]~P113(x60231)+P85(f341(f341(f242(x60231),f2(x60231)),f91(x60231,x60232)))+~P85(f341(f341(f242(x60231),f2(x60231)),x60232)) % 19.23/19.04 [6037]~P77(x60371)+~P85(f341(f341(f242(x60371),x60372),f2(x60371)))+P85(f341(f341(f242(x60371),f2(x60371)),f341(f88(x60371),x60372))) % 19.23/19.04 [6038]~P77(x60381)+~P85(f341(f341(f241(x60381),x60382),f2(x60381)))+P85(f341(f341(f241(x60381),f2(x60381)),f341(f88(x60381),x60382))) % 19.23/19.04 [6041]E(x60411,f2(a857))+P85(f341(f341(f241(a1),f2(a1)),x60412))+~P85(f341(f341(f288(a857),f341(a114,x60412)),x60411)) % 19.23/19.04 [6042]E(x60421,f248(f864(x60422,a850)))+~E(f341(f50(x60422),x60421),f341(f50(x60422),f248(f864(x60422,a850))))+~P85(f341(f71(x60422),f248(f864(x60422,a850)))) % 19.23/19.04 [6073]~P85(f341(f341(f242(a857),f2(a857)),x60732))+~P85(f341(f341(f288(a857),x60731),x60732))+P85(f341(f341(f241(a857),x60731),x60732)) % 19.23/19.04 [6074]~P85(f341(f341(f242(a1),f2(a1)),x60742))+~P85(f341(f341(f288(a1),x60741),x60742))+P85(f341(f341(f241(a1),x60741),x60742)) % 19.23/19.04 [6080]~P113(x60801)+P85(f341(f341(f242(x60801),x60802),f2(x60801)))+~P85(f341(f341(f242(x60801),x60802),f341(f88(x60801),x60802))) % 19.23/19.04 [6081]~P69(x60811)+P85(f341(f341(f241(x60811),x60812),f2(x60811)))+~P85(f341(f341(f241(x60811),x60812),f341(f88(x60811),x60812))) % 19.23/19.04 [6089]~P89(x60891)+P85(f341(f341(f343(x60891),f341(f113(x60891),x60892)),f182(x60891)))+~P85(f341(f341(f241(a1),a92),x60892)) % 19.23/19.04 [6119]E(x61191,f2(a857))+~P85(f341(f341(f242(a857),x61191),f341(a121,x61192)))+P85(f341(f341(f242(a857),f651(x61192,x61191)),x61192)) % 19.23/19.04 [6143]~P113(x61431)+~P85(f341(f341(f242(x61431),f2(x61431)),f91(x61431,x61432)))+P85(f341(f341(f242(x61431),f2(x61431)),x61432)) % 19.23/19.04 [6145]~E(f341(f113(a857),x61452),f341(f113(a857),x61451))+P85(f341(f341(f241(a1),f341(f113(a1),x61451)),f2(a1)))+~P85(f341(a191,f341(f113(a1),x61452))) % 19.23/19.04 [6173]E(f341(f249(a1,a1),f65(x61731,x61732)),f341(f341(f51(a1),x61731),x61732))+~P85(f341(f341(f242(a1),x61731),f2(a1)))+~P85(f341(f341(f242(a1),f2(a1)),x61732)) % 19.23/19.04 [6207]E(f341(f259(a1,a1),f65(x62071,x62072)),f60(a1,x62071,x62072))+~P85(f341(f341(f242(a1),x62071),f2(a1)))+~P85(f341(f341(f242(a1),f2(a1)),x62072)) % 19.23/19.04 [6209]E(x62091,f2(a1))+~P85(f341(f341(f288(a1),x62092),x62091))+P85(f341(f341(f241(a1),f341(f84(a1),x62092)),f341(f84(a1),x62091))) % 19.23/19.04 [6211]~P120(x62112)+~P85(f341(f341(f242(x62112),f2(x62112)),f341(f109(x62112),x62111)))+P85(f341(f341(f242(a857),f2(a857)),x62111)) % 19.23/19.04 [6212]~P113(x62122)+~P85(f341(f341(f242(x62122),f2(x62122)),f341(f112(x62122),x62121)))+P85(f341(f341(f242(a1),f2(a1)),x62121)) % 19.23/19.04 [6213]~P113(x62132)+~P85(f341(f341(f241(x62132),f2(x62132)),f341(f112(x62132),x62131)))+P85(f341(f341(f241(a1),f2(a1)),x62131)) % 19.23/19.04 [6217]~E(x62172,f2(a857))+P85(f341(f341(f288(a857),f341(a114,x62171)),x62172))+~P85(f341(f341(f288(a1),x62171),f341(f109(a1),x62172))) % 19.23/19.04 [6218]E(f341(f249(a1,a1),f62(x62181,x62182)),f341(f341(f51(a1),x62181),x62182))+~P85(f341(f341(f242(a1),f2(a1)),x62181))+~P85(f341(f341(f241(a1),f2(a1)),x62182)) % 19.23/19.04 [6231]E(f341(f259(a1,a1),f62(x62311,x62312)),f60(a1,x62311,x62312))+~P85(f341(f341(f242(a1),f2(a1)),x62311))+~P85(f341(f341(f241(a1),f2(a1)),x62312)) % 19.23/19.04 [6249]~P77(x62491)+P85(f341(f341(f242(x62491),x62492),f2(x62491)))+~P85(f341(f341(f242(x62491),f2(x62491)),f341(f88(x62491),x62492))) % 19.23/19.04 [6250]~P77(x62501)+P85(f341(f341(f241(x62501),x62502),f2(x62501)))+~P85(f341(f341(f241(x62501),f2(x62501)),f341(f88(x62501),x62502))) % 19.23/19.04 [6276]P85(f341(f64(x62761,x62762),f65(x62761,x62762)))+~P85(f341(f341(f242(a1),x62761),f2(a1)))+~P85(f341(f341(f242(a1),f2(a1)),x62762)) % 19.23/19.04 [6292]~P85(f341(f341(f242(a857),f2(a857)),x62921))+~P85(f341(f341(f288(a857),x62922),x62921))+~P85(f341(f341(f242(a857),x62921),x62922)) % 19.23/19.04 [6293]~P85(f341(f341(f242(a1),f2(a1)),x62931))+~P85(f341(f341(f288(a1),x62932),x62931))+~P85(f341(f341(f242(a1),x62931),x62932)) % 19.23/19.04 [6305]P85(f341(f64(x63051,x63052),f62(x63051,x63052)))+~P85(f341(f341(f242(a1),f2(a1)),x63052))+~P85(f341(f341(f241(a1),f2(a1)),x63051)) % 19.23/19.04 [6347]~P77(x63471)+P85(f341(f341(f242(x63471),f341(f88(x63471),x63472)),f2(x63471)))+~P85(f341(f341(f242(x63471),f2(x63471)),x63472)) % 19.23/19.04 [6348]~P77(x63481)+P85(f341(f341(f241(x63481),f341(f88(x63481),x63482)),f2(x63481)))+~P85(f341(f341(f241(x63481),f2(x63481)),x63482)) % 19.23/19.04 [6370]E(f341(f341(f3(a857),f341(a114,x63701)),f341(a114,x63702)),f341(a114,f193(x63701,x63702)))+~P85(f341(f341(f241(a1),f2(a1)),x63702))+~P85(f341(f341(f241(a1),f2(a1)),x63701)) % 19.23/19.04 [6388]P85(f341(f341(f241(a1),f2(a1)),f193(x63881,x63882)))+~P85(f341(f341(f241(a1),f2(a1)),x63882))+~P85(f341(f341(f241(a1),f2(a1)),x63881)) % 19.23/19.04 [6427]~P85(f341(x64271,x64272))+P85(f341(x64271,f2(a857)))+P85(f341(x64271,f341(f341(f89(a857),f803(x64272,x64271)),f87(a857)))) % 19.23/19.04 [6512]E(f341(f113(a857),x65121),f341(f113(a857),x65122))+~P85(f341(f341(f241(a1),f341(f113(a1),x65122)),f2(a1)))+~P85(f341(a191,f341(f113(a1),x65121))) % 19.23/19.04 [6525]~E(x65251,f2(a857))+~E(f757(x65252,x65251),f2(a857))+E(f341(f138(a857,a857,f89(a857),x65251),x65252),f2(a857)) % 19.23/19.04 [6551]~P85(f341(f71(x65511),f680(x65512,x65511)))+~P85(f341(f71(f864(x65511,a850)),x65512))+P85(f341(f71(x65511),f52(f864(x65511,a850),x65512))) % 19.23/19.04 [6557]E(x65571,x65572)+P85(f341(f341(f242(a1),x65571),x65572))+~P85(f341(f341(f242(a1),x65571),f341(f341(f89(a1),x65572),f87(a1)))) % 19.23/19.04 [6559]P85(f341(f341(f242(a857),f341(a114,x65591)),f341(a114,x65592)))+~P85(f341(f341(f242(a1),f2(a1)),x65592))+~P85(f341(f341(f242(a1),x65591),x65592)) % 19.23/19.04 [6560]P85(f341(f341(f242(a857),f341(a114,x65601)),f341(a114,x65602)))+~P85(f341(f341(f241(a1),f2(a1)),x65601))+~P85(f341(f341(f242(a1),x65601),x65602)) % 19.23/19.04 [6561]P85(f341(f341(f241(a857),f341(a114,x65611)),f341(a114,x65612)))+~P85(f341(f341(f242(a1),f2(a1)),x65611))+~P85(f341(f341(f241(a1),x65611),x65612)) % 19.23/19.04 [6562]P85(f341(f341(f241(a857),f341(a114,x65621)),f341(a114,x65622)))+~P85(f341(f341(f241(a1),f2(a1)),x65622))+~P85(f341(f341(f241(a1),x65621),x65622)) % 19.23/19.04 [6573]E(f60(a857,f341(a114,x65731),f341(a114,x65732)),f341(a114,f60(a1,x65731,x65732)))+~P85(f341(f341(f241(a1),f2(a1)),x65732))+~P85(f341(f341(f241(a1),f2(a1)),x65731)) % 19.23/19.04 [6593]~P77(x65931)+~P85(f341(f341(f242(x65931),f341(f88(x65931),x65932)),f2(x65931)))+P85(f341(f341(f242(x65931),f2(x65931)),x65932)) % 19.23/19.04 [6594]~P77(x65941)+~P85(f341(f341(f241(x65941),f341(f88(x65941),x65942)),f2(x65941)))+P85(f341(f341(f241(x65941),f2(x65941)),x65942)) % 19.23/19.04 [6611]~P85(f341(f341(f242(a1),a92),x66112))+~P85(f341(f341(f242(a1),x66111),x66112))+P85(f341(f341(f242(a857),f341(f113(a857),x66111)),f341(f113(a857),x66112))) % 19.23/19.04 [6707]~P85(f341(f341(f241(a1),f2(a1)),x67071))+P85(f341(f341(f242(a857),f341(a114,x67071)),x67072))+~P85(f341(f341(f242(a1),x67071),f341(f109(a1),x67072))) % 19.23/19.04 [6708]~P85(f341(f341(f241(a1),f2(a1)),x67081))+P85(f341(f341(f288(a857),f341(a114,x67081)),x67082))+~P85(f341(f341(f288(a1),x67081),f341(f109(a1),x67082))) % 19.23/19.04 [6724]E(x67241,f2(a1))+E(f60(a1,x67242,x67241),f2(a1))+E(f341(f341(f3(a1),f341(f88(a1),f341(f341(f51(a1),x67242),x67241))),f87(a1)),f341(f341(f51(a1),x67242),f341(f88(a1),x67241))) % 19.23/19.04 [6740]~P85(f341(f341(f241(a1),f2(a1)),x67401))+~P85(f341(f341(f242(a857),f341(a114,x67401)),x67402))+P85(f341(f341(f242(a1),x67401),f341(f109(a1),x67402))) % 19.23/19.04 [6741]~P85(f341(f341(f241(a1),f2(a1)),x67411))+~P85(f341(f341(f288(a857),f341(a114,x67411)),x67412))+P85(f341(f341(f288(a1),x67411),f341(f109(a1),x67412))) % 19.23/19.04 [6780]~P85(f341(f341(f241(a857),f341(a114,x67801)),f341(a114,x67802)))+~P85(f341(f341(f242(a1),f2(a1)),x67801))+P85(f341(f341(f241(a1),x67801),x67802)) % 19.23/19.04 [6781]~P85(f341(f341(f241(a857),f341(a114,x67811)),f341(a114,x67812)))+~P85(f341(f341(f241(a1),f2(a1)),x67812))+P85(f341(f341(f241(a1),x67811),x67812)) % 19.23/19.04 [6812]P85(f341(f341(f241(a1),x68121),x68122))+~P85(f341(f341(f241(a857),f341(f113(a857),x68121)),f341(f113(a857),x68122)))+P85(f341(f341(f241(a1),x68121),a92)) % 19.23/19.04 [6839]P85(f341(f341(f241(a1),f2(a1)),f60(a1,x68391,x68392)))+~P85(f341(f341(f241(a1),f2(a1)),x68392))+~P85(f341(f341(f241(a1),f2(a1)),x68391)) % 19.23/19.04 [6937]P85(f341(f341(f242(a1),a92),x69371))+~P85(f341(f341(f242(a1),x69372),x69371))+~P85(f341(f341(f242(a857),f341(f113(a857),x69372)),f341(f113(a857),x69371))) % 19.23/19.04 [6985]E(f341(f341(f250(a1,a1),f341(f341(f51(a1),x69851),x69852)),f60(a1,x69851,x69852)),f65(x69851,x69852))+~P85(f341(f341(f242(a1),x69851),f2(a1)))+~P85(f341(f341(f242(a1),f2(a1)),x69852)) % 19.23/19.04 [7006]E(f341(f341(f250(a1,a1),f341(f341(f51(a1),x70061),x70062)),f60(a1,x70061,x70062)),f62(x70061,x70062))+~P85(f341(f341(f241(a1),f2(a1)),x70062))+~P85(f341(f341(f241(a1),f2(a1)),x70061)) % 19.23/19.04 [7061]~P92(x70612)+E(x70611,f122(x70612))+E(f341(f138(x70612,x70612,f90(x70612),f341(f137(x70612),x70611)),f341(f162(x70612),x70611)),f341(f73(x70612,f90(x70612)),f341(f163(x70612),x70611))) % 19.23/19.04 [7174]~E(x71741,f2(a857))+E(f341(f138(a857,a857,f89(a857),x71741),x71742),f2(a857))+P85(f341(f341(f343(a857),f757(x71742,x71741)),f341(f163(a857),x71742))) % 19.23/19.04 [7228]~P85(f341(f341(f242(a1),x72282),f2(a1)))+P85(f341(f341(f242(a1),f341(f341(f51(a1),x72281),x72282)),f2(a1)))+~P85(f341(f341(f242(a1),f2(a1)),x72281)) % 19.23/19.04 [7230]~P85(f341(f341(f242(a1),x72301),f2(a1)))+P85(f341(f341(f242(a1),f341(f341(f51(a1),x72301),x72302)),f2(a1)))+~P85(f341(f341(f242(a1),f2(a1)),x72302)) % 19.23/19.04 [7231]~P85(f341(f341(f242(a1),x72312),f2(a1)))+P85(f341(f341(f241(a1),f341(f341(f51(a1),x72311),x72312)),f2(a1)))+~P85(f341(f341(f241(a1),f2(a1)),x72311)) % 19.23/19.04 [7232]~P85(f341(f341(f241(a1),x72321),f2(a1)))+P85(f341(f341(f241(a1),f341(f341(f51(a1),x72321),x72322)),f2(a1)))+~P85(f341(f341(f242(a1),f2(a1)),x72322)) % 19.23/19.04 [7241]P85(f341(f341(f343(f864(x72411,a850)),f680(x72412,x72411)),x72412))+~P85(f341(f71(f864(x72411,a850)),x72412))+P85(f341(f71(x72411),f52(f864(x72411,a850),x72412))) % 19.23/19.04 [7346]P26(x73461,x73461,x73462,f248(f864(x73461,a850)))+~E(f341(f312(x73461,x73461,x73462),f248(f864(x73461,a850))),f248(f864(x73461,a850)))+~P85(f341(f71(x73461),f248(f864(x73461,a850)))) % 19.23/19.04 [7474]~P26(x74741,x74741,x74742,f248(f864(x74741,a850)))+E(f341(f312(x74741,x74741,x74742),f248(f864(x74741,a850))),f248(f864(x74741,a850)))+~P85(f341(f71(x74741),f248(f864(x74741,a850)))) % 19.23/19.04 [7615]E(f341(f341(f51(a1),x76151),x76152),f341(f113(a1),a106))+~P85(f341(f341(f241(a1),f341(f341(f89(a1),x76151),x76152)),f2(a1)))+~P85(f341(f341(f242(a1),f2(a1)),x76151)) % 19.23/19.04 [7673]~P85(f341(f341(f242(a1),x76732),f2(a1)))+~P85(f341(f341(f242(a1),f341(f341(f51(a1),x76731),x76732)),f2(a1)))+P85(f341(f341(f242(a1),f2(a1)),x76731)) % 19.23/19.04 [7678]E(f341(f341(f89(a1),x76781),x76782),f60(a1,x76781,x76782))+~P85(f341(f341(f241(a1),f341(f341(f89(a1),x76781),x76782)),f2(a1)))+~P85(f341(f341(f242(a1),f2(a1)),x76781)) % 19.23/19.04 [7680]P85(f341(f341(f242(a1),x76801),f2(a1)))+~P85(f341(f341(f242(a1),f341(f341(f51(a1),x76801),x76802)),f2(a1)))+~P85(f341(f341(f242(a1),f2(a1)),x76802)) % 19.23/19.04 [7932]~P100(x79321)+P49(a857,x79321,f288(a857),x79322)+~P85(f341(f341(f241(x79321),f341(x79322,f349(x79322,x79321))),f341(x79322,f354(x79322,x79321)))) % 19.23/19.04 [8372]~P101(x83721)+P15(x83721,x83722)+~P85(f341(f341(f241(x83721),f341(f341(f158(x83721),x83722),f775(x83722,x83721))),f341(f341(f158(x83721),x83722),f776(x83722,x83721)))) % 19.23/19.04 [5565]E(x55651,f2(a1))+~E(f60(a1,x55652,x55651),f2(a1))+E(f341(f341(f51(a1),x55652),f341(f88(a1),x55651)),f341(f88(a1),f341(f341(f51(a1),x55652),x55651))) % 19.23/19.04 [5582]~P37(x55822)+~P37(x55821)+P37(f341(f341(f110(f864(a1,a850)),x55821),x55822)) % 19.23/19.04 [5583]~P37(x55832)+~P37(x55831)+P37(f341(f341(f111(f864(a1,a850)),x55831),x55832)) % 19.23/19.04 [5600]~P89(x56001)+~P59(x56001)+E(f341(f88(x56001),f341(f341(f292(x56001),f87(x56001)),x56002)),f341(f341(f292(x56001),f341(f113(x56001),a106)),x56002)) % 19.23/19.04 [5725]E(x57251,f2(a1))+~E(f60(a1,x57252,x57251),f2(a1))+E(f341(f341(f51(a1),f341(f88(a1),x57252)),x57251),f341(f88(a1),f341(f341(f51(a1),x57252),x57251))) % 19.23/19.04 [5860]~P101(x58601)+P15(x58601,x58602)+P85(f341(f341(f242(a857),f776(x58602,x58601)),f341(f186(f858(x58601)),x58602))) % 19.23/19.04 [6015]~P89(x60151)+~E(f341(f113(x60151),x60152),f2(x60151))+P32(x60151,f341(f113(x60151),f341(f341(f89(a1),x60152),f341(f88(a1),a92)))) % 19.23/19.04 [6016]~P89(x60161)+~E(f341(f113(x60161),x60162),f2(x60161))+P32(x60161,f341(f113(x60161),f341(f341(f89(a1),a92),f341(f88(a1),x60162)))) % 19.23/19.04 [6018]E(f341(a66,f62(f341(f88(a1),x60181),f341(f88(a1),x60182))),f61(x60181,x60182))+P85(f341(f341(f242(a1),f2(a1)),x60182))+P85(f341(f341(f241(a1),f2(a1)),x60181)) % 19.23/19.04 [6151]~E(x61512,f2(a857))+~E(x61511,f2(a857))+P85(f341(f341(f241(a1),f341(f109(a1),x61511)),f341(f88(a1),f341(f109(a1),x61512)))) % 19.23/19.04 [6177]E(f341(f341(f89(a857),f341(f113(a857),x61771)),f341(f113(a857),x61772)),f341(f113(a857),f341(f341(f89(a1),x61771),x61772)))+P85(f341(f341(f242(a1),x61771),a92))+P85(f341(f341(f242(a1),x61772),a92)) % 19.23/19.04 [6314]~P69(x63141)+~P85(f341(f341(f242(x63141),f2(x63141)),x63142))+P85(f341(f341(f242(x63141),f341(f88(x63141),x63142)),x63142)) % 19.23/19.04 [6315]~P69(x63151)+~P85(f341(f341(f241(x63151),f2(x63151)),x63152))+P85(f341(f341(f241(x63151),f341(f88(x63151),x63152)),x63152)) % 19.23/19.04 [6497]E(f341(f341(f3(a857),f341(a114,x64971)),f341(a114,x64972)),f341(a114,f341(f341(f3(a1),x64971),x64972)))+~P85(f341(f341(f241(a1),f2(a1)),x64972))+~P85(f341(f341(f241(a1),x64972),x64971)) % 19.23/19.04 [6534]E(f341(a114,f60(a1,f341(f113(a1),x65341),f341(f113(a1),x65342))),f60(a857,f341(f113(a857),x65341),f341(f113(a857),x65342)))+P85(f341(a191,f341(f113(a1),x65341)))+P85(f341(a191,f341(f113(a1),x65342))) % 19.23/19.04 [6552]~P69(x65521)+P85(f341(f341(f242(x65521),f2(x65521)),x65522))+~P85(f341(f341(f242(x65521),f341(f88(x65521),x65522)),x65522)) % 19.23/19.04 [6553]~P69(x65531)+P85(f341(f341(f241(x65531),f2(x65531)),x65532))+~P85(f341(f341(f241(x65531),f341(f88(x65531),x65532)),x65532)) % 19.23/19.04 [6564]~P69(x65641)+~P85(f341(f341(f242(x65641),f2(x65641)),x65642))+P85(f341(f341(f242(x65641),f2(x65641)),f341(f341(f89(x65641),x65642),x65642))) % 19.23/19.04 [6566]~P69(x65661)+~P85(f341(f341(f241(x65661),f2(x65661)),x65662))+P85(f341(f341(f241(x65661),f2(x65661)),f341(f341(f89(x65661),x65662),x65662))) % 19.23/19.04 [6577]E(f341(f341(f89(a857),f341(a114,x65771)),f341(a114,x65772)),f341(a114,f341(f341(f89(a1),x65771),x65772)))+~P85(f341(f341(f241(a1),f2(a1)),x65772))+~P85(f341(f341(f241(a1),f2(a1)),x65771)) % 19.23/19.04 [6589]E(x65891,f2(a857))+P85(f341(f341(f242(a857),f2(a857)),x65892))+~P85(f341(f341(f242(a857),f2(a857)),f341(f341(f251(a857),x65892),x65891))) % 19.23/19.04 [6622]~P89(x66221)+E(f341(f113(x66221),x66222),f2(x66221))+~P32(x66221,f341(f113(x66221),f341(f341(f89(a1),a92),f341(f88(a1),x66222)))) % 19.23/19.04 [6623]~P89(x66231)+E(f341(f113(x66231),x66232),f2(x66231))+~P32(x66231,f341(f113(x66231),f341(f341(f89(a1),x66232),f341(f88(a1),a92)))) % 19.23/19.04 [6684]~P85(f341(f71(x66841),x66842))+~P85(f341(f71(x66841),f248(f864(x66841,a850))))+P85(f341(f71(x66841),f341(f88(f864(x66841,a850)),x66842))) % 19.23/19.04 [6709]~P85(f341(f341(f242(a1),f2(a1)),x67092))+~P85(f341(f341(f241(a1),x67092),x67091))+P85(f341(f341(f242(a1),f2(a1)),f341(f341(f51(a1),x67091),x67092))) % 19.23/19.04 [6710]~P85(f341(f341(f242(a1),x67102),f2(a1)))+~P85(f341(f341(f241(a1),x67101),f2(a1)))+P85(f341(f341(f241(a1),f2(a1)),f341(f341(f51(a1),x67101),x67102))) % 19.23/19.04 [6751]~P85(f341(f341(f242(a857),f2(a857)),x67512))+~P85(f341(f341(f242(a857),f2(a857)),x67511))+P85(f341(f341(f242(a857),f2(a857)),f341(f341(f90(a857),x67511),x67512))) % 19.23/19.04 [6752]~P85(f341(f341(f241(a1),f2(a1)),x67522))+~P85(f341(f341(f241(a1),f2(a1)),x67521))+P85(f341(f341(f241(a1),f2(a1)),f341(f341(f89(a1),x67521),x67522))) % 19.23/19.04 [6753]~P85(f341(f341(f241(a1),f2(a1)),x67532))+~P85(f341(f341(f241(a1),f2(a1)),x67531))+P85(f341(f341(f241(a1),f2(a1)),f341(f341(f90(a1),x67531),x67532))) % 19.23/19.04 [6754]~P85(f341(f341(f242(a1),f2(a1)),x67542))+~P85(f341(f341(f241(a1),f2(a1)),x67541))+P85(f341(f341(f241(a1),f2(a1)),f341(f341(f51(a1),x67541),x67542))) % 19.23/19.04 [6755]~P85(f341(f341(f241(a1),f2(a1)),x67552))+~P85(f341(f341(f241(a1),f2(a1)),x67551))+P85(f341(f341(f241(a1),f2(a1)),f341(f341(f51(a1),x67551),x67552))) % 19.23/19.04 [6824]E(x68241,f2(a1))+E(f60(a1,x68242,x68241),f2(a1))+E(f341(f341(f3(a1),f341(f88(a1),f341(f341(f51(a1),x68242),x68241))),f87(a1)),f341(f341(f51(a1),f341(f88(a1),x68242)),x68241)) % 19.23/19.04 [6884]P85(f341(f341(f242(a857),f2(a857)),x68841))+P85(f341(f341(f242(a857),f2(a857)),x68842))+~P85(f341(f341(f242(a857),f2(a857)),f341(f341(f89(a857),x68842),x68841))) % 19.23/19.04 [6885]~P69(x68851)+P85(f341(f341(f242(x68851),f2(x68851)),x68852))+~P85(f341(f341(f242(x68851),f2(x68851)),f341(f341(f89(x68851),x68852),x68852))) % 19.23/19.04 [6886]~P69(x68861)+P85(f341(f341(f241(x68861),f2(x68861)),x68862))+~P85(f341(f341(f241(x68861),f2(x68861)),f341(f341(f89(x68861),x68862),x68862))) % 19.23/19.04 [6938]~P85(f341(f71(x69381),x69382))+P85(f341(f71(x69381),f248(f864(x69381,a850))))+~P85(f341(f71(x69381),f341(f88(f864(x69381,a850)),x69382))) % 19.23/19.04 [6998]P85(f341(f341(f241(a1),x69981),f2(a1)))+~P85(f341(f341(f242(a1),x69982),f2(a1)))+~P85(f341(f341(f241(a1),f2(a1)),f341(f341(f51(a1),x69981),x69982))) % 19.23/19.04 [7004]~P85(f341(f341(f242(a1),f2(a1)),x70041))+P85(f341(f341(f241(a1),x70041),x70042))+~P85(f341(f341(f242(a1),f2(a1)),f341(f341(f51(a1),x70042),x70041))) % 19.23/19.04 [7005]~P85(f341(f341(f241(a1),f2(a1)),x70052))+P85(f341(f341(f241(a1),x70051),x70052))+~P85(f341(f341(f242(a1),f2(a1)),f341(f341(f51(a1),x70052),x70051))) % 19.23/19.04 [7037]P85(f341(f341(f242(a1),f2(a1)),x70371))+~P85(f341(f341(f241(a1),f2(a1)),x70372))+~P85(f341(f341(f242(a1),f2(a1)),f341(f341(f51(a1),x70372),x70371))) % 19.23/19.04 [7038]P85(f341(f341(f241(a1),f2(a1)),x70381))+~P85(f341(f341(f242(a1),f2(a1)),x70382))+~P85(f341(f341(f241(a1),f2(a1)),f341(f341(f51(a1),x70381),x70382))) % 19.23/19.04 [7505]~P85(f341(f71(x75052),f248(f864(x75052,a850))))+~P85(f341(f71(x75051),f248(f864(x75051,a850))))+P85(f341(f71(f865(x75051,x75052)),f248(f864(f865(x75051,x75052),a850)))) % 19.23/19.04 [7506]~P85(f341(f71(x75062),f248(f864(x75062,a850))))+~P85(f341(f71(x75061),f248(f864(x75061,a850))))+P85(f341(f71(f863(x75061,x75062)),f248(f864(f863(x75061,x75062),a850)))) % 19.23/19.04 [7578]~P85(f341(f341(f242(a857),f341(a121,f2(a857))),x75781))+~P85(f341(f341(f242(a857),f341(a121,f2(a857))),x75782))+P85(f341(f341(f242(a857),x75781),f341(f341(f90(a857),x75782),x75781))) % 19.23/19.04 [7579]~P85(f341(f341(f242(a857),f341(a121,f2(a857))),x75791))+~P85(f341(f341(f242(a857),f341(a121,f2(a857))),x75792))+P85(f341(f341(f242(a857),x75791),f341(f341(f90(a857),x75791),x75792))) % 19.23/19.04 [7614]E(f341(f50(x76141),f248(f864(x76141,a850))),f341(a121,f2(a857)))+P85(f341(f71(x76142),f248(f864(x76142,a850))))+~P85(f341(f71(f864(x76142,x76141)),f248(f864(f864(x76142,x76141),a850)))) % 19.23/19.04 [7739]~P85(f341(f341(f242(a857),f341(a121,f2(a857))),x77392))+~P85(f341(f341(f242(a857),f341(a121,f2(a857))),x77391))+P85(f341(f341(f242(a857),f341(a121,f2(a857))),f341(f341(f90(a857),x77391),x77392))) % 19.23/19.04 [7740]~P85(f341(f341(f241(a857),f341(a121,f2(a857))),x77401))+~P85(f341(f341(f241(a857),f341(a121,f2(a857))),x77402))+P85(f341(f341(f241(a857),f341(a121,f2(a857))),f341(f341(f90(a857),x77401),x77402))) % 19.23/19.04 [8515]~P37(x85152)+~P37(x85151)+E(f341(f312(a857,a1,f109(a1)),f341(f341(f110(f864(a857,a850)),f341(f312(a1,a857,a114),x85151)),f341(f312(a1,a857,a114),x85152))),f341(f341(f110(f864(a1,a850)),x85151),x85152)) % 19.23/19.04 [8516]~P37(x85162)+~P37(x85161)+E(f341(f312(a857,a1,f109(a1)),f341(f341(f111(f864(a857,a850)),f341(f312(a1,a857,a114),x85161)),f341(f312(a1,a857,a114),x85162))),f341(f341(f111(f864(a1,a850)),x85161),x85162)) % 19.23/19.04 [9109]~P89(x91091)+~E(f341(f113(x91091),x91092),f87(x91091))+P32(x91091,f341(f113(x91091),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f88(a1),x91092)))) % 19.23/19.04 [9323]~P89(x93231)+E(f341(f113(x93231),x93232),f87(x93231))+~P32(x93231,f341(f113(x93231),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f88(a1),x93232)))) % 19.23/19.04 [9745]~P100(x97452)+P51(a857,x97452,f341(f341(f20(a857,f864(a857,a850),f864(a857,a850)),f341(f341(f10(f864(a857,f864(a850,a850)),f864(f864(a857,a850),f864(a857,a850)),a857),f20(a857,a850,a850)),f341(f341(f10(f864(a857,a850),f864(a857,f864(a850,a850)),a857),f341(f10(a850,f864(a850,a850),a857),a339)),f288(a857)))),f341(f341(f10(f864(a857,a850),f864(a857,a850),a857),f341(f10(a850,a850,a857),a337)),f341(f9(a857,a857,a850),f288(a857)))),x97451)+P85(f341(f341(f288(a857),f352(x97451,x97452)),f353(x97451,x97452))) % 19.23/19.04 [9748]~P100(x97481)+P51(a857,x97481,f341(f341(f20(a857,f864(a857,a850),f864(a857,a850)),f341(f341(f10(f864(a857,f864(a850,a850)),f864(f864(a857,a850),f864(a857,a850)),a857),f20(a857,a850,a850)),f341(f341(f10(f864(a857,a850),f864(a857,f864(a850,a850)),a857),f341(f10(a850,f864(a850,a850),a857),a339)),f288(a857)))),f341(f341(f10(f864(a857,a850),f864(a857,a850),a857),f341(f10(a850,a850,a857),a337)),f341(f9(a857,a857,a850),f288(a857)))),x97482)+~P85(f341(f341(f288(a857),f353(x97482,x97481)),f352(x97482,x97481))) % 19.23/19.04 [9749]~P100(x97491)+P51(a857,x97491,f341(f341(f20(a857,f864(a857,a850),f864(a857,a850)),f341(f341(f10(f864(a857,f864(a850,a850)),f864(f864(a857,a850),f864(a857,a850)),a857),f20(a857,a850,a850)),f341(f341(f10(f864(a857,a850),f864(a857,f864(a850,a850)),a857),f341(f10(a850,f864(a850,a850),a857),a339)),f288(a857)))),f341(f341(f10(f864(a857,a850),f864(a857,a850),a857),f341(f10(a850,a850,a857),a337)),f341(f9(a857,a857,a850),f288(a857)))),x97492)+~P85(f341(f341(f242(x97491),f341(x97492,f352(x97492,x97491))),f341(x97492,f353(x97492,x97491)))) % 19.23/19.04 [9841]~P100(x98411)+P49(a857,x98411,f288(a857),x98412)+~P51(a857,x98411,f341(f341(f20(a857,f864(a857,a850),f864(a857,a850)),f341(f341(f10(f864(a857,f864(a850,a850)),f864(f864(a857,a850),f864(a857,a850)),a857),f20(a857,a850,a850)),f341(f341(f10(f864(a857,a850),f864(a857,f864(a850,a850)),a857),f341(f10(a850,f864(a850,a850),a857),a339)),f288(a857)))),f341(f341(f10(f864(a857,a850),f864(a857,a850),a857),f341(f10(a850,a850,a857),a337)),f341(f9(a857,a857,a850),f288(a857)))),x98412) % 19.23/19.04 [10037]E(x100371,f2(a1))+E(x100372,f2(a1))+E(f341(f261(a1,a1,a1,a1,f41(a1),f341(f90(a1),f91(a1,x100372))),f341(f341(f341(f105(f863(a1,a1)),f341(f341(a338,f91(a1,x100371)),f91(a1,x100372))),f68(x100371,x100372)),f341(f341(f260(a1,a1,f863(a1,a1)),f341(f341(f20(a1,f864(a1,f863(a1,a1)),f864(a1,f863(a1,a1))),f341(f341(f10(f864(a1,f864(f863(a1,a1),f863(a1,a1))),f864(f864(a1,f863(a1,a1)),f864(a1,f863(a1,a1))),a1),f20(a1,f863(a1,a1),f863(a1,a1))),f341(f341(f10(f863(a1,a1),f864(a1,f864(f863(a1,a1),f863(a1,a1))),a1),f341(f9(a1,f863(a1,a1),f864(f863(a1,a1),f863(a1,a1))),f341(f341(f10(a850,f864(f863(a1,a1),f864(f863(a1,a1),f863(a1,a1))),a1),f105(f863(a1,a1))),f341(f341(f9(a1,a1,a850),a338),f2(a1))))),f341(f341(f9(a1,a1,f863(a1,a1)),f341(f341(f10(a1,f864(a1,f863(a1,a1)),a1),f250(a1,a1)),f88(a1))),f2(a1))))),f341(f341(f9(a1,f864(a1,a1),f864(a1,f863(a1,a1))),f341(f341(f10(f864(a1,f863(a1,a1)),f864(f864(a1,a1),f864(a1,f863(a1,a1))),a1),f10(a1,f863(a1,a1),a1)),f341(f341(f10(a1,f864(a1,f863(a1,a1)),a1),f250(a1,a1)),f341(f341(f9(a1,a1,a1),f341(f341(f10(a1,f864(a1,a1),a1),f3(a1)),f88(a1))),f87(a1))))),f341(f3(a1),f341(f84(a1),x100372))))),f68(x100371,x100372)))),f61(x100371,x100372)) % 19.23/19.04 [10038]E(x100381,f2(a1))+E(x100382,f2(a1))+E(f341(f261(a1,a1,a1,a1,f41(a1),f341(f90(a1),f91(a1,x100382))),f341(f341(f341(f105(f863(a1,a1)),f341(f341(a340,f341(f341(a339,f341(f341(f242(a1),f2(a1)),x100382)),f341(f341(f241(a1),f2(a1)),x100381))),f341(f341(a339,f341(f341(f242(a1),x100382),f2(a1))),f341(f341(f242(a1),x100381),f2(a1))))),f68(x100381,x100382)),f341(f341(f260(a1,a1,f863(a1,a1)),f341(f341(f20(a1,f864(a1,f863(a1,a1)),f864(a1,f863(a1,a1))),f341(f341(f10(f864(a1,f864(f863(a1,a1),f863(a1,a1))),f864(f864(a1,f863(a1,a1)),f864(a1,f863(a1,a1))),a1),f20(a1,f863(a1,a1),f863(a1,a1))),f341(f341(f10(f863(a1,a1),f864(a1,f864(f863(a1,a1),f863(a1,a1))),a1),f341(f9(a1,f863(a1,a1),f864(f863(a1,a1),f863(a1,a1))),f341(f341(f10(a850,f864(f863(a1,a1),f864(f863(a1,a1),f863(a1,a1))),a1),f105(f863(a1,a1))),f341(f341(f9(a1,a1,a850),a338),f2(a1))))),f341(f341(f9(a1,a1,f863(a1,a1)),f341(f341(f10(a1,f864(a1,f863(a1,a1)),a1),f250(a1,a1)),f88(a1))),f2(a1))))),f341(f341(f9(a1,f864(a1,a1),f864(a1,f863(a1,a1))),f341(f341(f10(f864(a1,f863(a1,a1)),f864(f864(a1,a1),f864(a1,f863(a1,a1))),a1),f10(a1,f863(a1,a1),a1)),f341(f341(f10(a1,f864(a1,f863(a1,a1)),a1),f250(a1,a1)),f341(f341(f9(a1,a1,a1),f341(f341(f10(a1,f864(a1,a1),a1),f3(a1)),f88(a1))),f87(a1))))),f341(f3(a1),f341(f84(a1),x100382))))),f68(x100381,x100382)))),f61(x100381,x100382)) % 19.23/19.04 [5590]~P113(x55901)+~P89(x55901)+E(f341(f84(x55901),f341(f341(f251(x55901),f341(f113(x55901),a106)),x55902)),f87(x55901)) % 19.23/19.04 [6090]~P136(x60901)+~P85(f341(f341(f242(a1),x60902),f2(a1)))+E(f341(f88(x60901),f341(f109(x60901),f341(a114,f341(f88(a1),x60902)))),f341(f112(x60901),x60902)) % 19.23/19.04 [6298]P85(f341(f341(f241(a108),x62981),f87(a108)))+E(f341(f341(f89(a108),f87(a108)),f276(x62981,f341(f341(f51(a108),x62982),x62981))),f276(x62981,x62982))+P85(f341(f341(f242(a108),x62982),x62981)) % 19.23/19.04 [6371]E(x63711,f2(a1))+~E(f341(f84(a1),x63712),f87(a1))+P85(f341(f341(f288(a1),f341(f341(f90(a1),x63711),x63712)),x63711)) % 19.23/19.04 [6793]~E(x67932,f87(a857))+~P85(f341(f341(f242(a857),f2(a857)),x67931))+P85(f341(f341(f288(a857),f341(f341(f90(a857),x67931),x67932)),x67931)) % 19.23/19.04 [6794]~E(x67941,f87(a857))+~P85(f341(f341(f242(a857),f2(a857)),x67942))+P85(f341(f341(f288(a857),f341(f341(f90(a857),x67941),x67942)),x67942)) % 19.23/19.04 [6927]~P88(x69271)+~P85(f341(f341(f343(x69271),x69272),f119(x69271)))+~E(f341(f341(f89(x69271),f341(f341(f89(x69271),f87(x69271)),x69272)),x69272),f2(x69271)) % 19.23/19.04 [7039]~P85(f341(f341(f242(a1),x70391),f2(a1)))+~P85(f341(f341(f241(a1),x70392),f2(a1)))+E(f341(f249(a1,a1),f341(a66,f62(f341(f88(a1),x70391),f341(f88(a1),x70392)))),f341(f341(f51(a1),x70391),x70392)) % 19.23/19.04 [7055]~P85(f341(f341(f242(a1),x70551),f2(a1)))+~P85(f341(f341(f241(a1),x70552),f2(a1)))+E(f341(f259(a1,a1),f341(a66,f62(f341(f88(a1),x70551),f341(f88(a1),x70552)))),f60(a1,x70551,x70552)) % 19.23/19.04 [7063]~P85(f341(f341(f242(a1),x70632),f2(a1)))+E(f341(f249(a1,a1),f341(a66,f65(f341(f88(a1),x70631),f341(f88(a1),x70632)))),f341(f341(f51(a1),x70631),x70632))+~P85(f341(f341(f242(a1),f2(a1)),x70631)) % 19.23/19.04 [7067]E(x70671,f2(a1))+E(f341(f84(a1),x70672),f87(a1))+~P85(f341(f341(f288(a1),f341(f341(f90(a1),x70671),x70672)),x70671)) % 19.23/19.04 [7082]~P85(f341(f341(f242(a1),x70822),f2(a1)))+E(f341(f259(a1,a1),f341(a66,f65(f341(f88(a1),x70821),f341(f88(a1),x70822)))),f60(a1,x70821,x70822))+~P85(f341(f341(f242(a1),f2(a1)),x70821)) % 19.23/19.04 [7132]E(f341(f341(f51(a1),f341(f341(f251(a1),x71321),x71322)),x71321),f341(f341(f251(a1),x71321),f341(f341(f3(a857),x71322),f341(a121,f2(a857)))))+~P85(f341(f341(f242(a857),f2(a857)),x71322))+~P85(f341(f341(f242(a1),f2(a1)),x71321)) % 19.23/19.04 [7237]~P85(f341(f341(f242(a857),f2(a857)),x72371))+~P85(f341(f341(f242(a857),f87(a857)),x72372))+P85(f341(f341(f242(a857),f341(f341(f51(a857),x72371),x72372)),x72371)) % 19.23/19.04 [7238]~P85(f341(f341(f242(a857),f2(a857)),x72381))+~P85(f341(f341(f242(a857),f2(a857)),x72382))+P85(f341(f341(f242(a857),f341(f341(f3(a857),x72381),x72382)),x72381)) % 19.23/19.04 [7239]~P85(f341(f341(f242(a1),f2(a1)),x72391))+~P85(f341(f341(f242(a1),f87(a1)),x72392))+P85(f341(f341(f242(a1),f341(f341(f51(a1),x72391),x72392)),x72391)) % 19.23/19.04 [7398]E(x73981,f2(a857))+~E(x73982,f2(a1))+~P85(f341(f341(f242(a1),f2(a1)),f341(f341(f251(a1),f341(f84(a1),x73982)),x73981))) % 19.23/19.04 [7435]E(x74351,f87(a857))+~P85(f341(f341(f242(a857),f2(a857)),x74352))+~P85(f341(f341(f288(a857),f341(f341(f90(a857),x74352),x74351)),x74352)) % 19.23/19.04 [7436]E(x74361,f87(a857))+~P85(f341(f341(f242(a857),f2(a857)),x74362))+~P85(f341(f341(f288(a857),f341(f341(f90(a857),x74361),x74362)),x74362)) % 19.23/19.04 [7822]~E(x78222,f122(f858(x78221)))+E(f341(f186(f858(f858(x78221))),f169(x78221,x78222)),f2(a857))+~P15(a857,f341(f148(a857),f341(f341(f149(f858(x78221),a857),f186(f858(x78221))),x78222))) % 19.23/19.04 [8071]P85(f341(x80711,x80712))+~P85(f341(x80711,f341(a117,f576(x80711,x80712))))+~P85(f341(f341(f343(f864(f863(a857,a857),a850)),x80712),a107)) % 19.23/19.04 [8085]E(x80851,f122(f858(x80852)))+E(f341(f186(f858(x80852)),f341(f341(f158(f858(x80852)),x80851),f2(a857))),f341(f186(f858(f858(x80852))),f169(x80852,x80851)))+~P15(a857,f341(f148(a857),f341(f341(f149(f858(x80852),a857),f186(f858(x80852))),x80851))) % 19.23/19.04 [8755]~P85(f341(f71(x87551),f341(f265(x87551),x87552)))+~P85(f341(f71(x87551),f248(f864(x87551,a850))))+P85(f341(f71(x87551),f341(f265(x87551),f341(f341(f10(a850,a850,x87551),a337),x87552)))) % 19.23/19.04 [8808]E(f341(f341(f250(a857,a857),f341(a121,f341(f341(f51(a857),f341(f341(f3(a857),x88081),x88082)),x88082))),f60(a857,f341(f341(f3(a857),x88081),x88082),x88082)),f94(f863(a857,a857),f63(x88081,x88082)))+~P85(f341(f341(f242(a857),f2(a857)),x88082))+~P85(f341(f341(f241(a857),x88082),x88081)) % 19.23/19.04 [9077]~P85(f341(f71(x90771),f341(f265(x90771),x90772)))+P85(f341(f71(x90771),f248(f864(x90771,a850))))+~P85(f341(f71(x90771),f341(f265(x90771),f341(f341(f10(a850,a850,x90771),a337),x90772)))) % 19.23/19.04 [9742]P27(x97421,x97422)+~P35(x97421,f341(f249(f864(f863(x97421,x97421),a850),f864(f863(x97421,x97421),a850)),x97422))+~P85(f341(f341(f241(f864(f863(x97421,x97421),a850)),f341(f341(f290(x97421,x97421,x97421),f341(f249(f864(f863(x97421,x97421),a850),f864(f863(x97421,x97421),a850)),x97422)),f341(f259(f864(f863(x97421,x97421),a850),f864(f863(x97421,x97421),a850)),x97422))),f341(f249(f864(f863(x97421,x97421),a850),f864(f863(x97421,x97421),a850)),x97422))) % 19.23/19.04 [9845]~E(f301(a857,f288(a857),f341(f341(f20(a857,f864(a857,a850),f864(a857,a850)),f341(f341(f10(f864(a857,f864(a850,a850)),f864(f864(a857,a850),f864(a857,a850)),a857),f20(a857,a850,a850)),f341(f341(f10(f864(a857,a850),f864(a857,f864(a850,a850)),a857),f341(f10(a850,f864(a850,a850),a857),a339)),f288(a857)))),f341(f341(f10(f864(a857,a850),f864(a857,a850),a857),f341(f10(a850,a850,a857),a337)),f341(f9(a857,a857,a850),f288(a857)))),x98452,x98451),f185(f864(a857,a850)))+~P85(f341(f341(f288(a857),x98452),x98451))+P85(f341(f341(f288(a857),x98451),x98452)) % 19.23/19.04 [9846]~E(f298(a857,f288(a857),f341(f341(f20(a857,f864(a857,a850),f864(a857,a850)),f341(f341(f10(f864(a857,f864(a850,a850)),f864(f864(a857,a850),f864(a857,a850)),a857),f20(a857,a850,a850)),f341(f341(f10(f864(a857,a850),f864(a857,f864(a850,a850)),a857),f341(f10(a850,f864(a850,a850),a857),a339)),f288(a857)))),f341(f341(f10(f864(a857,a850),f864(a857,a850),a857),f341(f10(a850,a850,a857),a337)),f341(f9(a857,a857,a850),f288(a857)))),x98462,x98461),f185(f864(a857,a850)))+~P85(f341(f341(f288(a857),x98462),x98461))+P85(f341(f341(f288(a857),x98461),x98462)) % 19.23/19.04 [7156]~P85(f341(f341(f242(a857),f2(a857)),x71562))+P85(f341(f341(f242(a857),x71561),x71562))+E(f341(a121,f341(f341(f51(a857),f341(f341(f3(a857),x71561),x71562)),x71562)),f341(f341(f51(a857),x71561),x71562)) % 19.23/19.04 [7313]~P85(f341(f341(f242(a857),f2(a857)),x73132))+~P85(f341(f341(f241(a857),x73132),x73131))+E(f341(a121,f341(f341(f51(a857),f341(f341(f3(a857),x73131),x73132)),x73132)),f341(f341(f51(a857),x73131),x73132)) % 19.23/19.04 [8283]~P89(x82831)+~P88(x82831)+~P32(x82831,f341(f113(x82831),f341(f341(f3(a1),f341(f341(f89(a1),x82832),x82832)),a106))) % 19.23/19.04 [8984]E(x89841,f2(a857))+E(f341(f341(f260(a857,a857,f863(a857,a857)),f341(f341(f10(a857,f864(a857,f863(a857,a857)),a857),f250(a857,a857)),a121)),f94(f863(a857,a857),f63(f341(f341(f3(a857),x89842),x89841),x89841))),f94(f863(a857,a857),f63(x89842,x89841)))+P85(f341(f341(f242(a857),x89842),x89841)) % 19.23/19.04 [9381]P85(f341(x93812,f707(x93812,x93811)))+P85(f341(x93811,f707(x93812,x93811)))+E(f341(f265(a1),f341(f341(f20(a1,a850,a850),f341(f341(f10(a850,f864(a850,a850),a1),a339),f341(f241(a1),f2(a1)))),x93811)),f341(f265(a1),f341(f341(f20(a1,a850,a850),f341(f341(f10(a850,f864(a850,a850),a1),a339),f341(f241(a1),f2(a1)))),x93812))) % 19.23/19.04 [9385]~P85(f341(x93852,f707(x93852,x93851)))+~P85(f341(x93851,f707(x93852,x93851)))+E(f341(f265(a1),f341(f341(f20(a1,a850,a850),f341(f341(f10(a850,f864(a850,a850),a1),a339),f341(f241(a1),f2(a1)))),x93851)),f341(f265(a1),f341(f341(f20(a1,a850,a850),f341(f341(f10(a850,f864(a850,a850),a1),a339),f341(f241(a1),f2(a1)))),x93852))) % 19.23/19.04 [9925]~P85(f341(f341(f288(a857),x99252),x99251))+P85(f341(f341(f288(a857),x99251),x99252))+P85(f341(f341(f343(a857),x99251),f296(a857,f341(f341(f20(a857,f864(a857,a850),f864(a857,a850)),f341(f341(f10(f864(a857,f864(a850,a850)),f864(f864(a857,a850),f864(a857,a850)),a857),f20(a857,a850,a850)),f341(f341(f10(f864(a857,a850),f864(a857,f864(a850,a850)),a857),f341(f10(a850,f864(a850,a850),a857),a339)),f288(a857)))),f341(f341(f10(f864(a857,a850),f864(a857,a850),a857),f341(f10(a850,a850,a857),a337)),f341(f9(a857,a857,a850),f288(a857)))),x99252))) % 19.23/19.04 [9926]~P85(f341(f341(f288(a857),x99262),x99261))+P85(f341(f341(f288(a857),x99261),x99262))+P85(f341(f341(f343(a857),x99262),f299(a857,f341(f341(f20(a857,f864(a857,a850),f864(a857,a850)),f341(f341(f10(f864(a857,f864(a850,a850)),f864(f864(a857,a850),f864(a857,a850)),a857),f20(a857,a850,a850)),f341(f341(f10(f864(a857,a850),f864(a857,f864(a850,a850)),a857),f341(f10(a850,f864(a850,a850),a857),a339)),f288(a857)))),f341(f341(f10(f864(a857,a850),f864(a857,a850),a857),f341(f10(a850,a850,a857),a337)),f341(f9(a857,a857,a850),f288(a857)))),x99261))) % 19.23/19.04 [7535]~P89(x75351)+~P60(x75351)+E(f341(f341(f292(x75351),x75352),f341(f113(x75351),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106))),x75352) % 19.23/19.04 [9108]~P89(x91081)+~E(f341(f113(x91081),x91082),f87(x91081))+P32(x91081,f341(f113(x91081),f341(f341(f89(a1),x91082),f341(f88(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106))))) % 19.23/19.04 [9261]~P135(x92611)+~E(x92612,f2(x92611))+E(f341(f341(f251(x92611),x92612),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),f2(x92611)) % 19.23/19.04 [9262]~P135(x92621)+~E(x92622,f87(x92621))+E(f341(f341(f251(x92621),x92622),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),f87(x92621)) % 19.23/19.04 [9276]~P135(x92761)+~E(x92762,f341(f88(x92761),f87(x92761)))+E(f341(f341(f251(x92761),x92762),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),f87(x92761)) % 19.23/19.04 [9324]~P89(x93241)+E(f341(f113(x93241),x93242),f87(x93241))+~P32(x93241,f341(f113(x93241),f341(f341(f89(a1),x93242),f341(f88(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106))))) % 19.23/19.04 [9683]~P113(x96832)+E(x96831,f2(x96832))+P85(f341(f341(f242(x96832),f2(x96832)),f341(f341(f251(x96832),x96831),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))))) % 19.23/19.04 [9741]~P113(x97412)+~E(x97411,f2(x97412))+~P85(f341(f341(f242(x97412),f2(x97412)),f341(f341(f251(x97412),x97411),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))))) % 19.23/19.04 [9780]P85(f341(f341(f241(a1),x97801),f2(a1)))+P85(f341(f341(f242(a1),x97802),x97801))+E(f341(f58(x97801),f62(x97802,f341(f341(f90(a1),f341(f113(a1),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),x97801))),f62(x97802,x97801)) % 19.23/19.04 [9781]~P85(f341(f341(f242(a1),f2(a1)),x97811))+P85(f341(f341(f242(a1),x97812),x97811))+E(f341(f58(x97811),f62(x97812,f341(f341(f90(a1),f341(f113(a1),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),x97811))),f62(x97812,x97811)) % 19.23/19.04 [9782]P85(f341(f341(f241(a1),x97821),f2(a1)))+P85(f341(f341(f241(a1),f2(a1)),f341(f341(f89(a1),x97822),x97821)))+E(f341(f58(x97821),f65(x97822,f341(f341(f90(a1),f341(f113(a1),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),x97821))),f65(x97822,x97821)) % 19.23/19.04 [9783]~P85(f341(f341(f242(a1),f2(a1)),x97831))+P85(f341(f341(f241(a1),f2(a1)),f341(f341(f89(a1),x97832),x97831)))+E(f341(f58(x97831),f65(x97832,f341(f341(f90(a1),f341(f113(a1),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),x97831))),f65(x97832,x97831)) % 19.23/19.04 [9784]~P112(x97841)+~P85(f341(f341(f241(a1),f2(a1)),x97842))+E(f341(f109(x97841),f341(a114,f341(f341(f90(a1),f341(f113(a1),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),x97842))),f341(f341(f89(x97841),f341(f109(x97841),f341(a114,x97842))),f341(f109(x97841),f341(a114,x97842)))) % 19.23/19.04 [4947]~P142(x49471,x49472,x49473)+~E(x49473,f2(a1))+P85(f341(x49471,x49472)) % 19.23/19.04 [5074]~P101(x50741)+~P15(x50741,x50743)+P15(x50741,f157(x50741,x50742,x50743)) % 19.23/19.04 [4660]~P70(x46602)+~E(x46603,f341(f88(x46602),x46601))+E(x46601,f341(f88(x46602),x46603)) % 19.23/19.04 [4662]~P70(x46621)+~E(f341(f88(x46621),x46623),x46622)+E(f341(f88(x46621),x46622),x46623) % 19.23/19.04 [4733]~P87(x47333)+E(x47331,x47332)+~E(f341(f109(x47333),x47331),f341(f109(x47333),x47332)) % 19.23/19.04 [4734]~P88(x47343)+E(x47341,x47342)+~E(f341(f112(x47343),x47341),f341(f112(x47343),x47342)) % 19.23/19.04 [4735]~P70(x47353)+E(x47351,x47352)+~E(f341(f88(x47353),x47351),f341(f88(x47353),x47352)) % 19.23/19.04 [4736]~P91(x47363)+E(x47361,x47362)+~E(f341(f88(x47363),x47361),f341(f88(x47363),x47362)) % 19.23/19.04 [4737]~P101(x47373)+E(x47371,x47372)+~E(f341(f302(x47373),x47371),f341(f302(x47373),x47372)) % 19.23/19.04 [4738]~P101(x47383)+E(x47381,x47382)+~E(f341(f266(x47383),x47381),f341(f266(x47383),x47382)) % 19.23/19.04 [4739]~P101(x47393)+E(x47391,x47392)+~E(f341(f267(x47393),x47391),f341(f267(x47393),x47392)) % 19.23/19.04 [4740]~P101(x47403)+E(x47401,x47402)+~E(f341(f305(x47403),x47401),f341(f305(x47403),x47402)) % 19.23/19.04 [4971]~P143(x49711,x49713,x49712)+~E(x49712,f2(a1))+P85(f341(x49711,f2(a1))) % 19.23/19.04 [5010]~E(x50101,f2(a857))+E(f374(x50101,x50102,x50103),f185(f864(x50103,a850)))+~E(f341(f50(x50103),x50102),f341(a121,x50101)) % 19.23/19.04 [5155]~E(x51552,f2(a857))+E(f341(f249(a857,a857),x51551),f2(a857))+~P85(f341(f63(x51553,x51552),x51551)) % 19.23/19.04 [5198]P85(f341(x51981,x51982))+~E(x51983,f341(f109(a1),x51982))+~P85(f341(x51981,f341(a114,x51983))) % 19.23/19.04 [5652]~E(x56523,f2(a857))+~P85(f341(x56521,x56522))+P85(f341(x56521,f60(a857,x56522,x56523))) % 19.23/19.04 [5799]~P85(f341(a26,x57993))+~P85(f341(a26,x57992))+P85(f341(a26,f35(x57991,x57992,x57993))) % 19.23/19.04 [6072]~E(x60723,f2(a857))+P85(f341(x60721,x60722))+~P85(f341(x60721,f60(a857,x60722,x60723))) % 19.23/19.04 [6777]E(x67771,f2(a857))+~P85(f341(x67772,f818(x67771,x67773,x67772)))+P85(f341(x67772,f60(a857,x67773,x67771))) % 19.23/19.04 [6890]~P6(x68901)+~P85(f341(f341(f241(x68901),x68902),f682(x68903,x68902,x68901)))+P85(f341(f341(f241(x68901),x68902),f53(x68901,x68903))) % 19.23/19.04 [6892]~P85(f341(x68921,x68922))+~P85(f341(x68921,f818(x68923,x68922,x68921)))+P85(f341(x68921,f60(a857,x68922,x68923))) % 19.23/19.04 [6991]E(x69911,f122(x69912))+E(f341(f341(f146(x69912),f758(x69913,x69911,x69912)),f766(x69913,x69911,x69912)),x69911)+~P85(f341(f341(f343(f858(x69912)),x69911),f155(x69912,x69913))) % 19.23/19.04 [7028]~P136(x70281)+~P85(f341(f341(f343(x70281),x70282),f119(x70281)))+P85(f341(f341(f343(x70281),f341(f341(f251(x70281),x70282),x70283)),f119(x70281))) % 19.23/19.04 [7365]P35(x73651,x73652)+~P85(f341(f341(f343(x73651),x73653),f702(x73652,x73651)))+P85(f341(f341(f343(x73651),f706(x73652,x73651,x73653)),f702(x73652,x73651))) % 19.23/19.04 [7640]E(x76401,f122(x76402))+~P85(f341(f341(f343(f858(x76402)),x76401),f155(x76402,x76403)))+P85(f341(f341(f343(f858(x76402)),f766(x76403,x76401,x76402)),f155(x76402,x76403))) % 19.23/19.04 [7690]E(x76901,f2(a857))+E(f341(f341(f89(a857),f341(f341(f90(a857),x76901),f814(x76901,x76902,x76903))),f818(x76901,x76902,x76903)),x76902)+P85(f341(x76903,f60(a857,x76902,x76901))) % 19.23/19.04 [7733]~P85(f341(x77333,x77332))+E(f341(f341(f89(a857),f341(f341(f90(a857),x77331),f814(x77331,x77332,x77333))),f818(x77331,x77332,x77333)),x77332)+P85(f341(x77333,f60(a857,x77332,x77331))) % 19.23/19.04 [7877]P85(f341(f341(f242(a1),x78771),f808(x78772,x78773,x78771)))+P85(f341(f341(x78773,f341(f341(f51(a1),x78772),x78771)),f60(a1,x78772,x78771)))+~P85(f341(f341(f242(a1),x78771),f2(a1))) % 19.23/19.04 [8141]P85(f341(f341(x81412,f341(f341(f51(a1),x81411),x81413)),f60(a1,x81411,x81413)))+~P85(f341(f341(f242(a1),x81413),f2(a1)))+P85(f341(f341(f241(a1),f808(x81411,x81412,x81413)),f2(a1))) % 19.23/19.04 [8320]E(f341(f341(f89(a1),f341(f341(f90(a1),x83201),f811(x83202,x83203,x83201))),f808(x83202,x83203,x83201)),x83202)+P85(f341(f341(x83203,f341(f341(f51(a1),x83202),x83201)),f60(a1,x83202,x83201)))+~P85(f341(f341(f242(a1),x83201),f2(a1))) % 19.23/19.04 [8553]~P85(f341(f341(x85531,f811(x85532,x85531,x85533)),f808(x85532,x85531,x85533)))+P85(f341(f341(x85531,f341(f341(f51(a1),x85532),x85533)),f60(a1,x85532,x85533)))+~P85(f341(f341(f242(a1),x85533),f2(a1))) % 19.23/19.04 [8765]~P101(x87651)+~P15(x87651,x87653)+P15(x87651,f145(x87651,x87651,f7(x87651),x87652,x87653)) % 19.23/19.04 [9212]~P122(x92122)+E(x92121,f2(x92122))+~P85(f341(f341(f241(x92122),f341(f341(f89(x92122),f341(f341(f90(x92122),x92123),x92123)),f341(f341(f90(x92122),x92121),x92121))),f2(x92122))) % 19.23/19.04 [9213]~P122(x92132)+E(x92131,f2(x92132))+~P85(f341(f341(f241(x92132),f341(f341(f89(x92132),f341(f341(f90(x92132),x92131),x92131)),f341(f341(f90(x92132),x92133),x92133))),f2(x92132))) % 19.23/19.04 [9981]~P113(x99811)+~P85(f341(f341(f242(x99811),x99812),f2(x99811)))+P85(f341(f341(f242(x99811),f341(f341(f251(x99811),x99812),f341(a121,f341(f341(f90(a857),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),x99813)))),f2(x99811))) % 19.23/19.04 [9991]~P113(x99912)+E(x99911,f2(x99912))+~P85(f341(f341(f241(x99912),f341(f341(f89(x99912),f341(f341(f251(x99912),x99913),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106))))),f341(f341(f251(x99912),x99911),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))))),f2(x99912))) % 19.23/19.04 [9992]~P113(x99922)+E(x99921,f2(x99922))+~P85(f341(f341(f241(x99922),f341(f341(f89(x99922),f341(f341(f251(x99922),x99921),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106))))),f341(f341(f251(x99922),x99923),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))))),f2(x99922))) % 19.23/19.04 [4691]~E(x46912,x46913)+~P70(x46911)+E(f341(f341(f3(x46911),x46912),x46913),f2(x46911)) % 19.23/19.04 [4692]~E(x46922,x46923)+~P3(x46921)+E(f341(f341(f3(x46921),x46922),x46923),f2(x46921)) % 19.23/19.04 [4705]~P111(x47051)+~E(x47053,f2(x47051))+E(f341(f341(f89(x47051),x47052),x47053),x47052) % 19.23/19.04 [4720]~P137(x47201)+~E(x47203,f2(x47201))+E(f341(f341(f90(x47201),x47202),x47203),f2(x47201)) % 19.23/19.04 [4721]~P137(x47211)+~E(x47212,f2(x47211))+E(f341(f341(f90(x47211),x47212),x47213),f2(x47211)) % 19.23/19.04 [4742]~E(x47423,f122(x47421))+~E(x47422,f122(x47421))+E(f341(f341(f132(x47421),x47422),x47423),f122(x47421)) % 19.23/19.04 [4825]~P111(x48252)+E(x48251,f2(x48252))+~E(f341(f341(f89(x48252),x48253),x48251),x48253) % 19.23/19.04 [4826]~P70(x48261)+~E(x48262,f341(f88(x48261),x48263))+E(f341(f341(f89(x48261),x48262),x48263),f2(x48261)) % 19.23/19.04 [4833]E(x48331,f122(x48332))+E(x48333,f2(a857))+~E(f341(f341(f164(x48332),x48333),x48331),f122(x48332)) % 19.23/19.04 [4841]~P70(x48413)+E(x48411,x48412)+~E(f341(f341(f3(x48413),x48411),x48412),f2(x48413)) % 19.23/19.04 [4842]~P3(x48423)+E(x48421,x48422)+~E(f341(f341(f3(x48423),x48421),x48422),f2(x48423)) % 19.23/19.04 [4851]~P135(x48512)+E(x48511,f2(x48512))+~E(f341(f341(f251(x48512),x48511),x48513),f2(x48512)) % 19.23/19.04 [4852]~P93(x48522)+E(x48521,f185(x48522))+~E(f341(f341(f110(x48522),x48523),x48521),f185(x48522)) % 19.23/19.04 [4853]~P93(x48532)+E(x48531,f185(x48532))+~E(f341(f341(f110(x48532),x48531),x48533),f185(x48532)) % 19.23/19.04 [4854]~P97(x48542)+E(x48541,f248(x48542))+~E(f341(f341(f111(x48542),x48543),x48541),f248(x48542)) % 19.23/19.04 [4855]~P97(x48552)+E(x48551,f248(x48552))+~E(f341(f341(f111(x48552),x48551),x48553),f248(x48552)) % 19.23/19.04 [4920]~P70(x49202)+E(x49201,f341(f88(x49202),x49203))+~E(f341(f341(f89(x49202),x49201),x49203),f2(x49202)) % 19.23/19.04 [4921]~P70(x49211)+E(f341(f88(x49211),x49212),x49213)+~E(f341(f341(f89(x49211),x49212),x49213),f2(x49211)) % 19.23/19.04 [4924]~E(x49242,x49243)+~P100(x49241)+P85(f341(f341(f241(x49241),x49242),x49243)) % 19.23/19.04 [4925]~E(x49252,x49253)+~P104(x49251)+P85(f341(f341(f241(x49251),x49252),x49253)) % 19.23/19.04 [5024]~P114(x50241)+~E(x50242,f341(f88(x50241),x50243))+E(f341(f341(f90(x50241),x50242),x50242),f341(f341(f90(x50241),x50243),x50243)) % 19.23/19.04 [5032]~P101(x50321)+~P15(x50321,x50323)+P15(x50321,f341(f341(f164(x50321),x50322),x50323)) % 19.23/19.04 [5033]~P101(x50331)+~P15(x50331,x50333)+P15(x50331,f341(f341(f135(x50331),x50332),x50333)) % 19.23/19.04 [5072]E(x50721,x50722)+E(x50723,f2(a857))+~E(f341(f341(f90(a857),x50723),x50721),f341(f341(f90(a857),x50723),x50722)) % 19.23/19.04 [5073]E(x50731,x50732)+E(x50733,f2(a857))+~E(f341(f341(f90(a857),x50731),x50733),f341(f341(f90(a857),x50732),x50733)) % 19.23/19.04 [5147]~E(x51472,x51473)+~P100(x51471)+E(f304(x51471,x51472,x51473),f341(f341(f311(x51471),x51472),f185(f864(x51471,a850)))) % 19.23/19.04 [5186]~P113(x51861)+~E(f341(f84(x51861),x51862),f341(f84(x51861),x51863))+P85(f341(f341(f288(x51861),x51862),x51863)) % 19.23/19.04 [5195]~E(x51951,x51952)+~P100(x51953)+~P85(f341(f341(f242(x51953),x51951),x51952)) % 19.23/19.04 [5196]~E(x51961,x51962)+~P101(x51963)+~P85(f341(f341(f242(x51963),x51961),x51962)) % 19.23/19.04 [5203]~P100(x52031)+E(f341(f303(x52031,x52032),x52033),f185(f864(x52031,a850)))+P85(f341(f341(f242(x52031),x52032),x52033)) % 19.23/19.04 [5248]~P100(x52481)+E(f306(x52481,x52482,x52483),f185(f864(x52481,a850)))+P85(f341(f341(f242(x52481),x52482),x52483)) % 19.23/19.04 [5249]~P100(x52491)+E(f304(x52491,x52492,x52493),f185(f864(x52491,a850)))+P85(f341(f341(f241(x52491),x52492),x52493)) % 19.23/19.04 [5250]~P100(x52501)+E(f185(f864(x52501,a850)),f306(x52501,x52502,x52503))+P85(f341(f341(f242(x52501),x52502),x52503)) % 19.23/19.04 [5251]~P100(x52511)+E(f185(f864(x52511,a850)),f304(x52511,x52512,x52513))+P85(f341(f341(f241(x52511),x52512),x52513)) % 19.23/19.04 [5259]~P101(x52591)+~E(f341(f341(f245(x52591),x52592),x52593),x52592)+P85(f341(f341(f241(x52591),x52592),x52593)) % 19.23/19.04 [5260]~P101(x52601)+~E(f341(f341(f240(x52601),x52602),x52603),x52603)+P85(f341(f341(f241(x52601),x52602),x52603)) % 19.23/19.04 [5261]~P98(x52611)+~E(f341(f341(f110(x52611),x52612),x52613),x52613)+P85(f341(f341(f241(x52611),x52612),x52613)) % 19.23/19.04 [5262]~P99(x52621)+~E(f341(f341(f111(x52621),x52622),x52623),x52622)+P85(f341(f341(f241(x52621),x52622),x52623)) % 19.23/19.04 [5278]~P101(x52781)+P15(x52781,x52782)+~P15(x52781,f341(f341(f146(x52781),x52783),x52782)) % 19.23/19.04 [5279]~P101(x52791)+P15(x52791,x52792)+~P15(x52791,f341(f341(f132(x52791),x52793),x52792)) % 19.23/19.04 [5280]~P101(x52801)+P15(x52801,x52802)+~P15(x52801,f341(f341(f132(x52801),x52802),x52803)) % 19.23/19.04 [5285]~P4(x52851)+~E(f60(x52851,x52853,x52852),f2(x52851))+P85(f341(f341(f288(x52851),x52852),x52853)) % 19.23/19.04 [5349]~P101(x53491)+P85(f341(f341(f241(x53491),x53493),x53492))+P85(f341(f341(f242(x53491),x53492),x53493)) % 19.23/19.04 [5351]~P101(x53511)+P85(f341(f341(f241(x53511),x53513),x53512))+P85(f341(f341(f241(x53511),x53512),x53513)) % 19.23/19.04 [5390]~P101(x53901)+E(f341(f341(f245(x53901),x53902),x53903),x53903)+~P85(f341(f341(f241(x53901),x53903),x53902)) % 19.23/19.04 [5392]~P101(x53921)+E(f341(f341(f245(x53921),x53922),x53923),x53922)+~P85(f341(f341(f241(x53921),x53922),x53923)) % 19.23/19.04 [5393]~P101(x53931)+E(f341(f341(f240(x53931),x53932),x53933),x53932)+~P85(f341(f341(f241(x53931),x53933),x53932)) % 19.23/19.04 [5395]~P101(x53951)+E(f341(f341(f240(x53951),x53952),x53953),x53953)+~P85(f341(f341(f241(x53951),x53952),x53953)) % 19.23/19.04 [5396]~P98(x53961)+E(f341(f341(f110(x53961),x53962),x53963),x53962)+~P85(f341(f341(f241(x53961),x53963),x53962)) % 19.23/19.04 [5398]~P98(x53981)+E(f341(f341(f110(x53981),x53982),x53983),x53983)+~P85(f341(f341(f241(x53981),x53982),x53983)) % 19.23/19.04 [5399]~P99(x53991)+E(f341(f341(f111(x53991),x53992),x53993),x53993)+~P85(f341(f341(f241(x53991),x53993),x53992)) % 19.23/19.04 [5401]~P99(x54011)+E(f341(f341(f111(x54011),x54012),x54013),x54012)+~P85(f341(f341(f241(x54011),x54012),x54013)) % 19.23/19.04 [5408]~P116(x54082)+E(x54081,f2(x54082))+E(f341(f341(f292(x54082),f341(f88(x54082),x54083)),f341(f88(x54082),x54081)),f341(f341(f292(x54082),x54083),x54081)) % 19.23/19.04 [5415]~P4(x54151)+E(f60(x54151,x54152,x54153),f2(x54151))+~P85(f341(f341(f288(x54151),x54153),x54152)) % 19.23/19.04 [5455]~P100(x54551)+E(f341(f303(x54551,x54552),x54553),f185(f864(x54551,a850)))+~P85(f341(f341(f241(x54551),x54553),x54552)) % 19.23/19.04 [5483]~P100(x54831)+E(f307(x54831,x54832,x54833),f185(f864(x54831,a850)))+~P85(f341(f341(f241(x54831),x54833),x54832)) % 19.23/19.04 [5484]~P100(x54841)+E(f306(x54841,x54842,x54843),f185(f864(x54841,a850)))+~P85(f341(f341(f241(x54841),x54843),x54842)) % 19.23/19.04 [5485]~P100(x54851)+E(f304(x54851,x54852,x54853),f185(f864(x54851,a850)))+~P85(f341(f341(f242(x54851),x54853),x54852)) % 19.23/19.04 [5535]~E(f341(f341(f3(a857),x55351),x55353),x55352)+E(x55351,f341(f341(f89(a857),x55352),x55353))+~P85(f341(f341(f241(a857),x55353),x55351)) % 19.23/19.04 [5536]~E(x55361,f341(f341(f89(a857),x55363),x55362))+E(f341(f341(f3(a857),x55361),x55362),x55363)+~P85(f341(f341(f241(a857),x55362),x55361)) % 19.23/19.04 [5579]~P85(f341(x55791,x55793))+P85(f341(x55791,f401(x55791,x55792)))+~P85(f341(f341(f241(a857),x55793),x55792)) % 19.23/19.04 [5580]~P85(f341(x55801,x55803))+P85(f341(x55801,f491(x55801,x55802)))+~P85(f341(f341(f242(a857),x55803),x55802)) % 19.23/19.04 [5588]~P100(x55881)+~E(f341(f303(x55881,x55882),x55883),f185(f864(x55881,a850)))+~P85(f341(f341(f242(x55881),x55882),x55883)) % 19.23/19.04 [5592]~P100(x55921)+~P85(f341(f341(f242(x55921),x55922),x55923))+P85(f341(f341(f241(x55921),x55922),x55923)) % 19.23/19.04 [5594]~P104(x55941)+~P85(f341(f341(f242(x55941),x55942),x55943))+P85(f341(f341(f241(x55941),x55942),x55943)) % 19.23/19.04 [5707]~P100(x57071)+~E(f306(x57071,x57072,x57073),f185(f864(x57071,a850)))+~P85(f341(f341(f242(x57071),x57072),x57073)) % 19.23/19.04 [5708]~P100(x57081)+~E(f304(x57081,x57082,x57083),f185(f864(x57081,a850)))+~P85(f341(f341(f241(x57081),x57082),x57083)) % 19.23/19.04 [5709]~P100(x57091)+~E(f185(f864(x57091,a850)),f306(x57091,x57092,x57093))+~P85(f341(f341(f242(x57091),x57092),x57093)) % 19.23/19.04 [5710]~P100(x57101)+~E(f185(f864(x57101,a850)),f304(x57101,x57102,x57103))+~P85(f341(f341(f241(x57101),x57102),x57103)) % 19.23/19.04 [5723]P85(f341(x57231,x57232))+~P85(f341(x57231,f458(x57231,x57233)))+~P85(f341(f341(f241(a857),x57232),x57233)) % 19.23/19.04 [5724]P85(f341(x57241,x57242))+~P85(f341(x57241,f492(x57241,x57243)))+~P85(f341(f341(f242(a857),x57242),x57243)) % 19.23/19.04 [5732]~E(x57321,f341(a121,x57323))+P85(f341(f341(f242(a857),x57321),f341(a121,x57322)))+~P85(f341(f341(f242(a857),x57323),x57322)) % 19.23/19.04 [5748]E(x57481,x57482)+~E(f341(f341(f90(a857),x57483),x57481),f341(f341(f90(a857),x57483),x57482))+~P85(f341(f341(f242(a857),f2(a857)),x57483)) % 19.23/19.04 [5809]E(f341(x58091,f496(x58091,x58092,x58093)),f87(a857))+~E(f341(f341(f8(x58093,a857),x58091),x58092),f87(a857))+~P85(f341(f71(x58093),x58092)) % 19.23/19.04 [5819]~P6(x58191)+P85(f341(f341(f241(x58191),x58192),f52(x58191,x58193)))+~P85(f341(f341(f343(x58191),x58192),x58193)) % 19.23/19.04 [5844]~P100(x58441)+~P85(f341(f341(f242(x58441),x58443),x58442))+~P85(f341(f341(f242(x58441),x58442),x58443)) % 19.23/19.04 [5845]~P101(x58451)+~P85(f341(f341(f242(x58451),x58453),x58452))+~P85(f341(f341(f242(x58451),x58452),x58453)) % 19.23/19.04 [5848]~P101(x58481)+~P85(f341(f341(f241(x58481),x58483),x58482))+~P85(f341(f341(f242(x58481),x58482),x58483)) % 19.23/19.04 [5852]~P104(x58521)+~P85(f341(f341(f242(x58521),x58523),x58522))+~P85(f341(f341(f242(x58521),x58522),x58523)) % 19.23/19.04 [5853]~P104(x58531)+~P85(f341(f341(f241(x58531),x58533),x58532))+~P85(f341(f341(f242(x58531),x58532),x58533)) % 19.23/19.04 [5872]~E(x58722,x58723)+~E(x58721,x58722)+E(f291(a857,f288(a857),x58721,x58722),f341(f341(f311(a857),x58723),f185(f864(a857,a850)))) % 19.23/19.04 [5880]~E(f341(x58802,f402(x58802,x58803,x58801)),f87(a857))+E(f341(f341(f11(x58801,a857),x58802),x58803),f87(a857))+~P85(f341(f71(x58801),x58803)) % 19.23/19.04 [5881]~E(f341(x58812,f497(x58812,x58813,x58811)),f2(a857))+E(f341(f341(f8(x58811,a857),x58812),x58813),f2(a857))+~P85(f341(f71(x58811),x58813)) % 19.23/19.04 [5895]~P105(x58951)+~P85(f341(f341(f288(x58951),x58952),x58953))+P85(f341(f341(f288(x58951),x58952),f341(f88(x58951),x58953))) % 19.23/19.04 [5896]~P113(x58961)+~P85(f341(f341(f288(x58961),x58962),x58963))+P85(f341(f341(f288(x58961),x58962),f341(f84(x58961),x58963))) % 19.23/19.04 [5897]~P103(x58971)+~P85(f341(f341(f241(x58971),x58973),x58972))+P85(f341(f341(f343(x58971),x58972),f341(f267(x58971),x58973))) % 19.23/19.04 [5898]~P103(x58981)+~P85(f341(f341(f242(x58981),x58983),x58982))+P85(f341(f341(f343(x58981),x58982),f341(f305(x58981),x58983))) % 19.23/19.04 [5899]~P103(x58991)+~P85(f341(f341(f241(x58991),x58992),x58993))+P85(f341(f341(f343(x58991),x58992),f341(f302(x58991),x58993))) % 19.23/19.04 [5900]~P103(x59001)+~P85(f341(f341(f242(x59001),x59002),x59003))+P85(f341(f341(f343(x59001),x59002),f341(f266(x59001),x59003))) % 19.23/19.04 [5911]E(f341(x59111,f509(x59111,x59112,x59113)),f341(a121,f2(a857)))+~E(f341(f341(f8(x59113,a857),x59111),x59112),f341(a121,f2(a857)))+~P85(f341(f71(x59113),x59112)) % 19.23/19.04 [5993]~P6(x59931)+~P85(f341(f341(f343(x59931),x59933),x59932))+P85(f341(f341(f241(x59931),f53(x59931,x59932)),x59933)) % 19.23/19.04 [6011]~P85(f341(f341(f241(a857),x60111),x60113))+P85(f341(f341(f241(a857),x60111),x60112))+~P85(f341(f341(f241(a857),x60113),x60112)) % 19.23/19.04 [6012]~P85(f341(f341(f241(a1),x60121),x60123))+P85(f341(f341(f241(a1),x60121),x60122))+~P85(f341(f341(f241(a1),x60123),x60122)) % 19.23/19.04 [6013]~P85(f341(f341(f288(a857),x60131),x60133))+P85(f341(f341(f288(a857),x60131),x60132))+~P85(f341(f341(f288(a857),x60133),x60132)) % 19.23/19.04 [6031]~P103(x60311)+~P85(f341(f341(f343(x60311),x60313),f341(f305(x60311),x60312)))+P85(f341(f341(f242(x60311),x60312),x60313)) % 19.23/19.04 [6032]~P103(x60321)+~P85(f341(f341(f343(x60321),x60322),f341(f266(x60321),x60323)))+P85(f341(f341(f242(x60321),x60322),x60323)) % 19.23/19.04 [6033]~P103(x60331)+~P85(f341(f341(f343(x60331),x60333),f341(f267(x60331),x60332)))+P85(f341(f341(f241(x60331),x60332),x60333)) % 19.23/19.04 [6034]~P103(x60341)+~P85(f341(f341(f343(x60341),x60342),f341(f302(x60341),x60343)))+P85(f341(f341(f241(x60341),x60342),x60343)) % 19.23/19.04 [6035]~P113(x60351)+~P85(f341(f341(f288(x60351),x60352),f341(f84(x60351),x60353)))+P85(f341(f341(f288(x60351),x60352),x60353)) % 19.23/19.04 [6036]~P105(x60361)+~P85(f341(f341(f288(x60361),x60362),f341(f88(x60361),x60363)))+P85(f341(f341(f288(x60361),x60362),x60363)) % 19.23/19.04 [6259]~P61(x62591)+P85(f341(f341(f242(x62591),f2(x62591)),f817(x62593,x62592,x62591)))+P85(f341(f341(f241(x62591),x62592),x62593)) % 19.23/19.04 [6260]~P62(x62601)+P85(f341(f341(f242(x62601),f2(x62601)),f826(x62603,x62602,x62601)))+P85(f341(f341(f241(x62601),x62602),x62603)) % 19.23/19.04 [6331]~P77(x63311)+~P85(f341(f341(f242(x63311),x63313),f341(f88(x63311),x63312)))+P85(f341(f341(f242(x63311),x63312),f341(f88(x63311),x63313))) % 19.23/19.04 [6333]~P77(x63331)+~P85(f341(f341(f241(x63331),x63333),f341(f88(x63331),x63332)))+P85(f341(f341(f241(x63331),x63332),f341(f88(x63331),x63333))) % 19.23/19.04 [6344]~P85(f341(f341(f242(a857),x63441),x63443))+~P85(f341(f341(f242(a857),x63443),x63442))+P85(f341(f341(f242(a857),f341(a121,x63441)),x63442)) % 19.23/19.04 [6377]~P113(x63771)+P85(f341(f341(f242(x63771),f341(f112(x63771),x63772)),f341(f112(x63771),x63773)))+~P85(f341(f341(f242(a1),x63772),x63773)) % 19.23/19.04 [6378]~P120(x63781)+P85(f341(f341(f242(x63781),f341(f109(x63781),x63782)),f341(f109(x63781),x63783)))+~P85(f341(f341(f242(a857),x63782),x63783)) % 19.23/19.04 [6379]~P120(x63791)+P85(f341(f341(f241(x63791),f341(f109(x63791),x63792)),f341(f109(x63791),x63793)))+~P85(f341(f341(f241(a857),x63792),x63793)) % 19.23/19.04 [6380]~P113(x63801)+P85(f341(f341(f241(x63801),f341(f112(x63801),x63802)),f341(f112(x63801),x63803)))+~P85(f341(f341(f241(a1),x63802),x63803)) % 19.23/19.04 [6386]~P101(x63861)+E(f341(f341(f110(f864(x63861,a850)),f341(f266(x63861),x63862)),f341(f303(x63861,x63862),x63863)),f341(f266(x63861),x63863))+~P85(f341(f341(f241(x63861),x63862),x63863)) % 19.23/19.04 [6417]~P77(x64171)+~P85(f341(f341(f242(x64171),x64173),x64172))+P85(f341(f341(f242(x64171),f341(f88(x64171),x64172)),f341(f88(x64171),x64173))) % 19.23/19.04 [6419]~P77(x64191)+~P85(f341(f341(f241(x64191),x64193),x64192))+P85(f341(f341(f241(x64191),f341(f88(x64191),x64192)),f341(f88(x64191),x64193))) % 19.23/19.04 [6421]~P91(x64211)+~P85(f341(f341(f241(x64211),x64213),x64212))+P85(f341(f341(f241(x64211),f341(f88(x64211),x64212)),f341(f88(x64211),x64213))) % 19.23/19.04 [6456]~P101(x64561)+E(f341(f341(f110(f864(x64561,a850)),f341(f302(x64561),x64562)),f307(x64561,x64562,x64563)),f341(f266(x64561),x64563))+~P85(f341(f341(f242(x64561),x64562),x64563)) % 19.23/19.04 [6457]~P101(x64571)+E(f341(f341(f110(f864(x64571,a850)),f341(f302(x64571),x64572)),f306(x64571,x64572,x64573)),f341(f302(x64571),x64573))+~P85(f341(f341(f241(x64571),x64572),x64573)) % 19.23/19.04 [6458]~P101(x64581)+E(f341(f341(f110(f864(x64581,a850)),f341(f266(x64581),x64582)),f304(x64581,x64582,x64583)),f341(f302(x64581),x64583))+~P85(f341(f341(f241(x64581),x64582),x64583)) % 19.23/19.04 [6495]~P101(x64951)+E(f341(f341(f110(f864(x64951,a850)),f341(f303(x64951,x64952),x64953)),f341(f267(x64951),x64953)),f341(f267(x64951),x64952))+~P85(f341(f341(f241(x64951),x64952),x64953)) % 19.23/19.04 [6656]~P101(x66561)+E(f341(f341(f110(f864(x66561,a850)),f307(x66561,x66562,x66563)),f341(f267(x66561),x66563)),f341(f305(x66561),x66562))+~P85(f341(f341(f242(x66561),x66562),x66563)) % 19.23/19.04 [6657]~P101(x66571)+E(f341(f341(f110(f864(x66571,a850)),f306(x66571,x66572,x66573)),f341(f305(x66571),x66573)),f341(f305(x66571),x66572))+~P85(f341(f341(f241(x66571),x66572),x66573)) % 19.23/19.04 [6658]~P101(x66581)+E(f341(f341(f110(f864(x66581,a850)),f304(x66581,x66582,x66583)),f341(f305(x66581),x66583)),f341(f267(x66581),x66582))+~P85(f341(f341(f241(x66581),x66582),x66583)) % 19.23/19.04 [6675]P85(f341(x66751,x66752))+~P85(f341(f341(f241(a857),x66752),x66753))+P85(f341(f341(f343(a857),f458(x66751,x66753)),f304(a857,f2(a857),x66753))) % 19.23/19.04 [6685]P85(f341(f341(f288(a1),x66851),f60(a1,x66852,x66853)))+~P85(f341(f341(f288(a1),x66851),x66852))+~P85(f341(f341(f288(a1),x66851),x66853)) % 19.23/19.04 [6711]E(x67111,x67112)+~E(f341(f341(f158(x67113),x67111),f733(x67113,x67112,x67111)),f341(f341(f158(x67113),x67112),f733(x67113,x67112,x67111)))+~E(f341(f186(f858(x67113)),x67111),f341(f186(f858(x67113)),x67112)) % 19.23/19.04 [6717]~E(x67173,f341(f341(f51(a857),x67171),x67172))+~P85(f341(f341(f242(a857),f2(a857)),x67172))+P85(f341(f341(f242(a857),x67171),f341(f341(f90(a857),x67172),f341(a121,x67173)))) % 19.23/19.04 [6732]~P85(f341(x67321,x67323))+~P85(f341(f341(f241(a857),x67323),x67322))+P85(f341(f341(f343(a857),f401(x67321,x67322)),f304(a857,f2(a857),x67322))) % 19.23/19.04 [6774]~P85(f341(x67741,x67743))+P85(f341(x67741,f455(x67741,x67742)))+~P85(f341(f341(f343(a857),x67743),f304(a857,f2(a857),x67742))) % 19.23/19.04 [6797]~P120(x67973)+~P85(f341(f341(f242(x67973),f341(f109(x67973),x67971)),f341(f109(x67973),x67972)))+P85(f341(f341(f242(a857),x67971),x67972)) % 19.23/19.04 [6798]~P113(x67983)+~P85(f341(f341(f242(x67983),f341(f112(x67983),x67981)),f341(f112(x67983),x67982)))+P85(f341(f341(f242(a1),x67981),x67982)) % 19.23/19.04 [6799]~P120(x67993)+~P85(f341(f341(f241(x67993),f341(f109(x67993),x67991)),f341(f109(x67993),x67992)))+P85(f341(f341(f241(a857),x67991),x67992)) % 19.23/19.04 [6800]~P113(x68003)+~P85(f341(f341(f241(x68003),f341(f112(x68003),x68001)),f341(f112(x68003),x68002)))+P85(f341(f341(f241(a1),x68001),x68002)) % 19.23/19.04 [6816]~P120(x68161)+~P85(f341(f341(f242(x68161),f87(x68161)),x68162))+P85(f341(f341(f242(x68161),f87(x68161)),f341(f341(f251(x68161),x68162),f341(a121,x68163)))) % 19.23/19.04 [6820]~P77(x68201)+~P85(f341(f341(f242(x68201),f341(f88(x68201),x68203)),f341(f88(x68201),x68202)))+P85(f341(f341(f242(x68201),x68202),x68203)) % 19.23/19.04 [6821]~P77(x68211)+~P85(f341(f341(f241(x68211),f341(f88(x68211),x68213)),f341(f88(x68211),x68212)))+P85(f341(f341(f241(x68211),x68212),x68213)) % 19.23/19.04 [6822]~P91(x68221)+~P85(f341(f341(f241(x68221),f341(f88(x68221),x68223)),f341(f88(x68221),x68222)))+P85(f341(f341(f241(x68221),x68222),x68223)) % 19.23/19.04 [6848]P85(f341(x68481,x68482))+~P85(f341(x68481,f459(x68481,x68483)))+~P85(f341(f341(f343(a857),x68482),f304(a857,f2(a857),x68483))) % 19.23/19.04 [6869]~P61(x68691)+P85(f341(f341(f242(x68691),f817(x68693,x68692,x68691)),f87(x68691)))+P85(f341(f341(f241(x68691),x68692),x68693)) % 19.23/19.04 [6888]~E(f60(a857,x68883,x68882),f60(a857,x68881,x68882))+E(f341(f341(f89(a857),x68881),f341(f341(f90(a857),x68882),f822(x68881,x68882,x68883))),x68883)+~P85(f341(f341(f241(a857),x68881),x68883)) % 19.23/19.04 [6906]E(f341(x69061,f612(x69061,x69062,x69063)),f188(x69062))+~P85(f341(f71(x69063),f174(x69063,x69062,x69061)))+P85(f341(f71(x69063),f248(f864(x69063,a850)))) % 19.23/19.04 [6946]E(f341(f341(f11(x69461,a857),x69462),x69463),f87(a857))+~P85(f341(f71(x69461),x69463))+P85(f341(f341(f343(x69461),f402(x69462,x69463,x69461)),x69463)) % 19.23/19.04 [6947]E(f341(f341(f8(x69471,a857),x69472),x69473),f2(a857))+~P85(f341(f71(x69471),x69473))+P85(f341(f341(f343(x69471),f497(x69472,x69473,x69471)),x69473)) % 19.23/19.04 [6969]~P101(x69691)+~P85(f341(f341(f242(x69691),x69692),x69693))+P85(f341(f341(f242(f864(x69691,a850)),f341(f266(x69691),x69692)),f341(f266(x69691),x69693))) % 19.23/19.04 [6970]~P100(x69701)+~P85(f341(f341(f241(x69701),x69702),x69703))+P85(f341(f341(f241(f864(x69701,a850)),f341(f302(x69701),x69702)),f341(f302(x69701),x69703))) % 19.23/19.04 [6971]~P101(x69711)+~P85(f341(f341(f241(x69711),x69712),x69713))+P85(f341(f341(f241(f864(x69711,a850)),f341(f266(x69711),x69712)),f341(f266(x69711),x69713))) % 19.23/19.04 [6972]~P100(x69721)+~P85(f341(f341(f241(x69721),x69723),x69722))+P85(f341(f341(f241(f864(x69721,a850)),f341(f267(x69721),x69722)),f341(f267(x69721),x69723))) % 19.23/19.04 [6973]~P101(x69731)+~P85(f341(f341(f241(x69731),x69733),x69732))+P85(f341(f341(f241(f864(x69731,a850)),f341(f305(x69731),x69732)),f341(f305(x69731),x69733))) % 19.23/19.04 [6978]~P6(x69781)+P85(f341(f341(f241(x69781),x69782),f53(x69781,x69783)))+P85(f341(f341(f343(x69781),f682(x69783,x69782,x69781)),x69783)) % 19.23/19.04 [6983]~P77(x69831)+P85(f341(f341(f242(x69831),f341(f341(f3(x69831),x69832),x69833)),f2(x69831)))+~P85(f341(f341(f242(x69831),x69832),x69833)) % 19.23/19.04 [6984]~P77(x69841)+P85(f341(f341(f241(x69841),f341(f341(f3(x69841),x69842),x69843)),f2(x69841)))+~P85(f341(f341(f241(x69841),x69842),x69843)) % 19.23/19.04 [7022]~P85(f341(f341(f288(a1),x70221),f60(a1,x70222,x70223)))+~P85(f341(f341(f288(a1),x70221),x70223))+P85(f341(f341(f288(a1),x70221),x70222)) % 19.23/19.04 [7029]P85(f341(x70291,x70292))+P85(f341(f341(f241(a857),f459(x70291,x70293)),x70293))+~P85(f341(f341(f343(a857),x70292),f304(a857,f2(a857),x70293))) % 19.23/19.04 [7071]~E(f341(f341(f8(x70711,a857),x70712),x70713),f87(a857))+~P85(f341(f71(x70711),x70713))+P85(f341(f341(f343(x70711),f496(x70712,x70713,x70711)),x70713)) % 19.23/19.04 [7072]~P85(f341(x70721,x70723))+P85(f341(f341(f241(a857),f455(x70721,x70722)),x70722))+~P85(f341(f341(f343(a857),x70723),f304(a857,f2(a857),x70722))) % 19.23/19.04 [7109]~P6(x71091)+P85(f341(f341(f343(x71091),f683(x71093,x71092,x71091)),x71092))+P85(f341(f341(f241(x71091),f52(x71091,x71092)),x71093)) % 19.23/19.04 [7139]~E(f341(f341(f8(x71391,a857),x71392),x71393),f341(a121,f2(a857)))+~P85(f341(f71(x71391),x71393))+P85(f341(f341(f343(x71391),f509(x71392,x71393,x71391)),x71393)) % 19.23/19.04 [7150]E(x71501,f2(a857))+P85(f341(x71502,f60(a857,x71503,x71501)))+P85(f341(f341(f242(a857),f818(x71501,x71503,x71502)),x71501)) % 19.23/19.04 [7274]~P85(f341(x72741,x72742))+P85(f341(x72741,f60(a857,x72742,x72743)))+P85(f341(f341(f242(a857),f818(x72743,x72742,x72741)),x72743)) % 19.23/19.04 [7401]E(x74011,f122(x74012))+~P85(f341(f341(f343(f858(x74012)),x74011),f155(x74012,x74013)))+P85(f341(f341(f343(x74012),f758(x74013,x74011,x74012)),x74013)) % 19.23/19.04 [7421]~P101(x74211)+E(f341(f341(f110(f864(x74211,a850)),f341(f341(f311(x74211),x74212),f185(f864(x74211,a850)))),f307(x74211,x74212,x74213)),f341(f303(x74211,x74212),x74213))+~P85(f341(f341(f242(x74211),x74212),x74213)) % 19.23/19.04 [7445]~P101(x74451)+E(f341(f341(f110(f864(x74451,a850)),f341(f341(f311(x74451),x74452),f185(f864(x74451,a850)))),f306(x74451,x74452,x74453)),f304(x74451,x74452,x74453))+~P85(f341(f341(f241(x74451),x74452),x74453)) % 19.23/19.04 [7557]~P101(x75571)+P85(f341(f341(f242(x75571),x75572),x75573))+~P85(f341(f341(f242(f864(x75571,a850)),f341(f266(x75571),x75572)),f341(f266(x75571),x75573))) % 19.23/19.04 [7558]~P100(x75581)+P85(f341(f341(f241(x75581),x75582),x75583))+~P85(f341(f341(f241(f864(x75581,a850)),f341(f267(x75581),x75583)),f341(f267(x75581),x75582))) % 19.23/19.04 [7559]~P101(x75591)+P85(f341(f341(f241(x75591),x75592),x75593))+~P85(f341(f341(f241(f864(x75591,a850)),f341(f305(x75591),x75593)),f341(f305(x75591),x75592))) % 19.23/19.04 [7560]~P100(x75601)+P85(f341(f341(f241(x75601),x75602),x75603))+~P85(f341(f341(f241(f864(x75601,a850)),f341(f302(x75601),x75602)),f341(f302(x75601),x75603))) % 19.23/19.04 [7561]~P101(x75611)+P85(f341(f341(f241(x75611),x75612),x75613))+~P85(f341(f341(f241(f864(x75611,a850)),f341(f266(x75611),x75612)),f341(f266(x75611),x75613))) % 19.23/19.04 [7585]~P77(x75851)+~P85(f341(f341(f242(x75851),f341(f341(f3(x75851),x75852),x75853)),f2(x75851)))+P85(f341(f341(f242(x75851),x75852),x75853)) % 19.23/19.04 [7586]~P77(x75861)+~P85(f341(f341(f241(x75861),f341(f341(f3(x75861),x75862),x75863)),f2(x75861)))+P85(f341(f341(f241(x75861),x75862),x75863)) % 19.23/19.04 [7746]E(x77461,f2(a857))+~E(f341(f138(a857,a857,f89(a857),x77462),x77463),f2(a857))+~P85(f341(f341(f343(a857),x77461),f341(f163(a857),x77463))) % 19.23/19.04 [7750]~P6(x77501)+~P85(f341(f341(f241(x77501),f683(x77503,x77502,x77501)),x77503))+P85(f341(f341(f241(x77501),f52(x77501,x77502)),x77503)) % 19.23/19.04 [7901]P85(f341(f341(f241(a1),f2(a1)),f809(x79011,x79012,x79013)))+P85(f341(f341(x79012,f341(f341(f51(a1),x79011),x79013)),f60(a1,x79011,x79013)))+~P85(f341(f341(f242(a1),f2(a1)),x79013)) % 19.23/19.04 [7994]E(x79941,x79942)+~E(f341(f186(f858(x79943)),x79941),f341(f186(f858(x79943)),x79942))+~P85(f341(f341(f260(x79943,x79943,a850),a338),f722(x79943,x79941,x79942))) % 19.23/19.04 [8059]~P35(x80592,x80593)+E(x80591,f185(f864(x80592,a850)))+~P85(f341(f341(f241(f864(x80592,a850)),x80591),f341(f286(x80592,x80592,x80593),x80591))) % 19.23/19.04 [8087]~P62(x80871)+~P85(f341(f341(f241(x80871),x80872),f341(f341(f89(x80871),x80873),f826(x80873,x80872,x80871))))+P85(f341(f341(f241(x80871),x80872),x80873)) % 19.23/19.04 [8123]P46(x81231,x81232,x81233)+P85(f341(f341(f343(x81231),f600(x81233,x81232,x81231)),x81232))+P85(f341(f341(f343(f863(x81231,x81231)),f601(x81233,x81232,x81231)),x81233)) % 19.23/19.04 [8144]P85(f341(f341(x81442,f341(f341(f51(a1),x81441),x81443)),f60(a1,x81441,x81443)))+~P85(f341(f341(f242(a1),f2(a1)),x81443))+P85(f341(f341(f242(a1),f809(x81441,x81442,x81443)),x81443)) % 19.23/19.04 [8168]E(f341(f312(a857,a857,f341(f341(f9(a857,a857,a857),f3(a857)),x81681)),f341(f303(a857,x81682),x81683)),f185(f864(a857,a850)))+P85(f341(f341(f242(a857),x81681),x81683))+P85(f341(f341(f242(a857),x81682),x81683)) % 19.23/19.04 [8271]E(f341(f312(a857,a857,f341(f341(f9(a857,a857,a857),f3(a857)),x82711)),f341(f303(a857,x82712),x82713)),f341(f341(f311(a857),f2(a857)),f185(f864(a857,a850))))+P85(f341(f341(f242(a857),x82711),x82713))+~P85(f341(f341(f242(a857),x82712),x82713)) % 19.23/19.04 [8286]~P101(x82861)+E(f145(x82861,x82861,f7(x82861),x82862,x82863),x82863)+~P85(f341(f341(f343(x82861),x82862),f341(f163(x82861),x82863))) % 19.23/19.04 [8301]P26(x83011,x83011,x83012,x83013)+~P85(f341(f71(x83011),x83013))+~P85(f341(f341(f241(f864(x83011,a850)),x83013),f341(f312(x83011,x83011,x83012),x83013))) % 19.23/19.04 [8328]E(f341(f341(f89(a1),f341(f341(f90(a1),x83281),f810(x83282,x83283,x83281))),f809(x83282,x83283,x83281)),x83282)+P85(f341(f341(x83283,f341(f341(f51(a1),x83282),x83281)),f60(a1,x83282,x83281)))+~P85(f341(f341(f242(a1),f2(a1)),x83281)) % 19.23/19.04 [8558]~P85(f341(f341(x85581,f810(x85582,x85581,x85583)),f809(x85582,x85581,x85583)))+P85(f341(f341(x85581,f341(f341(f51(a1),x85582),x85583)),f60(a1,x85582,x85583)))+~P85(f341(f341(f242(a1),f2(a1)),x85583)) % 19.23/19.04 [9351]~P85(f341(f71(x93511),x93512))+~P85(f341(f341(f343(x93511),x93513),x93512))+P85(f341(f341(f242(a857),f341(f50(x93511),f341(f341(f3(f864(x93511,a850)),x93512),f341(f341(f311(x93511),x93513),f185(f864(x93511,a850)))))),f341(f50(x93511),x93512))) % 19.23/19.04 [9935]P46(x99351,x99352,x99353)+~P85(f341(f341(f260(x99351,x99351,a850),f341(f341(f9(x99351,f864(x99351,a850),f864(x99351,a850)),f341(f341(f10(f864(a850,a850),f864(f864(x99351,a850),f864(x99351,a850)),x99351),f10(a850,a850,x99351)),f341(f341(f10(a850,f864(a850,a850),x99351),a339),f341(f341(f9(x99351,f864(x99351,a850),a850),f343(x99351)),x99352)))),f341(f341(f9(x99351,f864(x99351,a850),a850),f343(x99351)),x99352))),f601(x99353,x99352,x99351)))+P85(f341(f341(f343(x99351),f600(x99353,x99352,x99351)),x99352)) % 19.23/19.04 [5369]~P116(x53692)+E(x53691,f2(x53692))+E(f341(f341(f292(x53692),x53693),f341(f88(x53692),x53691)),f341(f88(x53692),f341(f341(f292(x53692),x53693),x53691))) % 19.23/19.04 [5499]~E(x54993,f185(f864(x54991,a850)))+~E(x54992,f185(f864(x54991,a850)))+E(f341(f341(f110(f864(x54991,a850)),x54992),x54993),f185(f864(x54991,a850))) % 19.23/19.04 [5554]~E(x55543,f2(a857))+~P85(f341(x55541,f2(a857)))+P85(f341(x55541,f341(f341(f51(a857),x55542),x55543))) % 19.23/19.04 [5702]~P62(x57022)+E(x57021,f2(x57022))+E(f341(f341(f292(x57022),f341(f84(x57022),x57023)),f341(f84(x57022),x57021)),f341(f84(x57022),f341(f341(f292(x57022),x57023),x57021))) % 19.23/19.04 [5797]~P86(x57971)+~E(x57972,f87(x57971))+P85(f341(f341(f288(x57971),x57972),f341(f341(f251(x57971),x57972),x57973))) % 19.23/19.04 [5814]~P4(x58141)+E(f341(f341(f90(x58141),x58142),f341(f341(f51(x58141),x58143),x58142)),x58143)+~P85(f341(f341(f288(x58141),x58142),x58143)) % 19.23/19.04 [5869]~P85(f341(f71(x58691),x58693))+E(f341(f50(x58691),f341(f341(f311(x58691),x58692),x58693)),f341(a121,f341(f50(x58691),x58693)))+P85(f341(f341(f343(x58691),x58692),x58693)) % 19.23/19.04 [5944]~E(x59442,f2(a857))+P85(f341(x59441,f2(a857)))+~P85(f341(x59441,f341(f341(f51(a857),x59443),x59442))) % 19.23/19.04 [5962]~P85(f341(f71(x59621),x59623))+E(f341(f50(x59621),f341(f341(f311(x59621),x59622),x59623)),f341(f50(x59621),x59623))+~P85(f341(f341(f343(x59621),x59622),x59623)) % 19.23/19.04 [5995]~P85(f341(f71(x59951),x59953))+E(f341(f50(x59951),f341(f341(f311(x59951),x59952),x59953)),f341(f341(f89(a857),f87(a857)),f341(f50(x59951),x59953)))+P85(f341(f341(f343(x59951),x59952),x59953)) % 19.23/19.04 [6002]~P5(x60021)+E(f341(f341(f51(x60021),x60022),f341(f88(x60021),x60023)),f341(f88(x60021),f341(f341(f51(x60021),x60022),x60023)))+~P85(f341(f341(f288(x60021),x60023),x60022)) % 19.23/19.04 [6117]E(f341(f341(f89(a857),x61171),f816(x61171,x61172,x61173)),x61172)+~P85(f341(x61173,f2(a857)))+P85(f341(x61173,f341(f341(f3(a857),x61172),x61171))) % 19.23/19.04 [6118]E(f341(f341(f89(a857),x61181),f820(x61181,x61182,x61183)),x61182)+~P85(f341(x61183,f2(a857)))+P85(f341(x61183,f341(f341(f3(a857),x61182),x61181))) % 19.23/19.04 [6142]~P5(x61421)+E(f341(f341(f51(x61421),f341(f88(x61421),x61422)),x61423),f341(f88(x61421),f341(f341(f51(x61421),x61422),x61423)))+~P85(f341(f341(f288(x61421),x61423),x61422)) % 19.23/19.04 [6165]~P6(x61651)+~P85(f341(f71(x61651),x61653))+E(f341(f341(f74(x61651,x61651,f110(x61651)),x61652),x61653),f341(f341(f110(x61651),x61652),f52(x61651,x61653))) % 19.23/19.04 [6166]~P6(x61661)+~P85(f341(f71(x61661),x61663))+E(f341(f341(f74(x61661,x61661,f111(x61661)),x61662),x61663),f341(f341(f111(x61661),x61662),f53(x61661,x61663))) % 19.23/19.04 [6172]~P89(x61721)+~E(f341(f113(x61721),x61722),f341(f113(x61721),x61723))+P32(x61721,f341(f113(x61721),f341(f341(f89(a1),x61722),f341(f88(a1),x61723)))) % 19.23/19.04 [6179]~P136(x61791)+E(f341(f341(f3(x61791),f341(f109(x61791),x61792)),f341(f109(x61791),x61793)),f341(f109(x61791),f341(f341(f3(a857),x61792),x61793)))+~P85(f341(f341(f241(a857),x61793),x61792)) % 19.23/19.04 [6185]~P105(x61851)+~P85(f341(f341(f288(x61851),x61852),x61853))+P85(f341(f341(f288(x61851),f341(f88(x61851),x61852)),x61853)) % 19.23/19.04 [6186]~P113(x61861)+~P85(f341(f341(f288(x61861),x61862),x61863))+P85(f341(f341(f288(x61861),f341(f84(x61861),x61862)),x61863)) % 19.23/19.04 [6270]E(f341(f341(f89(a857),x62701),f816(x62701,x62702,x62703)),x62702)+P85(f341(f341(f242(a857),x62702),x62701))+P85(f341(x62703,f341(f341(f3(a857),x62702),x62701))) % 19.23/19.04 [6271]E(f341(f341(f89(a857),x62711),f820(x62711,x62712,x62713)),x62712)+P85(f341(f341(f242(a857),x62712),x62711))+P85(f341(x62713,f341(f341(f3(a857),x62712),x62711))) % 19.23/19.04 [6289]~P113(x62891)+E(f341(f341(f90(x62891),f341(f84(x62891),x62892)),x62893),f341(f84(x62891),f341(f341(f90(x62891),x62892),x62893)))+~P85(f341(f341(f241(x62891),f2(x62891)),x62893)) % 19.23/19.04 [6290]~P61(x62901)+E(f341(f341(f292(x62901),f341(f84(x62901),x62902)),x62903),f341(f84(x62901),f341(f341(f292(x62901),x62902),x62903)))+~P85(f341(f341(f242(x62901),f2(x62901)),x62903)) % 19.23/19.04 [6299]~P95(x62991)+~P85(f341(f71(x62991),x62993))+E(f341(f341(f74(x62991,x62991,f110(x62991)),x62992),x62993),f15(x62991,f341(f341(f311(x62991),x62992),x62993))) % 19.23/19.04 [6300]~P95(x63001)+~P85(f341(f71(x63001),x63003))+E(f341(f341(f74(x63001,x63001,f111(x63001)),x63002),x63003),f12(x63001,f341(f341(f311(x63001),x63002),x63003))) % 19.23/19.04 [6301]~P101(x63011)+~P85(f341(f71(x63011),x63013))+E(f341(f341(f74(x63011,x63011,f240(x63011)),x63012),x63013),f16(x63011,f341(f341(f311(x63011),x63012),x63013))) % 19.23/19.04 [6302]~P101(x63021)+~P85(f341(f71(x63021),x63023))+E(f341(f341(f74(x63021,x63021,f245(x63021)),x63022),x63023),f17(x63021,f341(f341(f311(x63021),x63022),x63023))) % 19.23/19.04 [6346]E(x63461,f122(x63462))+~E(f169(x63462,x63463),f122(f858(x63462)))+~P85(f341(f341(f343(f858(x63462)),x63461),f341(f163(f858(x63462)),x63463))) % 19.23/19.04 [6365]~P86(x63651)+~P85(f341(f341(f242(a857),f2(a857)),x63653))+P85(f341(f341(f288(x63651),x63652),f341(f341(f251(x63651),x63652),x63653))) % 19.23/19.04 [6396]~P85(f341(f134(x63961),x63963))+P85(f341(f341(f343(x63961),x63962),f341(f163(x63961),x63963)))+P85(f341(f134(x63961),f341(f341(f146(x63961),x63962),x63963))) % 19.23/19.04 [6408]~P92(x64081)+~P85(f341(f71(x64081),x64083))+E(f341(f73(x64081,f90(x64081)),f341(f341(f311(x64081),x64082),x64083)),f341(f341(f74(x64081,x64081,f90(x64081)),x64082),x64083)) % 19.23/19.04 [6429]~P101(x64291)+~P85(f341(f71(x64291),x64293))+E(f13(x64291,f240(x64291),f341(f341(f311(x64291),x64292),x64293)),f341(f341(f74(x64291,x64291,f240(x64291)),x64292),x64293)) % 19.23/19.04 [6430]~P101(x64301)+~P85(f341(f71(x64301),x64303))+E(f14(x64301,f245(x64301),f341(f341(f311(x64301),x64302),x64303)),f341(f341(f74(x64301,x64301,f245(x64301)),x64302),x64303)) % 19.23/19.04 [6432]P85(f341(x64321,f2(a857)))+~P85(f341(f341(f242(a857),x64322),x64323))+~P85(f341(x64321,f341(f341(f3(a857),x64322),x64323))) % 19.23/19.04 [6451]~P113(x64511)+P85(f341(f341(f242(x64511),x64512),x64513))+~P85(f341(f341(f242(x64511),f341(f84(x64511),x64512)),x64513)) % 19.23/19.04 [6453]~P79(x64531)+P85(f341(f341(f241(x64531),x64532),x64533))+~P85(f341(f341(f241(x64531),f341(f84(x64531),x64532)),x64533)) % 19.23/19.04 [6454]~P113(x64541)+P85(f341(f341(f288(x64541),x64542),x64543))+~P85(f341(f341(f288(x64541),f341(f84(x64541),x64542)),x64543)) % 19.23/19.04 [6455]~P105(x64551)+P85(f341(f341(f288(x64551),x64552),x64553))+~P85(f341(f341(f288(x64551),f341(f88(x64551),x64552)),x64553)) % 19.23/19.04 [6474]E(x64741,f122(x64742))+E(f341(f137(x64742),f341(f341(f135(x64742),x64743),x64741)),f341(f341(f158(x64742),x64741),x64743))+~P85(f341(f341(f242(a857),x64743),f341(f186(f858(x64742)),x64741))) % 19.23/19.04 [6527]~P85(f341(x65271,x65273))+P85(f341(x65271,f498(x65271,x65272)))+~P85(f341(f341(f343(a857),x65273),f341(f303(a857,f2(a857)),x65272))) % 19.23/19.04 [6550]P85(f341(x65501,x65502))+~P85(f341(f341(f242(a857),x65502),x65503))+P85(f341(f341(f343(a857),f492(x65501,x65503)),f341(f303(a857,f2(a857)),x65503))) % 19.23/19.04 [6565]~P120(x65651)+~P85(f341(f341(f242(x65651),f2(x65651)),x65652))+P85(f341(f341(f242(x65651),f2(x65651)),f341(f341(f251(x65651),x65652),x65653))) % 19.23/19.04 [6567]~P120(x65671)+~P85(f341(f341(f241(x65671),f2(x65671)),x65672))+P85(f341(f341(f241(x65671),f2(x65671)),f341(f341(f251(x65671),x65672),x65673))) % 19.23/19.04 [6568]~P120(x65681)+~P85(f341(f341(f241(x65681),f87(x65681)),x65682))+P85(f341(f341(f241(x65681),f87(x65681)),f341(f341(f251(x65681),x65682),x65683))) % 19.23/19.04 [6592]~P85(f341(x65921,x65923))+~P85(f341(f341(f242(a857),x65923),x65922))+P85(f341(f341(f343(a857),f491(x65921,x65922)),f341(f303(a857,f2(a857)),x65922))) % 19.23/19.04 [6597]P85(f341(f71(x65971),x65972))+~P85(f341(f71(x65971),x65973))+~P85(f341(f341(f241(f864(x65971,a850)),x65972),x65973)) % 19.23/19.04 [6606]~P85(f341(f341(f288(a857),x66061),x66062))+~P85(f341(f341(f288(a857),x66061),x66063))+P85(f341(f341(f288(a857),x66061),f341(f341(f3(a857),x66062),x66063))) % 19.23/19.04 [6607]P85(f341(x66071,x66072))+~P85(f341(x66071,f493(x66071,x66073)))+~P85(f341(f341(f343(a857),x66072),f341(f303(a857,f2(a857)),x66073))) % 19.23/19.04 [6620]E(x66201,f2(a857))+P85(f341(x66202,f807(x66201,x66203,x66202)))+~P85(f341(x66202,f341(f341(f51(a857),x66203),x66201))) % 19.23/19.04 [6629]~P122(x66292)+E(x66291,f2(x66292))+~E(f341(f341(f89(x66292),f341(f341(f90(x66292),x66293),x66293)),f341(f341(f90(x66292),x66291),x66291)),f2(x66292)) % 19.23/19.04 [6630]~P122(x66302)+E(x66301,f2(x66302))+~E(f341(f341(f89(x66302),f341(f341(f90(x66302),x66301),x66301)),f341(f341(f90(x66302),x66303),x66303)),f2(x66302)) % 19.23/19.04 [6676]E(x66761,f2(a857))+~P85(f341(x66762,f812(x66761,x66763,x66762)))+P85(f341(x66762,f341(f341(f51(a857),x66763),x66761))) % 19.23/19.04 [6681]~P101(x66811)+~P15(x66811,x66813)+P15(x66811,f341(f341(f144(x66811,x66811,f7(x66811)),x66812),x66813)) % 19.23/19.04 [6725]P85(f341(x67251,f807(x67252,x67253,x67251)))+P85(f341(x67251,f2(a857)))+~P85(f341(x67251,f341(f341(f51(a857),x67253),x67252))) % 19.23/19.04 [6731]~P89(x67311)+E(f341(f113(x67311),x67312),f341(f113(x67311),x67313))+~P32(x67311,f341(f113(x67311),f341(f341(f89(a1),x67312),f341(f88(a1),x67313)))) % 19.23/19.04 [6803]E(x68031,f2(a1))+E(x68032,f2(a1))+~P85(f341(f64(x68032,x68032),f341(f341(f250(a1,a1),x68033),x68031))) % 19.23/19.04 [6804]E(x68041,f87(a1))+E(x68042,f2(a1))+~P85(f341(f64(x68042,x68042),f341(f341(f250(a1,a1),x68041),x68043))) % 19.23/19.04 [6818]P85(f341(x68181,x68182))+P85(f341(f341(f242(a857),f493(x68181,x68183)),x68183))+~P85(f341(f341(f343(a857),x68182),f341(f303(a857,f2(a857)),x68183))) % 19.23/19.04 [6843]~P85(f341(x68431,f812(x68433,x68432,x68431)))+~P85(f341(x68431,f2(a857)))+P85(f341(x68431,f341(f341(f51(a857),x68432),x68433))) % 19.23/19.04 [6844]~P85(f341(x68441,f816(x68443,x68442,x68441)))+~P85(f341(x68441,f2(a857)))+P85(f341(x68441,f341(f341(f3(a857),x68442),x68443))) % 19.23/19.04 [6845]~P85(f341(x68451,f820(x68453,x68452,x68451)))+~P85(f341(x68451,f2(a857)))+P85(f341(x68451,f341(f341(f3(a857),x68452),x68453))) % 19.23/19.04 [6865]~P85(f341(x68651,x68653))+P85(f341(f341(f242(a857),f498(x68651,x68652)),x68652))+~P85(f341(f341(f343(a857),x68653),f341(f303(a857,f2(a857)),x68652))) % 19.23/19.04 [6866]E(f341(f341(f3(a857),f341(f341(f3(a857),x68661),x68662)),f341(f341(f3(a857),x68663),x68662)),f341(f341(f3(a857),x68661),x68663))+~P85(f341(f341(f241(a857),x68662),x68661))+~P85(f341(f341(f241(a857),x68662),x68663)) % 19.23/19.04 [6900]~P77(x69001)+~P85(f341(f341(f242(x69001),f341(f88(x69001),x69003)),x69002))+P85(f341(f341(f242(x69001),f341(f88(x69001),x69002)),x69003)) % 19.23/19.04 [6901]~P113(x69011)+~P85(f341(f341(f242(x69011),f341(f84(x69011),x69012)),x69013))+P85(f341(f341(f242(x69011),f341(f88(x69011),x69012)),x69013)) % 19.23/19.04 [6903]~P77(x69031)+~P85(f341(f341(f241(x69031),f341(f88(x69031),x69033)),x69032))+P85(f341(f341(f241(x69031),f341(f88(x69031),x69032)),x69033)) % 19.23/19.04 [6905]~P79(x69051)+~P85(f341(f341(f241(x69051),f341(f84(x69051),x69052)),x69053))+P85(f341(f341(f241(x69051),f341(f88(x69051),x69052)),x69053)) % 19.23/19.04 [6908]~P85(f341(f341(f288(a1),x69081),x69083))+P85(f341(f341(f288(a1),x69081),x69082))+~P85(f341(f341(f288(a1),x69081),f341(f341(f3(a1),x69082),x69083))) % 19.23/19.04 [6940]~P85(f341(x69403,f816(x69402,x69401,x69403)))+P85(f341(f341(f242(a857),x69401),x69402))+P85(f341(x69403,f341(f341(f3(a857),x69401),x69402))) % 19.23/19.04 [6941]~P85(f341(x69413,f820(x69412,x69411,x69413)))+P85(f341(f341(f242(a857),x69411),x69412))+P85(f341(x69413,f341(f341(f3(a857),x69411),x69412))) % 19.23/19.04 [6987]~E(f691(x69873,x69872,x69871),f690(x69873,x69872,x69871))+E(f341(f341(f111(f864(x69871,a850)),x69872),f52(f864(x69871,a850),x69873)),f185(f864(x69871,a850)))+P85(f341(f341(f343(f864(x69871,a850)),x69872),x69873)) % 19.23/19.04 [6996]~P85(f341(f71(x69961),x69963))+P85(f341(f71(x69961),f53(f864(x69961,a850),x69962)))+~P85(f341(f341(f343(f864(x69961,a850)),x69963),x69962)) % 19.23/19.04 [7057]~P101(x70571)+E(f341(f341(f110(f864(x70571,a850)),f341(f303(x70571,x70572),x70573)),f341(f341(f311(x70571),x70573),f185(f864(x70571,a850)))),f304(x70571,x70572,x70573))+~P85(f341(f341(f241(x70571),x70572),x70573)) % 19.23/19.04 [7060]E(x70601,f2(a857))+P85(f341(f341(f242(a857),f813(x70601,x70603,x70602)),x70601))+P85(f341(x70602,f341(f341(f51(a857),x70603),x70601))) % 19.23/19.04 [7095]E(x70951,x70952)+~P85(f341(f341(f241(f864(x70953,a850)),x70951),x70952))+P85(f341(f341(f242(f864(x70953,a850)),x70951),x70952)) % 19.23/19.04 [7106]E(x71061,x71062)+~E(f341(f186(f858(x71063)),x71061),f341(f186(f858(x71063)),x71062))+P85(f341(f341(f242(a857),f733(x71063,x71061,x71062)),f341(f186(f858(x71063)),x71062))) % 19.23/19.04 [7151]P9(x71511,x71512,x71513)+~E(f341(f270(x71511,x71511),x71513),x71512)+~E(f341(f341(f290(x71511,x71511,x71511),f341(f287(x71511,x71511),x71513)),x71513),x71513) % 19.23/19.04 [7233]E(x72331,f2(a1))+~P85(f341(f341(f288(a1),x72332),x72333))+P85(f341(f341(f288(a1),f341(f341(f90(a1),x72331),x72332)),f341(f341(f90(a1),x72331),x72333))) % 19.23/19.04 [7236]~P85(f341(x72361,f2(a857)))+P85(f341(f341(f242(a857),f813(x72363,x72362,x72361)),x72363))+P85(f341(x72361,f341(f341(f51(a857),x72362),x72363))) % 19.23/19.04 [7249]~P101(x72491)+E(f341(f341(f110(f864(x72491,a850)),f307(x72491,x72492,x72493)),f341(f341(f311(x72491),x72493),f185(f864(x72491,a850)))),f306(x72491,x72492,x72493))+~P85(f341(f341(f242(x72491),x72492),x72493)) % 19.23/19.04 [7354]~P85(f341(f71(x73541),x73543))+P85(f341(f341(f242(a857),f341(f50(x73541),x73542)),f341(f50(x73541),x73543)))+~P85(f341(f341(f242(f864(x73541,a850)),x73542),x73543)) % 19.23/19.04 [7355]~P85(f341(f71(x73551),x73553))+P85(f341(f341(f241(a857),f341(f50(x73551),x73552)),f341(f50(x73551),x73553)))+~P85(f341(f341(f241(f864(x73551,a850)),x73552),x73553)) % 19.23/19.04 [7396]~P85(f341(x73963,x73962))+P85(f341(f341(f192(x73961),x73962),f456(x73962,x73961,x73963)))+~P85(f341(f341(f192(f37(x73963,x73961)),x73962),x73962)) % 19.23/19.04 [7493]E(x74931,x74932)+~P85(f341(f341(f241(f864(x74933,a850)),x74932),x74931))+~P85(f341(f341(f241(f864(x74933,a850)),x74931),x74932)) % 19.23/19.04 [7496]~P101(x74961)+P15(x74961,x74962)+~P15(x74961,f341(f341(f144(x74961,x74961,f7(x74961)),x74963),x74962)) % 19.23/19.04 [7565]~P85(f341(f341(f242(a857),x75653),x75652))+~P85(f341(f341(f242(a857),x75653),x75651))+P85(f341(f341(f242(a857),f341(f341(f3(a857),x75651),x75652)),f341(f341(f3(a857),x75651),x75653))) % 19.23/19.04 [7566]~P85(f341(f341(f242(a857),x75661),x75663))+~P85(f341(f341(f241(a857),x75662),x75661))+P85(f341(f341(f242(a857),f341(f341(f3(a857),x75661),x75662)),f341(f341(f3(a857),x75663),x75662))) % 19.23/19.04 [7583]~P85(f341(f341(f242(a1),x75832),f2(a1)))+~P85(f341(f341(f241(a1),x75833),x75831))+P85(f341(f341(f241(a1),f341(f341(f51(a1),x75831),x75832)),f341(f341(f51(a1),x75833),x75832))) % 19.23/19.04 [7603]~P85(f341(f341(f242(a857),f2(a857)),x76032))+~P85(f341(f341(f242(a857),x76031),x76033))+P85(f341(f341(f242(a857),f341(f341(f90(a857),x76031),x76032)),f341(f341(f90(a857),x76033),x76032))) % 19.23/19.04 [7604]~P85(f341(f341(f242(a857),f2(a857)),x76041))+~P85(f341(f341(f242(a857),x76042),x76043))+P85(f341(f341(f242(a857),f341(f341(f90(a857),x76041),x76042)),f341(f341(f90(a857),x76041),x76043))) % 19.23/19.04 [7605]~P85(f341(f341(f242(a1),f2(a1)),x76051))+~P85(f341(f341(f242(a1),x76052),x76053))+P85(f341(f341(f242(a1),f341(f341(f90(a1),x76051),x76052)),f341(f341(f90(a1),x76051),x76053))) % 19.23/19.04 [7607]~P85(f341(f341(f242(a857),f2(a857)),x76073))+~P85(f341(f341(f241(a857),x76073),x76072))+P85(f341(f341(f241(a857),f341(f341(f51(a857),x76071),x76072)),f341(f341(f51(a857),x76071),x76073))) % 19.23/19.04 [7608]~P85(f341(f341(f242(a1),f2(a1)),x76082))+~P85(f341(f341(f241(a1),x76081),x76083))+P85(f341(f341(f241(a1),f341(f341(f51(a1),x76081),x76082)),f341(f341(f51(a1),x76083),x76082))) % 19.23/19.04 [7657]E(x76571,f2(a857))+E(f341(f341(f89(a857),f341(f341(f90(a857),x76571),f812(x76571,x76572,x76573))),f813(x76571,x76572,x76573)),x76572)+P85(f341(x76573,f341(f341(f51(a857),x76572),x76571))) % 19.23/19.04 [7715]E(f341(f341(f89(a857),f341(f341(f90(a857),x77151),f812(x77151,x77152,x77153))),f813(x77151,x77152,x77153)),x77152)+~P85(f341(x77153,f2(a857)))+P85(f341(x77153,f341(f341(f51(a857),x77152),x77151))) % 19.23/19.04 [7731]~P85(f341(f71(x77311),x77313))+P85(f341(f341(f343(x77311),f408(x77312,x77313,x77311)),x77313))+P85(f341(f341(f242(a857),f2(a857)),f341(f341(f11(x77311,a857),x77312),x77313))) % 19.23/19.04 [7732]~P85(f341(f71(x77321),x77323))+P85(f341(f341(f343(x77321),f569(x77322,x77323,x77321)),x77323))+P85(f341(f341(f242(a857),f2(a857)),f341(f341(f11(x77321,a857),x77322),x77323))) % 19.23/19.04 [7837]E(x78371,f2(a857))+P85(f341(f341(f288(a857),x78372),x78373))+~P85(f341(f341(f288(a857),f341(f341(f90(a857),x78371),x78372)),f341(f341(f90(a857),x78371),x78373))) % 19.23/19.04 [7839]E(x78391,f2(a1))+P85(f341(f341(f288(a1),x78392),x78393))+~P85(f341(f341(f288(a1),f341(f341(f90(a1),x78391),x78392)),f341(f341(f90(a1),x78391),x78393))) % 19.23/19.04 [8024]E(x80241,f185(f864(x80242,a850)))+E(x80241,f341(f341(f311(x80242),x80243),f185(f864(x80242,a850))))+~P85(f341(f341(f241(f864(x80242,a850)),x80241),f341(f341(f311(x80242),x80243),f185(f864(x80242,a850))))) % 19.23/19.04 [8061]~P85(f341(f341(f242(a857),f2(a857)),x80613))+P85(f341(f341(f242(a857),x80611),x80612))+~P85(f341(f341(f242(a857),f341(f341(f251(a857),x80613),x80611)),f341(f341(f251(a857),x80613),x80612))) % 19.23/19.04 [8063]~P85(f341(f341(f242(a857),f2(a857)),x80633))+P85(f341(f341(f241(a857),x80631),x80632))+~P85(f341(f341(f241(a857),f341(f341(f90(a857),x80633),x80631)),f341(f341(f90(a857),x80633),x80632))) % 19.23/19.04 [8064]~P85(f341(f341(f242(a857),f87(a857)),x80643))+P85(f341(f341(f241(a857),x80641),x80642))+~P85(f341(f341(f288(a857),f341(f341(f251(a857),x80643),x80641)),f341(f341(f251(a857),x80643),x80642))) % 19.23/19.04 [8065]~P85(f341(f341(f242(a857),f2(a857)),x80653))+P85(f341(f341(f241(a857),x80651),x80652))+~P85(f341(f341(f241(a857),f341(f341(f90(a857),x80651),x80653)),f341(f341(f90(a857),x80652),x80653))) % 19.23/19.04 [8067]~P85(f341(f341(f242(a857),f2(a857)),x80673))+P85(f341(f341(f288(a857),x80671),x80672))+~P85(f341(f341(f288(a857),f341(f341(f90(a857),x80673),x80671)),f341(f341(f90(a857),x80673),x80672))) % 19.23/19.04 [8095]~P85(f341(x80951,x80953))+P85(f341(f341(f192(f37(x80951,x80952)),f456(x80953,x80952,x80951)),x80953))+~P85(f341(f341(f192(f37(x80951,x80952)),x80953),x80953)) % 19.23/19.04 [8103]~E(f341(f341(f111(f864(x81031,a850)),f690(x81033,x81032,x81031)),f691(x81033,x81032,x81031)),f185(f864(x81031,a850)))+E(f341(f341(f111(f864(x81031,a850)),x81032),f52(f864(x81031,a850),x81033)),f185(f864(x81031,a850)))+P85(f341(f341(f343(f864(x81031,a850)),x81032),x81033)) % 19.23/19.04 [8118]E(x81181,f122(x81182))+~E(f341(f138(f858(x81182),f858(x81182),f132(x81182),f122(x81182)),x81183),f122(x81182))+~P85(f341(f341(f343(f858(x81182)),x81181),f341(f163(f858(x81182)),x81183))) % 19.23/19.04 [8173]E(x81731,f185(f864(f864(x81732,a850),a850)))+P85(f341(f341(f343(f864(x81732,a850)),f693(x81733,x81731,x81732)),x81731))+P85(f341(f341(f241(f864(x81732,a850)),f53(f864(x81732,a850),x81731)),x81733)) % 19.23/19.04 [8179]~P68(x81791)+~P71(x81791)+E(f341(f341(f11(a1,x81791),f341(f341(f10(a857,x81791,a1),x81792),a114)),f341(f312(a857,a1,f109(a1)),x81793)),f341(f341(f11(a857,x81791),x81792),x81793)) % 19.23/19.04 [8180]~P68(x81801)+~P71(x81801)+E(f341(f341(f8(a1,x81801),f341(f341(f10(a857,x81801,a1),x81802),a114)),f341(f312(a857,a1,f109(a1)),x81803)),f341(f341(f8(a857,x81801),x81802),x81803)) % 19.23/19.04 [8217]~P85(f341(f71(x82171),x82173))+~P85(f341(f341(f242(a857),f2(a857)),f341(x82172,f408(x82172,x82173,x82171))))+P85(f341(f341(f242(a857),f2(a857)),f341(f341(f11(x82171,a857),x82172),x82173))) % 19.23/19.04 [8218]~P85(f341(f71(x82181),x82183))+~P85(f341(f341(f242(a857),f2(a857)),f341(x82182,f569(x82182,x82183,x82181))))+P85(f341(f341(f242(a857),f2(a857)),f341(f341(f11(x82181,a857),x82182),x82183))) % 19.23/19.04 [8254]~P60(x82542)+E(x82541,f87(x82542))+E(f341(f341(f292(x82542),f341(f341(f3(x82542),f341(f341(f251(x82542),x82541),x82543)),f87(x82542))),f341(f341(f3(x82542),x82541),f87(x82542))),f341(f341(f8(a857,x82542),f341(f251(x82542),x82541)),f341(f303(a857,f2(a857)),x82543))) % 19.23/19.04 [8313]E(x83131,f2(a857))+~P85(f341(x83133,f341(f341(f51(a857),x83132),x83131)))+P85(f341(f341(f242(a857),x83132),f341(f341(f90(a857),x83131),f341(a121,f807(x83131,x83132,x83133))))) % 19.23/19.04 [8334]P85(f341(x83341,f2(a857)))+~P85(f341(x83341,f341(f341(f51(a857),x83342),x83343)))+P85(f341(f341(f242(a857),x83342),f341(f341(f90(a857),x83343),f341(a121,f807(x83343,x83342,x83341))))) % 19.23/19.04 [8373]E(x83731,f2(a857))+~P85(f341(x83733,f341(f341(f51(a857),x83732),x83731)))+P85(f341(f341(f241(a857),f341(f341(f90(a857),x83731),f807(x83731,x83732,x83733))),x83732)) % 19.23/19.04 [8410]P85(f341(x84101,f2(a857)))+~P85(f341(x84101,f341(f341(f51(a857),x84103),x84102)))+P85(f341(f341(f241(a857),f341(f341(f90(a857),x84102),f807(x84102,x84103,x84101))),x84103)) % 19.23/19.04 [8413]~P101(x84131)+E(f341(f341(f144(x84131,x84131,f7(x84131)),x84132),x84133),f145(x84131,x84131,f7(x84131),x84132,x84133))+P85(f341(f341(f343(x84131),x84132),f341(f163(x84131),x84133))) % 19.23/19.04 [8452]~E(f341(x84523,f614(x84522,x84523,x84521)),f341(x84523,f616(x84522,x84523,x84521)))+~P57(x84521,f341(x84523,f615(x84522,x84523,x84521)))+P57(x84521,f341(f341(f54(x84522,f864(x84521,f864(x84521,a850))),f248(f864(x84522,a850))),x84523)) % 19.23/19.04 [8460]E(x84601,f185(f864(f864(x84602,a850),a850)))+~P85(f341(f341(f241(f864(x84602,a850)),f693(x84603,x84601,x84602)),x84603))+P85(f341(f341(f241(f864(x84602,a850)),f53(f864(x84602,a850),x84601)),x84603)) % 19.23/19.04 [8518]~P62(x85181)+~P85(f341(f341(f242(x85181),x85182),x85183))+P85(f341(f341(f242(x85181),x85182),f341(f341(f292(x85181),f341(f341(f89(x85181),x85182),x85183)),f341(f341(f89(x85181),f87(x85181)),f87(x85181))))) % 19.23/19.04 [8561]~P85(f341(f341(x85611,f834(x85611,x85613,x85612)),f835(x85611,x85613,x85612)))+P85(f341(f341(x85611,x85612),x85613))+~P85(f341(f330(f863(a1,a1),a67),f341(f341(f250(a1,a1),x85612),x85613))) % 19.23/19.04 [8562]~P85(f341(f341(x85621,f836(x85621,x85623,x85622)),f840(x85621,x85623,x85622)))+P85(f341(f341(x85621,x85622),x85623))+~P85(f341(f330(f863(a1,a1),a70),f341(f341(f250(a1,a1),x85622),x85623))) % 19.23/19.04 [8563]~P85(f341(f341(x85631,f841(x85631,x85633,x85632)),f842(x85631,x85633,x85632)))+P85(f341(f341(x85631,x85632),x85633))+~P85(f341(f330(f863(a1,a1),a224),f341(f341(f250(a1,a1),x85632),x85633))) % 19.23/19.04 [8564]~P85(f341(f341(x85641,f843(x85641,x85643,x85642)),f844(x85641,x85643,x85642)))+P85(f341(f341(x85641,x85642),x85643))+~P85(f341(f330(f863(a857,a857),a222),f341(f341(f250(a857,a857),x85642),x85643))) % 19.23/19.04 [8565]~P85(f341(f341(x85651,f741(x85651,x85653,x85652)),f744(x85651,x85653,x85652)))+P85(f341(f341(x85651,x85652),x85653))+~P85(f341(f330(f863(a1,a1),a173),f341(f341(f250(a1,a1),x85652),x85653))) % 19.23/19.04 [8800]P85(f341(f341(x88001,x88002),x88003))+P85(f341(f330(f863(a857,a857),a222),f341(f341(f250(a857,a857),f843(x88001,x88003,x88002)),f844(x88001,x88003,x88002))))+~P85(f341(f330(f863(a857,a857),a222),f341(f341(f250(a857,a857),x88002),x88003))) % 19.23/19.04 [8801]P85(f341(f341(x88011,x88012),x88013))+P85(f341(f330(f863(a1,a1),a67),f341(f341(f250(a1,a1),f834(x88011,x88013,x88012)),f835(x88011,x88013,x88012))))+~P85(f341(f330(f863(a1,a1),a67),f341(f341(f250(a1,a1),x88012),x88013))) % 19.23/19.04 [8802]P85(f341(f341(x88021,x88022),x88023))+P85(f341(f330(f863(a1,a1),a70),f341(f341(f250(a1,a1),f836(x88021,x88023,x88022)),f840(x88021,x88023,x88022))))+~P85(f341(f330(f863(a1,a1),a70),f341(f341(f250(a1,a1),x88022),x88023))) % 19.23/19.04 [8803]P85(f341(f341(x88031,x88032),x88033))+P85(f341(f330(f863(a1,a1),a224),f341(f341(f250(a1,a1),f841(x88031,x88033,x88032)),f842(x88031,x88033,x88032))))+~P85(f341(f330(f863(a1,a1),a224),f341(f341(f250(a1,a1),x88032),x88033))) % 19.23/19.04 [8804]P85(f341(f341(x88041,x88042),x88043))+P85(f341(f330(f863(a1,a1),a173),f341(f341(f250(a1,a1),f741(x88041,x88043,x88042)),f744(x88041,x88043,x88042))))+~P85(f341(f330(f863(a1,a1),a173),f341(f341(f250(a1,a1),x88042),x88043))) % 19.23/19.04 [9119]~P85(f341(f71(x91191),x91193))+P85(f341(f341(f343(f863(f864(x91191,a850),f864(x91191,a850))),f341(f341(f250(f864(x91191,a850),f864(x91191,a850)),x91192),x91193)),f308(x91191)))+~P85(f341(f341(f242(f864(x91191,a850)),x91192),x91193)) % 19.23/19.04 [9172]~P57(x91721,f341(x91723,f615(x91722,x91723,x91721)))+P57(x91721,f341(f341(f54(x91722,f864(x91721,f864(x91721,a850))),f248(f864(x91722,a850))),x91723))+~E(f341(f341(f111(f864(x91721,a850)),f255(x91721,x91721,f341(x91723,f614(x91722,x91723,x91721)))),f256(x91721,x91721,f341(x91723,f616(x91722,x91723,x91721)))),f185(f864(x91721,a850))) % 19.23/19.04 [9363]P46(x93631,x93632,x93633)+P85(f341(f341(f343(f863(x93631,x93631)),f601(x93633,x93632,x93631)),x93633))+~P85(f341(f341(f343(f863(x93631,x93631)),f341(f341(f250(x93631,x93631),f600(x93633,x93632,x93631)),f600(x93633,x93632,x93631))),x93633)) % 19.23/19.04 [9937]P46(x99371,x99372,x99373)+~P85(f341(f341(f260(x99371,x99371,a850),f341(f341(f9(x99371,f864(x99371,a850),f864(x99371,a850)),f341(f341(f10(f864(a850,a850),f864(f864(x99371,a850),f864(x99371,a850)),x99371),f10(a850,a850,x99371)),f341(f341(f10(a850,f864(a850,a850),x99371),a339),f341(f341(f9(x99371,f864(x99371,a850),a850),f343(x99371)),x99372)))),f341(f341(f9(x99371,f864(x99371,a850),a850),f343(x99371)),x99372))),f601(x99373,x99372,x99371)))+~P85(f341(f341(f343(f863(x99371,x99371)),f341(f341(f250(x99371,x99371),f600(x99373,x99372,x99371)),f600(x99373,x99372,x99371))),x99373)) % 19.23/19.04 [5537]~P4(x55372)+E(x55371,f2(x55372))+E(f341(f341(f51(x55372),f341(f341(f90(x55372),x55373),x55371)),x55371),x55373) % 19.23/19.04 [5538]~P4(x55382)+E(x55381,f2(x55382))+E(f341(f341(f51(x55382),f341(f341(f90(x55382),x55381),x55383)),x55381),x55383) % 19.23/19.04 [6180]~P4(x61801)+E(f341(f341(f90(x61801),f341(f341(f51(x61801),x61802),x61803)),x61803),x61802)+~P85(f341(f341(f288(x61801),x61803),x61802)) % 19.23/19.04 [6345]~P68(x63451)+~E(f341(x63452,f2(a857)),f2(x63451))+E(f341(f341(f8(a857,x63451),x63452),f341(f303(a857,f341(a121,f2(a857))),x63453)),f341(f341(f8(a857,x63451),x63452),f341(f303(a857,f2(a857)),x63453))) % 19.23/19.04 [6487]~P4(x64872)+E(x64871,f2(x64872))+E(f341(f341(f51(x64872),f341(f341(f89(x64872),x64873),x64871)),x64871),f341(f341(f89(x64872),f341(f341(f51(x64872),x64873),x64871)),f87(x64872))) % 19.23/19.04 [6488]~P4(x64882)+E(x64881,f2(x64882))+E(f341(f341(f51(x64882),f341(f341(f89(x64882),x64881),x64883)),x64881),f341(f341(f89(x64882),f341(f341(f51(x64882),x64883),x64881)),f87(x64882))) % 19.23/19.04 [6715]~P85(f341(x67153,f2(a1)))+P85(f341(f341(f241(a857),x67151),x67152))+P85(f341(x67153,f341(f109(a1),f341(f341(f3(a857),x67152),x67151)))) % 19.23/19.04 [6825]P85(f341(f341(f241(a857),x68252),x68251))+P85(f341(f341(f242(a857),x68251),x68252))+P85(f341(x68253,f341(f109(a1),f341(f341(f3(a857),x68251),x68252)))) % 19.23/19.04 [6898]E(f341(f341(f89(a857),f341(f113(a857),x68981)),f341(f341(f89(a857),f341(f113(a857),x68982)),x68983)),f341(f341(f89(a857),f341(f113(a857),x68981)),x68983))+P85(f341(a191,f341(f113(a1),x68981)))+~P85(f341(a191,f341(f113(a1),x68982))) % 19.23/19.04 [6975]~E(x69752,f341(f341(f51(a857),x69753),x69751))+~P85(f341(f341(f242(a857),f2(a857)),x69751))+P85(f341(f341(f241(a857),f341(f341(f90(a857),x69751),x69752)),x69753)) % 19.23/19.04 [7093]~P85(f341(f71(x70931),x70933))+~P85(f341(f71(x70931),x70932))+P85(f341(f71(x70931),f341(f341(f110(f864(x70931,a850)),x70932),x70933))) % 19.23/19.04 [7407]~P101(x74071)+~P85(f341(f71(x74071),x74072))+E(f136(x74071,f341(f341(f3(f864(x74071,a850)),x74072),f341(f341(f311(x74071),x74073),f185(f864(x74071,a850))))),f157(x74071,x74073,f136(x74071,x74072))) % 19.23/19.04 [7472]P85(f341(x74721,f2(a1)))+~P85(f341(f341(f242(a857),x74722),x74723))+~P85(f341(x74721,f341(f109(a1),f341(f341(f3(a857),x74722),x74723)))) % 19.23/19.04 [7490]~P85(f341(f71(x74901),x74902))+E(f341(f50(x74901),f341(f341(f3(f864(x74901,a850)),x74902),f341(f341(f311(x74901),x74903),f185(f864(x74901,a850))))),f341(f50(x74901),x74902))+P85(f341(f341(f343(x74901),x74903),x74902)) % 19.23/19.04 [7624]~P120(x76241)+~P85(f341(f341(f242(x76241),f87(x76241)),x76242))+P85(f341(f341(f242(x76241),f87(x76241)),f341(f341(f90(x76241),x76242),f341(f341(f251(x76241),x76242),x76243)))) % 19.23/19.04 [7668]~P85(f341(f71(x76681),x76683))+E(f341(f341(f3(a857),f341(f50(x76681),x76682)),f341(f50(x76681),x76683)),f341(f50(x76681),f341(f341(f3(f864(x76681,a850)),x76682),x76683)))+~P85(f341(f341(f241(f864(x76681,a850)),x76683),x76682)) % 19.23/19.04 [7723]~P85(f341(f341(f241(a857),x77232),x77233))+~P85(f341(f341(f241(a857),x77231),f341(f341(f3(a857),x77233),x77232)))+P85(f341(f341(f241(a857),f341(f341(f89(a857),x77231),x77232)),x77233)) % 19.23/19.04 [7780]P85(f341(f71(x77801),x77802))+~P85(f341(f71(x77801),x77803))+~P85(f341(f71(x77801),f341(f341(f3(f864(x77801,a850)),x77802),x77803))) % 19.23/19.04 [7787]~P85(f341(f71(x77871),x77872))+E(f341(f50(x77871),f341(f341(f3(f864(x77871,a850)),x77872),f341(f341(f311(x77871),x77873),f185(f864(x77871,a850))))),f341(f341(f3(a857),f341(f50(x77871),x77872)),f87(a857)))+~P85(f341(f341(f343(x77871),x77873),x77872)) % 19.23/19.04 [7862]P57(x78621,x78622)+~P57(x78621,x78623)+~P85(f341(f341(f241(f864(x78621,f864(x78621,a850))),x78622),x78623)) % 19.23/19.04 [7900]~P85(f341(f341(f241(a857),x79003),x79002))+P85(f341(f341(f241(a857),x79001),f341(f341(f3(a857),x79002),x79003)))+~P85(f341(f341(f241(a857),f341(f341(f89(a857),x79001),x79003)),x79002)) % 19.23/19.04 [7920]P35(x79201,x79202)+~P35(x79201,x79203)+~P85(f341(f341(f241(f864(f863(x79201,x79201),a850)),x79202),x79203)) % 19.23/19.04 [7921]P55(x79211,x79212)+~P55(x79211,x79213)+~P85(f341(f341(f241(f864(f863(x79211,x79211),a850)),x79212),x79213)) % 19.23/19.04 [8151]~P120(x81511)+~P85(f341(f341(f242(x81511),f87(x81511)),x81512))+P85(f341(f341(f242(x81511),f341(f341(f251(x81511),x81512),x81513)),f341(f341(f90(x81511),x81512),f341(f341(f251(x81511),x81512),x81513)))) % 19.23/19.04 [8237]~P85(f341(x82371,f2(a1)))+~P85(f341(x82371,f341(f341(f3(a1),f341(f109(a1),x82372)),f341(f109(a1),x82373))))+P85(f341(x82371,f341(f109(a1),f341(f341(f3(a857),x82372),x82373)))) % 19.23/19.04 [8250]~P85(f341(f341(f241(a857),x82503),x82502))+P85(f341(x82501,f341(f341(f3(a1),f341(f109(a1),x82502)),f341(f109(a1),x82503))))+~P85(f341(x82501,f341(f109(a1),f341(f341(f3(a857),x82502),x82503)))) % 19.23/19.04 [8268]P85(f341(f341(f242(a857),x82681),x82682))+~P85(f341(x82683,f341(f341(f3(a1),f341(f109(a1),x82681)),f341(f109(a1),x82682))))+P85(f341(x82683,f341(f109(a1),f341(f341(f3(a857),x82681),x82682)))) % 19.23/19.04 [8325]~P122(x83252)+E(x83251,f2(x83252))+P85(f341(f341(f242(x83252),f2(x83252)),f341(f341(f89(x83252),f341(f341(f90(x83252),x83253),x83253)),f341(f341(f90(x83252),x83251),x83251)))) % 19.23/19.04 [8326]~P122(x83262)+E(x83261,f2(x83262))+P85(f341(f341(f242(x83262),f2(x83262)),f341(f341(f89(x83262),f341(f341(f90(x83262),x83261),x83261)),f341(f341(f90(x83262),x83263),x83263)))) % 19.23/19.04 [8431]~P85(f341(f341(f242(a857),f2(a857)),x84311))+~P85(f341(f341(f242(a1),x84312),x84313))+P85(f341(f341(f242(a1),f341(f341(f90(a1),f341(f109(a1),x84311)),x84312)),f341(f341(f90(a1),f341(f109(a1),x84311)),x84313))) % 19.23/19.04 [8490]E(f341(f341(f111(f864(x84901,a850)),x84902),f52(f864(x84901,a850),x84903)),f185(f864(x84901,a850)))+P85(f341(f341(f343(f864(x84901,a850)),x84902),x84903))+P85(f341(f341(f343(f864(x84901,a850)),f690(x84903,x84902,x84901)),f341(f341(f311(f864(x84901,a850)),x84902),x84903))) % 19.23/19.04 [8491]E(f341(f341(f111(f864(x84911,a850)),x84912),f52(f864(x84911,a850),x84913)),f185(f864(x84911,a850)))+P85(f341(f341(f343(f864(x84911,a850)),x84912),x84913))+P85(f341(f341(f343(f864(x84911,a850)),f691(x84913,x84912,x84911)),f341(f341(f311(f864(x84911,a850)),x84912),x84913))) % 19.23/19.04 [8517]E(x85171,x85172)+~E(f341(f186(f858(x85173)),x85171),f341(f186(f858(x85173)),x85172))+P85(f341(f341(f343(f863(x85173,x85173)),f722(x85173,x85171,x85172)),f341(f163(f863(x85173,x85173)),f341(f341(f172(x85173,x85173),x85172),x85171)))) % 19.23/19.04 [8728]E(f309(x87281,x87282),f309(x87281,x87283))+~P85(f341(f341(f241(f864(f863(x87281,x87281),a850)),x87283),f309(x87281,x87282)))+~P85(f341(f341(f241(f864(f863(x87281,x87281),a850)),x87282),x87283)) % 19.23/19.04 [8781]~P46(x87811,f248(f864(x87811,a850)),x87813)+P85(f341(f341(f241(f864(f863(f858(x87811),f858(x87811)),a850)),f152(x87811,x87812)),f153(x87811,x87813)))+~P85(f341(f341(f241(f864(f863(x87811,x87811),a850)),x87812),x87813)) % 19.23/19.04 [8961]P35(x89611,x89612)+~P85(f341(f341(f343(x89611),x89613),f702(x89612,x89611)))+P85(f341(f341(f343(f863(x89611,x89611)),f341(f341(f250(x89611,x89611),f706(x89612,x89611,x89613)),x89613)),x89612)) % 19.23/19.04 [9000]~P85(f341(f71(x90001),x90002))+P85(f341(f71(f864(x90001,a850)),f341(f341(f69(x90001),x90002),x90003)))+~P85(f341(f341(f241(f864(f863(x90001,x90001),a850)),x90003),f341(f341(f257(x90001,x90001),x90002),f341(f18(f864(x90001,a850),x90001),x90002)))) % 19.23/19.04 [9032]P46(x90321,x90322,x90323)+P85(f341(f341(f343(x90321),f571(x90323,x90322,x90321)),x90322))+~P85(f341(f341(f241(f864(f863(x90321,x90321),a850)),x90323),f341(f341(f257(x90321,x90321),x90322),f341(f18(f864(x90321,a850),x90321),x90322)))) % 19.23/19.04 [9033]P46(x90331,x90332,x90333)+P85(f341(f341(f343(x90331),f573(x90332,x90333,x90331)),x90332))+~P85(f341(f341(f241(f864(f863(x90331,x90331),a850)),x90333),f341(f341(f257(x90331,x90331),x90332),f341(f18(f864(x90331,a850),x90331),x90332)))) % 19.23/19.04 [9067]~P62(x90671)+~P85(f341(f341(f242(x90671),x90672),x90673))+P85(f341(f341(f242(x90671),f341(f341(f292(x90671),f341(f341(f89(x90671),x90672),x90673)),f341(f341(f89(x90671),f87(x90671)),f87(x90671)))),x90673)) % 19.23/19.04 [9095]~P61(x90951)+P85(f341(f341(f241(x90951),x90952),x90953))+~P85(f341(f341(f241(x90951),f341(f341(f90(x90951),f817(x90953,x90952,x90951)),x90952)),x90953)) % 19.23/19.04 [9203]E(f341(f186(f858(f858(x92031))),f341(f133(f858(x92031),f341(f341(f10(a857,a850,f858(x92031)),f341(f242(a857),x92032)),f186(f858(x92031)))),f169(x92031,x92033))),f341(f186(f858(x92031)),f341(f341(f158(f858(x92031)),x92033),x92032)))+~P15(a857,f341(f148(a857),f341(f341(f149(f858(x92031),a857),f186(f858(x92031))),x92033)))+~P85(f341(f341(f242(a857),x92032),f341(f186(f858(f858(x92031))),x92033))) % 19.23/19.04 [9314]~P35(x93141,x93142)+P27(x93141,f341(f341(f250(f864(f863(x93141,x93141),a850),f864(f863(x93141,x93141),a850)),x93142),x93143))+~P85(f341(f341(f241(f864(f863(x93141,x93141),a850)),f341(f341(f290(x93141,x93141,x93141),x93142),x93143)),x93142)) % 19.23/19.04 [9321]E(f341(f341(f149(f858(x93211),x93211),f341(f341(f9(f858(x93211),a857,x93211),f158(x93211)),x93212)),f341(f133(f858(x93211),f341(f341(f10(a857,a850,f858(x93211)),f341(f242(a857),x93212)),f186(f858(x93211)))),f169(x93211,x93213))),f341(f341(f158(f858(x93211)),x93213),x93212))+~P15(a857,f341(f148(a857),f341(f341(f149(f858(x93211),a857),f186(f858(x93211))),x93213)))+~P85(f341(f341(f242(a857),x93212),f341(f186(f858(f858(x93211))),x93213))) % 19.23/19.04 [9446]P46(x94461,x94462,x94463)+~P85(f341(f341(f343(f863(x94461,x94461)),f341(f341(f250(x94461,x94461),f571(x94463,x94462,x94461)),f571(x94463,x94462,x94461))),x94463))+~P85(f341(f341(f241(f864(f863(x94461,x94461),a850)),x94463),f341(f341(f257(x94461,x94461),x94462),f341(f18(f864(x94461,a850),x94461),x94462)))) % 19.23/19.04 [9447]P46(x94471,x94472,x94473)+~P85(f341(f341(f343(f863(x94471,x94471)),f341(f341(f250(x94471,x94471),f573(x94472,x94473,x94471)),f573(x94472,x94473,x94471))),x94473))+~P85(f341(f341(f241(f864(f863(x94471,x94471),a850)),x94473),f341(f341(f257(x94471,x94471),x94472),f341(f18(f864(x94471,a850),x94471),x94472)))) % 19.23/19.04 [9618]~P136(x96181)+~P119(x96181)+E(f341(f341(f292(x96181),f341(f112(x96181),f341(f341(f82(f863(a1,a1),a1,x96182,f249(a1,a1)),f215(x96182)),x96183))),f341(f112(x96181),f341(f341(f82(f863(a1,a1),a1,x96182,f259(a1,a1)),f215(x96182)),x96183))),f225(x96182,x96181,x96183)) % 19.23/19.04 [9812]~E(x98123,f2(a857))+~E(f341(f186(f858(x98121)),f341(f341(f158(f858(x98121)),x98122),f785(x98123,x98121,x98122))),x98123)+E(f341(f341(f149(a857,f858(x98121)),f341(f341(f9(a857,f858(a857),f858(x98121)),f341(f341(f10(f864(a857,x98121),f864(f858(a857),f858(x98121)),a857),f149(a857,x98121)),f341(f9(a857,a857,x98121),f341(f341(f10(f858(x98121),f864(a857,x98121),a857),f158(x98121)),f341(f158(f858(x98121)),x98122))))),f136(a857,f341(f303(a857,f2(a857)),f341(f186(f858(f858(x98121))),x98122))))),f136(a857,f341(f303(a857,f2(a857)),x98123))),f169(x98121,x98122)) % 19.23/19.04 [9813]E(x98131,f122(f858(x98132)))+~E(f341(f186(f858(x98132)),f341(f341(f158(f858(x98132)),x98131),f785(x98133,x98132,x98131))),x98133)+E(f341(f341(f149(a857,f858(x98132)),f341(f341(f9(a857,f858(a857),f858(x98132)),f341(f341(f10(f864(a857,x98132),f864(f858(a857),f858(x98132)),a857),f149(a857,x98132)),f341(f9(a857,a857,x98132),f341(f341(f10(f858(x98132),f864(a857,x98132),a857),f158(x98132)),f341(f158(f858(x98132)),x98131))))),f136(a857,f341(f303(a857,f2(a857)),f341(f186(f858(f858(x98132))),x98131))))),f136(a857,f341(f303(a857,f2(a857)),x98133))),f169(x98132,x98131)) % 19.23/19.04 [9814]~E(x98143,f2(a857))+E(f341(f341(f149(a857,f858(x98141)),f341(f341(f9(a857,f858(a857),f858(x98141)),f341(f341(f10(f864(a857,x98141),f864(f858(a857),f858(x98141)),a857),f149(a857,x98141)),f341(f9(a857,a857,x98141),f341(f341(f10(f858(x98141),f864(a857,x98141),a857),f158(x98141)),f341(f158(f858(x98141)),x98142))))),f136(a857,f341(f303(a857,f2(a857)),f341(f186(f858(f858(x98141))),x98142))))),f136(a857,f341(f303(a857,f2(a857)),x98143))),f169(x98141,x98142))+P85(f341(f341(f242(a857),f785(x98143,x98141,x98142)),f341(f186(f858(f858(x98141))),x98142))) % 19.23/19.04 [9815]E(x98151,f122(f858(x98152)))+E(f341(f341(f149(a857,f858(x98152)),f341(f341(f9(a857,f858(a857),f858(x98152)),f341(f341(f10(f864(a857,x98152),f864(f858(a857),f858(x98152)),a857),f149(a857,x98152)),f341(f9(a857,a857,x98152),f341(f341(f10(f858(x98152),f864(a857,x98152),a857),f158(x98152)),f341(f158(f858(x98152)),x98151))))),f136(a857,f341(f303(a857,f2(a857)),f341(f186(f858(f858(x98152))),x98151))))),f136(a857,f341(f303(a857,f2(a857)),x98153))),f169(x98152,x98151))+P85(f341(f341(f242(a857),f785(x98153,x98152,x98151)),f341(f186(f858(f858(x98152))),x98151))) % 19.23/19.04 [7665]E(f341(f341(f89(a857),f341(f113(a857),x76651)),f341(f341(f89(a857),f341(f113(a857),x76652)),x76653)),f341(f341(f89(a857),f341(f113(a857),f341(f341(f89(a1),x76651),x76652))),x76653))+P85(f341(a191,f341(f113(a1),x76651)))+P85(f341(a191,f341(f113(a1),x76652))) % 19.23/19.04 [8422]~P85(f341(f71(x84221),x84222))+~P85(f341(f341(f343(x84221),x84223),x84222))+E(f341(a121,f341(f50(x84221),f341(f341(f3(f864(x84221,a850)),x84222),f341(f341(f311(x84221),x84223),f185(f864(x84221,a850)))))),f341(f50(x84221),x84222)) % 19.23/19.04 [8442]~P85(f341(f71(x84421),x84422))+~P85(f341(f341(f343(x84421),x84423),x84422))+E(f341(f341(f89(a857),f87(a857)),f341(f50(x84421),f341(f341(f3(f864(x84421,a850)),x84422),f341(f341(f311(x84421),x84423),f185(f864(x84421,a850)))))),f341(f50(x84421),x84422)) % 19.23/19.04 [8525]~P101(x85251)+~P85(f341(f71(x85251),x85253))+E(f341(f341(f144(x85251,x85251,f7(x85251)),x85252),f136(x85251,f341(f341(f3(f864(x85251,a850)),x85253),f341(f341(f311(x85251),x85252),f185(f864(x85251,a850)))))),f136(x85251,f341(f341(f311(x85251),x85252),x85253))) % 19.23/19.04 [8664]~P85(f341(f71(x86641),x86643))+~P85(f341(f71(x86641),x86642))+E(f341(f341(f89(a857),f341(f50(x86641),f341(f341(f110(f864(x86641,a850)),x86642),x86643))),f341(f50(x86641),f341(f341(f111(f864(x86641,a850)),x86642),x86643))),f341(f341(f89(a857),f341(f50(x86641),x86642)),f341(f50(x86641),x86643))) % 19.23/19.04 [9761]~P26(x97611,f864(f864(x97611,a850),a850),f341(f341(f9(x97611,f864(f863(x97611,x97611),a850),f864(f864(x97611,a850),a850)),f341(f341(f10(f864(x97611,a850),f864(f864(f863(x97611,x97611),a850),f864(f864(x97611,a850),a850)),x97611),f69(x97611)),f341(f341(f9(x97611,f864(x97611,a850),f864(x97611,a850)),f311(x97611)),f185(f864(x97611,a850))))),x97613),x97612)+~P85(f341(f71(x97611),x97612))+E(f341(f50(f864(x97611,a850)),f341(f341(f69(x97611),x97612),x97613)),f341(f50(x97611),x97612)) % 19.23/19.04 [7937]~P89(x79371)+P85(f341(f341(f241(a1),f2(a1)),f341(f113(a1),x79373)))+E(f341(f341(f251(x79371),x79372),f341(f113(a857),f341(f341(f3(a1),f341(f341(f89(a1),x79373),x79373)),a106))),f87(x79371)) % 19.23/19.04 [9297]~P89(x92971)+~P85(f341(f341(f241(a1),f2(a1)),f341(f113(a1),x92973)))+E(f341(f341(f251(x92971),x92972),f341(f113(a857),f341(f341(f3(a1),f341(f341(f89(a1),x92973),x92973)),a106))),f341(f341(f95(x92971,x92971),f341(f341(f251(x92971),x92972),f341(f113(a857),x92973))),f341(f341(f20(x92971,x92971,x92971),f341(f341(f10(x92971,f864(x92971,x92971),x92971),f90(x92971)),f341(f90(x92971),x92972))),f7(x92971)))) % 19.23/19.04 [9726]P85(f341(f341(f241(f864(f863(x97261,x97261),a850)),f309(x97261,x97262)),x97263))+~P85(f341(f341(f241(f864(f863(x97261,x97261),a850)),f309(x97261,f185(f864(f863(x97261,x97261),a850)))),x97263))+~P85(f341(f341(f241(f864(f863(x97261,x97261),a850)),f341(f341(f290(x97261,x97261,x97261),f341(f341(f111(f864(f863(x97261,x97261),a850)),f309(x97261,x97262)),x97263)),x97262)),x97263)) % 19.23/19.04 [9590]~P85(f341(f71(x95901),f341(f265(x95901),x95903)))+~P85(f341(f71(x95901),f341(f265(x95901),x95902)))+P85(f341(f71(x95901),f341(f265(x95901),f341(f341(f20(x95901,a850,a850),f341(f341(f10(a850,f864(a850,a850),x95901),a340),x95902)),x95903)))) % 19.23/19.04 [9882]P85(f341(f341(f241(f864(f863(x98821,x98821),a850)),f341(f341(f290(x98821,x98821,x98821),x98822),f309(x98821,x98822))),x98823))+~P85(f341(f341(f241(f864(f863(x98821,x98821),a850)),x98822),x98823))+~P85(f341(f341(f241(f864(f863(x98821,x98821),a850)),f341(f341(f290(x98821,x98821,x98821),f341(f341(f111(f864(f863(x98821,x98821),a850)),f341(f341(f290(x98821,x98821,x98821),x98822),f309(x98821,x98822))),x98823)),x98822)),x98823)) % 19.23/19.04 [9829]~P113(x98292)+E(x98291,f2(x98292))+~E(f341(f341(f89(x98292),f341(f341(f251(x98292),x98293),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106))))),f341(f341(f251(x98292),x98291),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106))))),f2(x98292)) % 19.23/19.04 [9830]~P113(x98302)+E(x98301,f2(x98302))+~E(f341(f341(f89(x98302),f341(f341(f251(x98302),x98301),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106))))),f341(f341(f251(x98302),x98303),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106))))),f2(x98302)) % 19.23/19.04 [9922]~P113(x99222)+E(x99221,f2(x99222))+P85(f341(f341(f242(x99222),f2(x99222)),f341(f341(f89(x99222),f341(f341(f251(x99222),x99223),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106))))),f341(f341(f251(x99222),x99221),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106))))))) % 19.23/19.04 [9923]~P113(x99232)+E(x99231,f2(x99232))+P85(f341(f341(f242(x99232),f2(x99232)),f341(f341(f89(x99232),f341(f341(f251(x99232),x99231),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106))))),f341(f341(f251(x99232),x99233),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106))))))) % 19.23/19.04 [9973]~P113(x99731)+P85(f341(f341(f241(x99731),f2(x99731)),x99732))+~P85(f341(f341(f241(x99731),f2(x99731)),f341(f341(f251(x99731),x99732),f341(a121,f341(f341(f90(a857),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),x99733))))) % 19.23/19.04 [5382]~P25(x53821,x53824,x53823)+P25(x53821,x53822,x53823)+~P25(x53821,x53822,x53824) % 19.23/19.04 [4861]~E(x48612,f99(x48613,x48611))+P85(f341(x48611,x48612))+~P85(f341(x48611,x48614)) % 19.23/19.04 [6621]~P35(x66212,x66214)+~P35(x66211,x66213)+P35(f863(x66211,x66212),f335(x66211,x66212,x66213,x66214)) % 19.23/19.04 [8008]~P38(f37(x80084,x80081),x80082,x80083,x80082)+P38(x80081,x80082,x80083,f424(x80083,x80082,x80081,x80084))+~P85(f341(x80084,x80082)) % 19.23/19.04 [8034]~P38(f37(x80341,x80342),x80344,x80343,x80344)+P38(f37(x80341,x80342),f424(x80343,x80344,x80342,x80341),x80343,x80344)+~P85(f341(x80341,x80344)) % 19.23/19.04 [5043]~P8(x50434,x50431)+~E(f341(x50431,x50432),f341(x50431,x50433))+P85(f341(f341(x50431,x50432),x50433)) % 19.23/19.04 [5201]~P8(x52014,x52011)+E(f341(x52011,x52012),f341(x52011,x52013))+~P85(f341(f341(x52011,x52012),x52013)) % 19.23/19.04 [5288]~P19(x52883,x52884,x52881)+E(f341(x52881,x52882),f341(f73(x52883,x52884),x52882))+~P85(f341(f71(x52883),x52882)) % 19.23/19.04 [5289]~P11(x52893,x52894,x52891)+E(f341(x52891,x52892),f341(f73(x52893,x52894),x52892))+~P85(f341(f71(x52893),x52892)) % 19.23/19.04 [5417]~P8(x54174,x54171)+~P85(f341(f341(x54171,x54173),x54172))+P85(f341(f341(x54171,x54172),x54173)) % 19.23/19.04 [5480]E(x54801,x54802)+~E(f341(f249(x54803,x54804),x54801),f341(f249(x54803,x54804),x54802))+~E(f341(f259(x54803,x54804),x54801),f341(f259(x54803,x54804),x54802)) % 19.23/19.04 [5506]E(x55061,x55062)+~P85(f341(f63(x55063,x55064),x55062))+~P85(f341(f63(x55063,x55064),x55061)) % 19.23/19.04 [5701]~P68(x57012)+E(f233(x57011,x57012,x57013,x57014),f2(x57012))+P85(f341(f71(x57011),x57014)) % 19.23/19.04 [5839]~P85(f341(f330(x58391,x58392),x58394))+P85(f341(f330(x58391,x58392),x58393))+~P85(f341(f341(x58392,x58393),x58394)) % 19.23/19.04 [8078]~P85(f341(f71(x80782),x80784))+~P85(f341(f71(x80781),x80783))+P85(f341(f71(f865(x80781,x80782)),f323(x80781,x80782,x80783,x80784))) % 19.23/19.04 [8081]P85(f341(f341(f343(f858(x80811)),f341(f341(f132(x80811),x80812),x80813)),f155(x80811,x80814)))+~P85(f341(f341(f343(f858(x80811)),x80813),f155(x80811,x80814)))+~P85(f341(f341(f343(f858(x80811)),x80812),f155(x80811,x80814))) % 19.23/19.04 [8654]~P85(f341(f341(f343(f863(x86541,x86541)),f341(f341(f250(x86541,x86541),x86542),x86544)),f309(x86541,x86543)))+P85(f341(f341(f343(x86541),x86542),f331(x86541,x86543)))+~P85(f341(f341(f343(x86541),x86544),f331(x86541,x86543))) % 19.23/19.04 [5027]~P71(x50272)+E(f341(f341(f11(x50271,x50272),x50273),x50274),f87(x50272))+P85(f341(f71(x50271),x50274)) % 19.23/19.04 [5030]~P68(x50302)+E(f341(f341(f8(x50301,x50302),x50303),x50304),f2(x50302))+P85(f341(f71(x50301),x50304)) % 19.23/19.04 [5171]~P63(x51713)+E(x51711,x51712)+~E(f341(f341(f89(x51713),x51714),x51711),f341(f341(f89(x51713),x51714),x51712)) % 19.23/19.04 [5172]~P64(x51723)+E(x51721,x51722)+~E(f341(f341(f89(x51723),x51724),x51721),f341(f341(f89(x51723),x51724),x51722)) % 19.23/19.04 [5174]~P63(x51743)+E(x51741,x51742)+~E(f341(f341(f89(x51743),x51741),x51744),f341(f341(f89(x51743),x51742),x51744)) % 19.23/19.04 [5258]~P115(x52581)+~E(x52583,f341(f341(f90(x52581),x52582),x52584))+P85(f341(f341(f288(x52581),x52582),x52583)) % 19.23/19.04 [5283]~P6(x52833)+E(x52831,f185(f864(x52832,a850)))+E(f341(f341(f54(x52832,x52833),x52831),f341(f18(x52833,x52832),x52834)),x52834) % 19.23/19.04 [5284]~P6(x52843)+E(x52841,f185(f864(x52842,a850)))+E(f341(f341(f55(x52842,x52843),x52841),f341(f18(x52843,x52842),x52844)),x52844) % 19.23/19.04 [5494]~P100(x54943)+E(x54941,x54942)+~E(f304(x54943,x54944,x54941),f341(f341(f311(x54943),x54942),f185(f864(x54943,a850)))) % 19.23/19.04 [5495]~P100(x54953)+E(x54951,x54952)+~E(f304(x54953,x54951,x54952),f341(f341(f311(x54953),x54954),f185(f864(x54953,a850)))) % 19.23/19.04 [5800]P85(f341(x58001,x58002))+~P85(f341(f254(x58003,x58001),x58004))+~P85(f341(f341(f343(x58003),x58002),x58004)) % 19.23/19.04 [5830]E(x58301,x58302)+~P85(f341(f341(f192(x58303),x58304),x58302))+~P85(f341(f341(f192(x58303),x58304),x58301)) % 19.23/19.04 [5912]~P68(x59121)+E(f341(f341(f8(a857,x59121),x59122),f341(f303(a857,x59123),f341(a121,x59124))),f2(x59121))+~P85(f341(f341(f242(a857),x59124),x59123)) % 19.23/19.04 [5916]~P5(x59161)+~E(f60(x59161,x59162,x59163),f60(x59161,x59164,x59163))+E(f60(x59161,f341(f88(x59161),x59162),x59163),f60(x59161,f341(f88(x59161),x59164),x59163)) % 19.23/19.04 [5984]P85(f341(x59841,x59842))+~E(f341(f133(x59843,x59841),x59844),x59844)+~P85(f341(f341(f343(x59843),x59842),f341(f163(x59843),x59844))) % 19.23/19.04 [6003]~E(f341(f341(f89(a857),x60033),x60032),f341(f341(f89(a857),x60031),x60034))+~P85(f341(f341(f242(a857),x60033),x60034))+P85(f341(f341(f242(a857),x60031),x60032)) % 19.23/19.04 [6010]~P4(x60101)+E(f60(x60101,f60(x60101,x60102,x60103),x60104),f60(x60101,x60102,x60104))+~P85(f341(f341(f288(x60101),x60104),x60103)) % 19.23/19.04 [6048]~E(f341(f133(x60481,x60482),x60483),f122(x60481))+~P85(f341(x60482,x60484))+~P85(f341(f341(f343(x60481),x60484),f341(f163(x60481),x60483))) % 19.23/19.04 [6049]~E(f167(x60493,x60491,x60494),x60494)+P85(f341(x60491,x60492))+~P85(f341(f341(f343(x60493),x60492),f341(f163(x60493),x60494))) % 19.23/19.04 [6084]~E(x60844,f185(f864(x60842,a850)))+~E(x60843,f185(f864(x60841,a850)))+E(f323(x60841,x60842,x60843,x60844),f185(f864(f865(x60841,x60842),a850))) % 19.23/19.04 [6516]~P68(x65161)+E(f341(f341(f8(a857,x65161),x65162),f304(a857,x65163,f341(a121,x65164))),f2(x65161))+~P85(f341(f341(f242(a857),f341(a121,x65164)),x65163)) % 19.23/19.04 [6663]~P101(x66631)+E(f341(f341(f3(f864(x66631,a850)),f341(f303(x66631,x66632),x66633)),f341(f303(x66631,x66632),x66634)),f341(f303(x66631,x66634),x66633))+~P85(f341(f341(f241(x66631),x66632),x66634)) % 19.23/19.04 [7023]~P85(f341(f341(f343(f858(x70231)),x70234),f155(x70231,x70233)))+P85(f341(f341(f343(x70231),x70232),x70233))+~P85(f341(f341(f343(x70231),x70232),f341(f163(x70231),x70234))) % 19.23/19.04 [7030]~P35(x70301,x70302)+P85(f341(f341(f343(x70301),f703(x70302,x70301,x70303)),x70303))+~P85(f341(f341(f343(x70301),x70304),x70303)) % 19.23/19.04 [7087]~P71(x70871)+E(f341(f341(f341(f75(x70871,x70872,f90(x70871)),x70873),f87(x70871)),x70874),f341(f341(f11(x70872,x70871),x70873),x70874))+~P85(f341(f71(x70872),x70874)) % 19.23/19.04 [7089]~P68(x70891)+E(f341(f341(f341(f75(x70891,x70892,f89(x70891)),x70893),f2(x70891)),x70894),f341(f341(f8(x70892,x70891),x70893),x70894))+~P85(f341(f71(x70892),x70894)) % 19.23/19.04 [7115]P26(x71151,x71152,x71153,x71154)+~E(f341(f50(x71152),f341(f312(x71151,x71152,x71153),x71154)),f341(f50(x71151),x71154))+~P85(f341(f71(x71151),x71154)) % 19.23/19.04 [7319]~P68(x73191)+E(f341(f341(f89(x73191),f341(x73192,x73193)),f341(f341(f8(a857,x73191),x73192),f306(a857,x73193,x73194))),f341(f341(f8(a857,x73191),x73192),f304(a857,x73193,x73194)))+~P85(f341(f341(f241(a857),x73193),x73194)) % 19.23/19.04 [7329]~P71(x73291)+~P26(x73292,x73291,x73293,x73294)+E(f341(f341(f11(x73291,x73291),f41(x73291)),f341(f312(x73292,x73291,x73293),x73294)),f341(f341(f11(x73292,x73291),x73293),x73294)) % 19.23/19.04 [7330]~P68(x73301)+~P26(x73302,x73301,x73303,x73304)+E(f341(f341(f8(x73301,x73301),f41(x73301)),f341(f312(x73302,x73301,x73303),x73304)),f341(f341(f8(x73302,x73301),x73303),x73304)) % 19.23/19.04 [7389]E(f341(f50(f865(x73891,x73892)),f323(x73891,x73892,x73893,x73894)),f341(f341(f89(a857),f341(f50(x73891),x73893)),f341(f50(x73892),x73894)))+~P85(f341(f71(x73892),x73894))+~P85(f341(f71(x73891),x73893)) % 19.23/19.04 [7473]E(x74731,x74732)+P85(f341(f341(f343(x74733),x74731),f341(f163(x74733),f157(x74733,x74732,x74734))))+~P85(f341(f341(f343(x74733),x74731),f341(f163(x74733),x74734))) % 19.23/19.04 [7699]~P68(x76991)+E(f341(f341(f89(x76991),f341(f341(f8(a857,x76991),x76992),f341(f303(a857,x76993),x76994))),f341(x76992,x76994)),f341(f341(f8(a857,x76991),x76992),f341(f303(a857,x76993),f341(a121,x76994))))+P85(f341(f341(f242(a857),x76994),x76993)) % 19.23/19.04 [7756]~P26(x77561,x77562,x77563,f248(f864(x77561,a850)))+~P85(f341(f71(x77562),x77564))+P85(f341(f71(x77561),f341(f314(x77561,x77562,x77563),x77564))) % 19.23/19.04 [7870]P85(f341(f341(f343(f858(x78701)),f341(f341(f146(x78701),x78702),x78703)),f155(x78701,x78704)))+~P85(f341(f341(f343(f858(x78701)),x78703),f155(x78701,x78704)))+~P85(f341(f341(f343(x78701),x78702),x78704)) % 19.23/19.04 [7961]~E(f341(f312(x79613,x79611,x79614),f248(f864(x79613,a850))),f248(f864(x79611,a850)))+P85(f341(f71(x79611),x79612))+~P85(f341(f71(x79613),f341(f314(x79613,x79611,x79614),x79612))) % 19.23/19.04 [8050]~P26(x80501,x80503,x80504,x80502)+P85(f341(f71(x80501),x80502))+~P85(f341(f71(x80503),f341(f312(x80501,x80503,x80504),x80502))) % 19.23/19.04 [8073]~E(x80732,x80733)+P85(f341(f341(f343(f863(x80731,x80731)),f341(f341(f250(x80731,x80731),x80732),x80733)),f269(x80731,x80734)))+~P85(f341(f341(f343(x80731),x80732),x80734)) % 19.23/19.04 [8104]~P68(x81041)+E(f341(f341(f89(x81041),f341(f341(f8(a857,x81041),x81042),f304(a857,x81043,x81044))),f341(x81042,f341(a121,x81044))),f341(f341(f8(a857,x81041),x81042),f304(a857,x81043,f341(a121,x81044))))+P85(f341(f341(f242(a857),f341(a121,x81044)),x81043)) % 19.23/19.04 [8165]P85(f341(x81651,x81652))+~P85(f341(x81651,f341(f341(f158(x81653),x81654),f735(x81651,x81654,x81653))))+~P85(f341(f341(f343(x81653),x81652),f341(f163(x81653),x81654))) % 19.23/19.04 [8300]~P85(f341(f341(f343(x83001),x83002),f331(x83001,x83004)))+P85(f341(f341(f343(f858(x83001)),f341(f341(f146(x83001),x83002),x83003)),f331(f858(x83001),f152(x83001,x83004))))+~P85(f341(f341(f343(f858(x83001)),x83003),f331(f858(x83001),f152(x83001,x83004)))) % 19.23/19.04 [8316]~P26(x83162,x83163,x83164,f694(x83164,x83163,x83162,x83161))+P26(x83162,x83163,x83164,f53(f864(x83162,a850),x83161))+E(x83161,f185(f864(f864(x83162,a850),a850))) % 19.23/19.04 [8575]E(x85751,x85752)+~P85(f341(f341(f343(f863(x85753,x85753)),f341(f341(f250(x85753,x85753),x85751),x85752)),f309(x85753,x85754)))+P85(f341(f341(f343(x85753),x85751),f341(f270(x85753,x85753),x85754))) % 19.23/19.04 [8826]P26(x88262,x88263,x88264,f53(f864(x88262,a850),x88261))+E(x88261,f185(f864(f864(x88262,a850),a850)))+P85(f341(f341(f343(f864(x88262,a850)),f694(x88264,x88263,x88262,x88261)),x88261)) % 19.23/19.04 [8952]P85(f341(f71(x89521),x89522))+~P85(f341(f71(x89524),f341(f312(x89521,x89524,x89523),x89522)))+P85(f341(f341(f343(x89521),f602(x89523,x89524,x89522,x89521)),x89522)) % 19.23/19.04 [9046]~P6(x90462)+E(f341(f341(f74(x90461,x90462,f341(f341(f10(x90462,f864(x90462,x90462),x90461),f110(x90462)),x90463)),f185(x90462)),x90464),f341(f341(f54(x90461,x90462),x90464),x90463))+~P85(f341(f71(x90461),x90464)) % 19.23/19.04 [9047]~P6(x90472)+E(f341(f341(f74(x90471,x90472,f341(f341(f10(x90472,f864(x90472,x90472),x90471),f111(x90472)),x90473)),f248(x90472)),x90474),f341(f341(f55(x90471,x90472),x90474),x90473))+~P85(f341(f71(x90471),x90474)) % 19.23/19.04 [9074]~P85(f341(f341(f288(a857),x90743),x90744))+P85(f341(f341(f288(a857),x90741),x90742))+P85(f341(f341(f242(f864(a857,a850)),f291(a857,f288(a857),x90741,x90742)),f291(a857,f288(a857),x90743,x90744))) % 19.23/19.04 [9085]~P85(f341(f341(f288(a857),x90852),x90854))+~P85(f341(f341(f288(a857),x90853),x90851))+P85(f341(f341(f241(f864(a857,a850)),f291(a857,f288(a857),x90851,x90852)),f291(a857,f288(a857),x90853,x90854))) % 19.23/19.04 [9142]E(x91421,x91422)+~P85(f341(f341(f343(f863(x91423,x91423)),f341(f341(f250(x91423,x91423),x91421),x91422)),f309(x91423,x91424)))+P85(f341(f341(f343(f863(x91423,x91423)),f341(f341(f250(x91423,x91423),x91421),x91422)),f341(f341(f290(x91423,x91423,x91423),x91424),f309(x91423,x91424)))) % 19.23/19.04 [9173]~E(f341(f186(f858(x91731)),x91732),f341(f186(f858(x91731)),x91733))+~P85(f341(f341(f343(f863(f858(x91731),f858(x91731))),f341(f341(f250(f858(x91731),f858(x91731)),x91732),x91733)),f143(x91731,x91734)))+P85(f341(f341(f343(f863(f858(x91731),f858(x91731))),f341(f341(f250(f858(x91731),f858(x91731)),x91732),x91733)),f141(x91731,x91734))) % 19.23/19.04 [9284]P85(f341(f341(f288(a857),x92841),x92842))+~P85(f341(f341(f288(a857),x92843),x92841))+~P85(f341(f341(f242(f864(a857,a850)),f291(a857,f288(a857),x92843,x92841)),f291(a857,f288(a857),x92844,x92842))) % 19.23/19.04 [9285]P85(f341(f341(f288(a857),x92851),x92852))+~P85(f341(f341(f288(a857),x92853),x92851))+~P85(f341(f341(f241(f864(a857,a850)),f291(a857,f288(a857),x92853,x92851)),f291(a857,f288(a857),x92854,x92852))) % 19.23/19.04 [9286]P85(f341(f341(f288(a857),x92861),x92862))+~P85(f341(f341(f288(a857),x92862),x92863))+~P85(f341(f341(f242(f864(a857,a850)),f291(a857,f288(a857),x92862,x92863)),f291(a857,f288(a857),x92861,x92864))) % 19.23/19.04 [9287]P85(f341(f341(f288(a857),x92871),x92872))+~P85(f341(f341(f288(a857),x92872),x92873))+~P85(f341(f341(f241(f864(a857,a850)),f291(a857,f288(a857),x92872,x92873)),f291(a857,f288(a857),x92871,x92874))) % 19.23/19.04 [9593]~P3(x95931)+E(f341(f341(f8(a857,x95931),f341(f341(f20(a857,x95931,x95931),f341(f341(f10(x95931,f864(x95931,x95931),a857),f3(x95931)),x95932)),f341(f341(f10(a857,x95931,a857),x95932),f341(f341(f9(a857,a857,a857),f89(a857)),f87(a857))))),f304(a857,x95933,x95934)),f2(x95931))+P85(f341(f341(f241(a857),x95933),x95934)) % 19.23/19.04 [9827]~P35(x98272,x98274)+~P26(x98272,x98271,x98273,f248(f864(x98272,a850)))+P35(x98271,f341(f312(f863(x98272,x98272),f863(x98271,x98271),f261(x98272,x98271,x98272,x98271,x98273,x98273)),x98274)) % 19.23/19.04 [10001]~E(f341(f186(f858(x100011)),x100013),f341(f186(f858(x100011)),x100012))+P85(f341(f341(f343(f863(f858(x100011),f858(x100011))),f341(f341(f250(f858(x100011),f858(x100011)),x100012),x100013)),f153(x100011,x100014)))+~P85(f341(f341(f260(x100011,x100011,a850),f341(f341(f9(x100011,f864(f863(x100011,x100011),a850),f864(x100011,a850)),f341(f341(f10(f864(x100011,f864(f864(f863(x100011,x100011),a850),a850)),f864(f864(f863(x100011,x100011),a850),f864(x100011,a850)),x100011),f9(x100011,f864(f863(x100011,x100011),a850),a850)),f341(f341(f10(f864(x100011,f863(x100011,x100011)),f864(x100011,f864(f864(f863(x100011,x100011),a850),a850)),x100011),f341(f10(f863(x100011,x100011),f864(f864(f863(x100011,x100011),a850),a850),x100011),f343(f863(x100011,x100011)))),f250(x100011,x100011)))),x100014)),f726(x100014,x100013,x100012,x100011))) % 19.23/19.04 [5876]~E(x58764,x58762)+P85(f341(x58761,x58762))+P85(f341(f341(f192(f37(x58761,x58763)),x58762),x58764)) % 19.23/19.04 [5968]~P4(x59681)+~E(x59682,f2(x59681))+E(f341(f341(f51(x59681),f341(f341(f90(x59681),x59682),x59683)),f341(f341(f90(x59681),x59682),x59684)),f2(x59681)) % 19.23/19.04 [6007]E(x60071,f122(x60072))+E(x60073,f341(f341(f3(a857),f341(f186(f858(x60072)),x60071)),f87(a857)))+E(f140(x60072,f341(f341(f154(x60072,x60071),x60073),x60074)),f140(x60072,x60071)) % 19.23/19.04 [6039]E(x60391,x60392)+P85(f341(x60393,x60392))+~P85(f341(f341(f341(f311(x60394),x60391),x60393),x60392)) % 19.23/19.04 [6053]~P68(x60531)+~P85(f341(f134(x60532),x60534))+E(f341(f160(x60531),f341(f341(f149(x60532,x60531),x60533),x60534)),f341(f341(f8(x60532,x60531),x60533),f341(f163(x60532),x60534))) % 19.23/19.04 [6077]~P71(x60772)+~P85(f341(f71(x60771),x60774))+E(f341(f341(f11(x60771,x60772),f341(f18(x60772,x60771),x60773)),x60774),f341(f341(f251(x60772),x60773),f341(f50(x60771),x60774))) % 19.23/19.04 [6131]~P4(x61312)+E(x61311,f2(x61312))+E(f341(f341(f51(x61312),f341(f341(f90(x61312),x61313),x61311)),f341(f341(f90(x61312),x61314),x61311)),f341(f341(f51(x61312),x61313),x61314)) % 19.23/19.04 [6133]~P59(x61332)+E(x61331,f2(x61332))+E(f341(f341(f292(x61332),f341(f341(f90(x61332),x61333),x61331)),f341(f341(f90(x61332),x61334),x61331)),f341(f341(f292(x61332),x61333),x61334)) % 19.23/19.04 [6134]~P59(x61342)+E(x61341,f2(x61342))+E(f341(f341(f292(x61342),f341(f341(f90(x61342),x61341),x61343)),f341(f341(f90(x61342),x61341),x61344)),f341(f341(f292(x61342),x61343),x61344)) % 19.23/19.04 [6135]~P4(x61352)+E(x61351,f2(x61352))+E(f341(f341(f51(x61352),f341(f341(f90(x61352),x61351),x61353)),f341(f341(f90(x61352),x61351),x61354)),f341(f341(f51(x61352),x61353),x61354)) % 19.23/19.04 [6201]P85(f341(x62011,x62012))+~E(x62013,f341(f341(f89(a857),x62014),x62012))+~P85(f341(x62011,f341(f341(f3(a857),x62013),x62014))) % 19.23/19.04 [6283]P31(x62831,x62832,x62833)+P30(x62831,f608(x62833,x62832,x62831),x62834)+~P85(f341(f341(f343(f856(x62831)),x62834),x62832)) % 19.23/19.04 [6329]E(x63291,f122(x63292))+~E(x63293,f341(f341(f3(a857),f341(f186(f858(x63292)),x63291)),f87(a857)))+E(f140(x63292,f341(f341(f154(x63292,x63291),x63293),x63294)),x63294) % 19.23/19.04 [6352]~P101(x63521)+~P85(f341(f341(f242(x63521),x63522),x63524))+P85(f341(f341(f242(x63521),x63522),f341(f341(f240(x63521),x63523),x63524))) % 19.23/19.04 [6354]~P101(x63541)+~P85(f341(f341(f242(x63541),x63542),x63543))+P85(f341(f341(f242(x63541),x63542),f341(f341(f240(x63541),x63543),x63544))) % 19.23/19.04 [6355]~P98(x63551)+~P85(f341(f341(f242(x63551),x63552),x63554))+P85(f341(f341(f242(x63551),x63552),f341(f341(f110(x63551),x63553),x63554))) % 19.23/19.04 [6356]~P98(x63561)+~P85(f341(f341(f242(x63561),x63562),x63563))+P85(f341(f341(f242(x63561),x63562),f341(f341(f110(x63561),x63563),x63564))) % 19.23/19.04 [6358]~P101(x63581)+~P85(f341(f341(f241(x63581),x63582),x63584))+P85(f341(f341(f241(x63581),x63582),f341(f341(f240(x63581),x63583),x63584))) % 19.23/19.04 [6360]~P101(x63601)+~P85(f341(f341(f241(x63601),x63602),x63603))+P85(f341(f341(f241(x63601),x63602),f341(f341(f240(x63601),x63603),x63604))) % 19.23/19.04 [6361]~P98(x63611)+~P85(f341(f341(f241(x63611),x63612),x63614))+P85(f341(f341(f241(x63611),x63612),f341(f341(f110(x63611),x63613),x63614))) % 19.23/19.04 [6362]~P98(x63621)+~P85(f341(f341(f241(x63621),x63622),x63623))+P85(f341(f341(f241(x63621),x63622),f341(f341(f110(x63621),x63623),x63624))) % 19.23/19.04 [6363]~P86(x63631)+~P85(f341(f341(f288(x63631),x63632),x63634))+P85(f341(f341(f288(x63631),x63632),f341(f341(f90(x63631),x63633),x63634))) % 19.23/19.04 [6364]~P86(x63641)+~P85(f341(f341(f288(x63641),x63642),x63643))+P85(f341(f341(f288(x63641),x63642),f341(f341(f90(x63641),x63643),x63644))) % 19.23/19.04 [6459]~E(f341(f341(f158(x64591),x64592),x64593),x64594)+E(f341(f341(f154(x64591,x64592),x64593),x64594),x64592)+~P85(f341(f341(f242(a857),x64593),f341(f186(f858(x64591)),x64592))) % 19.23/19.04 [6479]E(x64791,x64792)+P85(f341(x64793,x64791))+~P85(f341(f341(f192(f37(x64793,x64794)),x64791),x64792)) % 19.23/19.04 [6499]P85(f341(x64991,x64992))+~P85(f341(x64993,x64992))+~P85(f341(f341(f241(f864(x64994,a850)),x64993),x64991)) % 19.23/19.04 [6535]~E(f341(f341(f154(x65351,x65352),x65353),x65354),x65352)+E(f341(f341(f158(x65351),x65352),x65353),x65354)+~P85(f341(f341(f242(a857),x65353),f341(f186(f858(x65351)),x65352))) % 19.23/19.04 [6660]E(x66601,f185(f864(x66602,a850)))+E(x66603,f185(f864(x66604,a850)))+~E(f341(f341(f257(x66604,x66602),x66603),f341(f18(f864(x66602,a850),x66604),x66601)),f185(f864(f863(x66604,x66602),a850))) % 19.23/19.04 [6678]E(x66781,x66782)+P85(f341(f341(f343(x66783),x66781),x66784))+~P85(f341(f341(f343(x66783),x66781),f341(f341(f311(x66783),x66782),x66784))) % 19.23/19.04 [6695]~P101(x66951)+P85(f341(f341(f242(x66951),x66952),x66953))+~P85(f341(f341(f242(x66951),x66952),f341(f341(f245(x66951),x66954),x66953))) % 19.23/19.04 [6696]~P101(x66961)+P85(f341(f341(f242(x66961),x66962),x66963))+~P85(f341(f341(f242(x66961),x66962),f341(f341(f245(x66961),x66963),x66964))) % 19.23/19.04 [6698]~P101(x66981)+P85(f341(f341(f241(x66981),x66982),x66983))+~P85(f341(f341(f241(x66981),x66982),f341(f341(f245(x66981),x66984),x66983))) % 19.23/19.04 [6700]~P101(x67001)+P85(f341(f341(f241(x67001),x67002),x67003))+~P85(f341(f341(f241(x67001),x67002),f341(f341(f245(x67001),x67003),x67004))) % 19.23/19.04 [6702]~P99(x67021)+P85(f341(f341(f241(x67021),x67022),x67023))+~P85(f341(f341(f241(x67021),x67022),f341(f341(f111(x67021),x67024),x67023))) % 19.23/19.04 [6704]~P99(x67041)+P85(f341(f341(f241(x67041),x67042),x67043))+~P85(f341(f341(f241(x67041),x67042),f341(f341(f111(x67041),x67043),x67044))) % 19.23/19.04 [6726]~E(f341(f341(f158(x67261),x67263),x67264),x67262)+P85(f341(f341(f343(x67261),x67262),f341(f163(x67261),x67263)))+~P85(f341(f341(f242(a857),x67264),f341(f186(f858(x67261)),x67263))) % 19.23/19.04 [6738]~P101(x67381)+~P15(x67381,f341(f341(f146(x67381),x67382),f341(f341(f146(x67381),x67383),x67384)))+P85(f341(f341(f241(x67381),x67382),x67383)) % 19.23/19.04 [6907]E(x69071,f2(a1))+E(f341(f341(f51(a1),x69072),x69071),x69073)+~P85(f341(f64(x69072,x69071),f341(f341(f250(a1,a1),x69073),x69074))) % 19.23/19.04 [6930]E(f60(a1,x69302,x69301),x69303)+E(x69301,f2(a1))+~P85(f341(f64(x69302,x69301),f341(f341(f250(a1,a1),x69304),x69303))) % 19.23/19.04 [7044]P85(f341(f341(f343(x70441),x70442),x70443))+~P85(f341(f341(f343(x70441),x70442),x70444))+~P85(f341(f341(f242(f864(x70441,a850)),x70444),x70443)) % 19.23/19.04 [7048]P85(f341(f341(f343(x70481),x70482),x70483))+~P85(f341(f341(f343(x70481),x70482),x70484))+~P85(f341(f341(f241(f864(x70481,a850)),x70484),x70483)) % 19.23/19.04 [7058]~P114(x70581)+~E(x70583,f2(x70581))+P85(f341(f341(f288(x70581),f341(f341(f90(x70581),x70582),x70583)),f341(f341(f90(x70581),x70584),x70583))) % 19.23/19.04 [7059]~P114(x70591)+~E(x70592,f2(x70591))+P85(f341(f341(f288(x70591),f341(f341(f90(x70591),x70592),x70593)),f341(f341(f90(x70591),x70592),x70594))) % 19.23/19.04 [7283]~P103(x72832)+~P85(f341(f341(f242(f864(x72831,x72832)),x72833),x72834))+P85(f341(f341(f241(f864(x72831,x72832)),x72833),x72834)) % 19.23/19.04 [7378]~P25(x73781,x73782,x73784)+P25(x73781,x73782,f341(f341(f311(f856(x73781)),x73783),x73784))+~P25(x73781,x73782,f341(f341(f311(f856(x73781)),x73783),f185(f864(f856(x73781),a850)))) % 19.23/19.04 [7417]~P85(f341(f341(f343(x74171),x74172),x74174))+P85(f341(f341(f343(x74171),x74172),f52(f864(x74171,a850),x74173)))+~P85(f341(f341(f343(f864(x74171,a850)),x74174),x74173)) % 19.23/19.04 [7419]~P86(x74191)+~P85(f341(f341(f241(a857),x74193),x74194))+P85(f341(f341(f288(x74191),f341(f341(f251(x74191),x74192),x74193)),f341(f341(f251(x74191),x74192),x74194))) % 19.23/19.04 [7448]~P74(x74481)+~P85(f341(f341(f242(x74481),x74483),x74484))+P85(f341(f341(f242(x74481),f341(f341(f89(x74481),x74482),x74483)),f341(f341(f89(x74481),x74482),x74484))) % 19.23/19.04 [7449]~P80(x74491)+~P85(f341(f341(f242(x74491),x74493),x74494))+P85(f341(f341(f242(x74491),f341(f341(f89(x74491),x74492),x74493)),f341(f341(f89(x74491),x74492),x74494))) % 19.23/19.04 [7450]~P74(x74501)+~P85(f341(f341(f242(x74501),x74502),x74504))+P85(f341(f341(f242(x74501),f341(f341(f89(x74501),x74502),x74503)),f341(f341(f89(x74501),x74504),x74503))) % 19.23/19.04 [7451]~P80(x74511)+~P85(f341(f341(f242(x74511),x74512),x74514))+P85(f341(f341(f242(x74511),f341(f341(f89(x74511),x74512),x74513)),f341(f341(f89(x74511),x74514),x74513))) % 19.23/19.04 [7452]~P74(x74521)+~P85(f341(f341(f241(x74521),x74523),x74524))+P85(f341(f341(f241(x74521),f341(f341(f89(x74521),x74522),x74523)),f341(f341(f89(x74521),x74522),x74524))) % 19.23/19.04 [7453]~P78(x74531)+~P85(f341(f341(f241(x74531),x74533),x74534))+P85(f341(f341(f241(x74531),f341(f341(f89(x74531),x74532),x74533)),f341(f341(f89(x74531),x74532),x74534))) % 19.23/19.04 [7454]~P74(x74541)+~P85(f341(f341(f241(x74541),x74542),x74544))+P85(f341(f341(f241(x74541),f341(f341(f89(x74541),x74542),x74543)),f341(f341(f89(x74541),x74544),x74543))) % 19.23/19.04 [7455]~P78(x74551)+~P85(f341(f341(f241(x74551),x74552),x74554))+P85(f341(f341(f241(x74551),f341(f341(f89(x74551),x74552),x74553)),f341(f341(f89(x74551),x74554),x74553))) % 19.23/19.04 [7456]~P114(x74561)+~P85(f341(f341(f288(x74561),x74563),x74564))+P85(f341(f341(f288(x74561),f341(f341(f90(x74561),x74562),x74563)),f341(f341(f90(x74561),x74562),x74564))) % 19.23/19.04 [7457]~P114(x74571)+~P85(f341(f341(f288(x74571),x74572),x74574))+P85(f341(f341(f288(x74571),f341(f341(f90(x74571),x74572),x74573)),f341(f341(f90(x74571),x74574),x74573))) % 19.23/19.04 [7458]~P86(x74581)+~P85(f341(f341(f288(x74581),x74582),x74584))+P85(f341(f341(f288(x74581),f341(f341(f251(x74581),x74582),x74583)),f341(f341(f251(x74581),x74584),x74583))) % 19.23/19.04 [7467]~P138(x74671)+~P90(x74671)+E(f341(f341(f89(x74671),f341(f341(f90(x74671),x74672),f341(f113(x74671),x74673))),f341(f341(f90(x74671),x74674),f341(f113(x74671),x74673))),f341(f341(f90(x74671),f341(f341(f89(x74671),x74672),x74674)),f341(f113(x74671),x74673))) % 19.23/19.04 [7468]~P123(x74681)+~P90(x74681)+E(f341(f341(f3(x74681),f341(f341(f90(x74681),x74682),f341(f113(x74681),x74683))),f341(f341(f90(x74681),x74684),f341(f113(x74681),x74683))),f341(f341(f90(x74681),f341(f341(f3(x74681),x74682),x74684)),f341(f113(x74681),x74683))) % 19.23/19.04 [7504]~P68(x75041)+E(f341(f341(f89(x75041),f341(x75042,x75043)),f341(f341(f8(a857,x75041),x75042),f304(a857,f341(a121,x75043),x75044))),f341(f341(f8(a857,x75041),x75042),f304(a857,x75043,x75044)))+~P85(f341(f341(f241(a857),x75043),x75044)) % 19.23/19.04 [7515]~P26(x75152,x75151,x75153,f341(f163(x75152),x75154))+~P85(f341(f134(x75152),x75154))+P85(f341(f134(x75151),f341(f341(f149(x75152,x75151),x75153),x75154))) % 19.23/19.04 [7564]~P85(f341(f341(f242(a857),x75642),x75644))+~P85(f341(f341(f242(a857),x75641),x75643))+P85(f341(f341(f242(a857),f341(f341(f89(a857),x75641),x75642)),f341(f341(f89(a857),x75643),x75644))) % 19.23/19.04 [7567]~P85(f341(f341(f242(a1),x75671),x75673))+~P85(f341(f341(f241(a1),x75672),x75674))+P85(f341(f341(f242(a1),f341(f341(f89(a1),x75671),x75672)),f341(f341(f89(a1),x75673),x75674))) % 19.23/19.04 [7568]~P85(f341(f341(f241(a857),x75682),x75684))+~P85(f341(f341(f241(a857),x75681),x75683))+P85(f341(f341(f241(a857),f341(f341(f89(a857),x75681),x75682)),f341(f341(f89(a857),x75683),x75684))) % 19.23/19.04 [7569]~P85(f341(f341(f241(a857),x75692),x75694))+~P85(f341(f341(f241(a857),x75691),x75693))+P85(f341(f341(f241(a857),f341(f341(f90(a857),x75691),x75692)),f341(f341(f90(a857),x75693),x75694))) % 19.23/19.04 [7619]P85(f341(f341(f343(x76191),x76192),x76193))+~P85(f341(f341(f343(x76191),x76192),f53(f864(x76191,a850),x76194)))+~P85(f341(f341(f343(f864(x76191,a850)),x76193),x76194)) % 19.23/19.04 [7635]~P85(f341(x76351,f734(x76351,x76353,x76352)))+P85(f341(x76351,f341(f341(f158(x76352),x76353),x76354)))+~P85(f341(f341(f242(a857),x76354),f341(f186(f858(x76352)),x76353))) % 19.23/19.04 [7639]P85(f341(x76391,x76392))+~P85(f341(f341(f343(x76394),x76392),f341(f163(x76394),x76393)))+P85(f341(f341(f242(a857),f735(x76391,x76393,x76394)),f341(f186(f858(x76394)),x76393))) % 19.23/19.04 [7658]~P85(f341(f341(f192(x76582),x76583),x76584))+~P85(f341(f341(f192(f37(x76581,x76582)),x76584),x76583))+P85(f341(f341(f192(f37(x76581,x76582)),x76583),x76583)) % 19.23/19.04 [7686]~P103(x76861)+~P85(f341(f341(f241(f864(x76862,x76861)),x76864),x76863))+~P85(f341(f341(f242(f864(x76862,x76861)),x76863),x76864)) % 19.23/19.04 [7729]~P85(f341(x77294,x77292))+~P85(f341(f341(f343(x77291),x77292),x77293))+P85(f341(f341(f343(x77291),x77292),f341(f341(f111(f864(x77291,a850)),x77293),f341(f265(x77291),x77294)))) % 19.23/19.04 [7878]~P85(f341(f341(f343(x78781),x78783),x78784))+~P85(f341(f341(f242(f864(x78781,a850)),x78782),x78784))+P85(f341(f341(f242(f864(x78781,a850)),x78782),f341(f341(f311(x78781),x78783),x78784))) % 19.23/19.04 [7880]E(f341(f341(f111(f864(x78801,a850)),x78802),x78803),f185(f864(x78801,a850)))+~E(f341(f341(f111(f864(x78801,a850)),f52(f864(x78801,a850),x78804)),x78803),f185(f864(x78801,a850)))+~P85(f341(f341(f343(f864(x78801,a850)),x78802),x78804)) % 19.23/19.04 [7957]P85(f341(f341(f343(x79571),x79572),x79573))+~P85(f341(f341(f241(f864(x79571,a850)),x79573),f341(f341(f311(x79571),x79572),x79574)))+P85(f341(f341(f241(f864(x79571,a850)),x79573),x79574)) % 19.23/19.04 [7977]P85(f341(f341(f343(x79772),f734(x79771,x79773,x79772)),f341(f163(x79772),x79773)))+P85(f341(x79771,f341(f341(f158(x79772),x79773),x79774)))+~P85(f341(f341(f242(a857),x79774),f341(f186(f858(x79772)),x79773))) % 19.23/19.04 [7985]~P85(f341(f341(f242(f864(x79851,a850)),x79852),x79854))+P85(f341(f341(f242(f864(x79851,a850)),x79852),x79853))+~P85(f341(f341(f242(f864(x79851,a850)),x79854),x79853)) % 19.23/19.04 [7986]~P85(f341(f341(f241(f864(x79861,a850)),x79862),x79864))+P85(f341(f341(f242(f864(x79861,a850)),x79862),x79863))+~P85(f341(f341(f242(f864(x79861,a850)),x79864),x79863)) % 19.23/19.04 [7987]~P85(f341(f341(f241(f864(x79871,a850)),x79874),x79873))+~P85(f341(f341(f242(f864(x79871,a850)),x79872),x79874))+P85(f341(f341(f242(f864(x79871,a850)),x79872),x79873)) % 19.23/19.04 [7988]~P85(f341(f341(f241(f864(x79881,a850)),x79882),x79884))+P85(f341(f341(f241(f864(x79881,a850)),x79882),x79883))+~P85(f341(f341(f241(f864(x79881,a850)),x79884),x79883)) % 19.23/19.04 [8023]~P85(f341(f341(f343(x80231),x80234),x80233))+~P85(f341(f341(f242(f864(x80231,a850)),x80232),f341(f341(f311(x80231),x80234),x80233)))+P85(f341(f341(f242(f864(x80231,a850)),x80232),x80233)) % 19.23/19.04 [8036]~P74(x80361)+P85(f341(f341(f242(x80361),x80362),x80363))+~P85(f341(f341(f242(x80361),f341(f341(f89(x80361),x80364),x80362)),f341(f341(f89(x80361),x80364),x80363))) % 19.23/19.04 [8038]~P74(x80381)+P85(f341(f341(f242(x80381),x80382),x80383))+~P85(f341(f341(f242(x80381),f341(f341(f89(x80381),x80382),x80384)),f341(f341(f89(x80381),x80383),x80384))) % 19.23/19.04 [8040]~P74(x80401)+P85(f341(f341(f241(x80401),x80402),x80403))+~P85(f341(f341(f241(x80401),f341(f341(f89(x80401),x80404),x80402)),f341(f341(f89(x80401),x80404),x80403))) % 19.23/19.04 [8042]~P74(x80421)+P85(f341(f341(f241(x80421),x80422),x80423))+~P85(f341(f341(f241(x80421),f341(f341(f89(x80421),x80422),x80424)),f341(f341(f89(x80421),x80423),x80424))) % 19.23/19.04 [8204]P85(f341(x82041,x82042))+~P85(f341(f341(f343(x82043),x82042),f341(f163(x82043),x82044)))+P85(f341(f341(f242(a857),f341(f186(f858(x82043)),f341(f133(x82043,x82041),x82044))),f341(f186(f858(x82043)),x82044))) % 19.23/19.04 [8335]E(x83351,x83352)+P85(f341(f341(f192(x83353),x83351),f436(x83352,x83351,x83353,x83354)))+~P85(f341(f341(f192(f37(x83354,x83353)),x83351),x83352)) % 19.23/19.04 [8336]E(x83361,x83362)+P85(f341(f341(f192(x83363),x83361),f588(x83362,x83361,x83363,x83364)))+~P85(f341(f341(f192(f37(x83364,x83363)),x83361),x83362)) % 19.23/19.04 [8363]~P85(f341(x83634,x83632))+P85(f341(f341(f192(x83631),x83632),f436(x83633,x83632,x83631,x83634)))+~P85(f341(f341(f192(f37(x83634,x83631)),x83632),x83633)) % 19.23/19.04 [8364]~P85(f341(x83644,x83642))+P85(f341(f341(f192(x83641),x83642),f588(x83643,x83642,x83641,x83644)))+~P85(f341(f341(f192(f37(x83644,x83641)),x83642),x83643)) % 19.23/19.04 [8687]~P26(x86874,x86873,x86871,f248(f864(x86874,a850)))+E(f341(x86871,f527(x86872,x86871,x86873,x86874)),x86872)+~P85(f341(f341(f343(x86873),x86872),f341(f312(x86874,x86873,x86871),f248(f864(x86874,a850))))) % 19.23/19.04 [8828]~P85(f341(f71(x88281),x88284))+P85(f341(f341(f343(x88281),f556(x88282,x88283,x88284,x88281)),x88284))+P85(f341(f71(f863(x88281,x88283)),f341(f341(f257(x88281,x88283),x88284),x88282))) % 19.23/19.04 [8871]E(x88711,x88712)+P85(f341(f341(f192(f37(x88713,x88714)),f436(x88711,x88712,x88714,x88713)),x88711))+~P85(f341(f341(f192(f37(x88713,x88714)),x88712),x88711)) % 19.23/19.04 [8872]E(x88721,x88722)+P85(f341(f341(f192(f37(x88723,x88724)),f588(x88721,x88722,x88724,x88723)),x88721))+~P85(f341(f341(f192(f37(x88723,x88724)),x88722),x88721)) % 19.23/19.04 [8892]~P85(f341(x88921,x88924))+P85(f341(f341(f192(f37(x88921,x88922)),f436(x88923,x88924,x88922,x88921)),x88923))+~P85(f341(f341(f192(f37(x88921,x88922)),x88924),x88923)) % 19.23/19.04 [8893]~P85(f341(x88931,x88934))+P85(f341(f341(f192(f37(x88931,x88932)),f588(x88933,x88934,x88932,x88931)),x88933))+~P85(f341(f341(f192(f37(x88931,x88932)),x88934),x88933)) % 19.23/19.04 [9133]~P85(f341(f71(x91331),x91333))+~P85(f341(f71(x91332),f341(x91334,f556(x91334,x91332,x91333,x91331))))+P85(f341(f71(f863(x91331,x91332)),f341(f341(f257(x91331,x91332),x91333),x91334))) % 19.23/19.04 [9148]~E(f341(f186(f858(x91484)),x91482),f341(f186(f858(x91484)),x91483))+P85(f341(f341(f343(f863(f858(x91484),f858(x91484))),f341(f341(f250(f858(x91484),f858(x91484)),x91483),x91482)),f153(x91484,x91481)))+P85(f341(f341(f242(a857),f742(x91481,x91482,x91483,x91484)),f341(f186(f858(x91484)),x91483))) % 19.23/19.04 [9258]E(f341(f341(f164(x92581),f743(x92582,x92583,x92584,x92581)),x92583),f341(f341(f164(x92581),f743(x92582,x92583,x92584,x92581)),x92584))+~P85(f341(f341(f343(f863(f858(x92581),f858(x92581))),f341(f341(f250(f858(x92581),f858(x92581)),x92584),x92583)),f143(x92581,x92582)))+P85(f341(f341(f242(a857),f341(f186(f858(x92581)),x92584)),f341(f186(f858(x92581)),x92583))) % 19.23/19.04 [9317]~P85(f341(f341(f242(a857),f2(a857)),x93173))+~P85(f341(f341(f242(a857),x93174),x93171))+P85(f341(f341(f242(a857),f341(f341(f89(a857),f341(f341(f90(a857),x93171),f60(a857,x93172,x93173))),x93174)),f341(f341(f90(a857),x93171),x93173))) % 19.23/19.04 [9500]~P103(x95002)+~P85(f341(f341(f241(x95002),f341(x95003,f781(x95004,x95003,x95001,x95002))),f341(x95004,f781(x95004,x95003,x95001,x95002))))+P85(f341(f341(f241(f864(x95001,x95002)),x95003),x95004)) % 19.23/19.04 [9598]~P3(x95981)+E(f341(f341(f8(a857,x95981),f341(f341(f20(a857,x95981,x95981),f341(f341(f10(x95981,f864(x95981,x95981),a857),f3(x95981)),x95982)),f341(f341(f10(a857,x95981,a857),x95982),f341(f341(f9(a857,a857,a857),f89(a857)),f87(a857))))),f304(a857,x95983,x95984)),f341(f341(f3(x95981),f341(x95982,x95983)),f341(x95982,f341(f341(f89(a857),x95984),f87(a857)))))+~P85(f341(f341(f241(a857),x95983),x95984)) % 19.23/19.04 [6641]~P4(x66411)+E(f341(f341(f51(x66411),f341(f341(f90(x66411),x66412),x66413)),x66414),f341(f341(f90(x66411),x66412),f341(f341(f51(x66411),x66413),x66414)))+~P85(f341(f341(f288(x66411),x66414),x66413)) % 19.23/19.04 [6730]E(f341(f341(f132(x67301),x67302),x67303),x67304)+~E(x67303,f341(f341(f135(x67301),f341(f186(f858(x67301)),x67302)),x67304))+~E(f341(f341(f164(x67301),f341(f186(f858(x67301)),x67302)),x67304),x67302) % 19.23/19.04 [6790]~P60(x67902)+E(x67901,f2(x67902))+E(f341(f341(f292(x67902),f341(f341(f251(x67902),x67903),x67904)),f341(f341(f251(x67902),x67901),x67904)),f341(f341(f251(x67902),f341(f341(f292(x67902),x67903),x67901)),x67904)) % 19.23/19.04 [6939]~P4(x69391)+E(f341(f341(f51(x69391),f341(f341(f90(x69391),x69392),x69393)),x69394),f341(f341(f90(x69391),f341(f341(f51(x69391),x69392),x69394)),x69393))+~P85(f341(f341(f288(x69391),x69394),x69392)) % 19.23/19.04 [6949]~P101(x69491)+~P85(f341(f341(f242(x69491),x69493),x69494))+P85(f341(f341(f242(x69491),f341(f341(f245(x69491),x69492),x69493)),x69494)) % 19.23/19.04 [6951]~P101(x69511)+~P85(f341(f341(f242(x69511),x69512),x69514))+P85(f341(f341(f242(x69511),f341(f341(f245(x69511),x69512),x69513)),x69514)) % 19.23/19.04 [6952]~P99(x69521)+~P85(f341(f341(f242(x69521),x69523),x69524))+P85(f341(f341(f242(x69521),f341(f341(f111(x69521),x69522),x69523)),x69524)) % 19.23/19.04 [6953]~P99(x69531)+~P85(f341(f341(f242(x69531),x69532),x69534))+P85(f341(f341(f242(x69531),f341(f341(f111(x69531),x69532),x69533)),x69534)) % 19.23/19.04 [6955]~P101(x69551)+~P85(f341(f341(f241(x69551),x69553),x69554))+P85(f341(f341(f241(x69551),f341(f341(f245(x69551),x69552),x69553)),x69554)) % 19.23/19.04 [6957]~P101(x69571)+~P85(f341(f341(f241(x69571),x69572),x69574))+P85(f341(f341(f241(x69571),f341(f341(f245(x69571),x69572),x69573)),x69574)) % 19.23/19.04 [6958]~P99(x69581)+~P85(f341(f341(f241(x69581),x69583),x69584))+P85(f341(f341(f241(x69581),f341(f341(f111(x69581),x69582),x69583)),x69584)) % 19.23/19.04 [6959]~P99(x69591)+~P85(f341(f341(f241(x69591),x69592),x69594))+P85(f341(f341(f241(x69591),f341(f341(f111(x69591),x69592),x69593)),x69594)) % 19.23/19.04 [6976]~P85(f341(x69763,x69764))+~P85(f341(x69762,x69764))+P85(f341(f341(f341(f111(f864(x69761,a850)),x69762),x69763),x69764)) % 19.23/19.04 [7008]~E(f341(f186(f858(x70081)),x70083),f341(f186(f858(x70082)),x70084))+~P85(f341(f134(x70081),x70083))+E(f174(x70081,x70082,f171(x70081,x70082,f341(f341(f172(x70081,x70082),x70083),x70084))),f341(f163(x70081),x70083)) % 19.23/19.04 [7102]P25(x71021,x71022,x71023)+~P25(x71021,x71022,x71024)+~P85(f341(f341(f241(f864(f856(x71021),a850)),x71023),x71024)) % 19.23/19.04 [7240]~P4(x72401)+E(f341(f341(f51(x72401),f341(f341(f251(x72401),x72402),x72403)),f341(f341(f251(x72401),x72404),x72403)),f341(f341(f251(x72401),f341(f341(f51(x72401),x72402),x72404)),x72403))+~P85(f341(f341(f288(x72401),x72404),x72402)) % 19.23/19.04 [7494]~P68(x74941)+E(f341(f341(f89(x74941),f341(x74942,x74943)),f341(f341(f8(a857,x74941),x74942),f341(f303(a857,f341(a121,x74943)),x74944))),f341(f341(f8(a857,x74941),x74942),f341(f303(a857,x74943),x74944)))+~P85(f341(f341(f242(a857),x74943),x74944)) % 19.23/19.04 [7522]~P101(x75221)+P85(f341(f341(f242(x75221),x75222),x75223))+~P85(f341(f341(f242(x75221),f341(f341(f240(x75221),x75224),x75222)),x75223)) % 19.23/19.04 [7523]~P101(x75231)+P85(f341(f341(f242(x75231),x75232),x75233))+~P85(f341(f341(f242(x75231),f341(f341(f240(x75231),x75232),x75234)),x75233)) % 19.23/19.04 [7525]~P101(x75251)+P85(f341(f341(f241(x75251),x75252),x75253))+~P85(f341(f341(f241(x75251),f341(f341(f240(x75251),x75254),x75252)),x75253)) % 19.23/19.04 [7527]~P101(x75271)+P85(f341(f341(f241(x75271),x75272),x75273))+~P85(f341(f341(f241(x75271),f341(f341(f240(x75271),x75272),x75274)),x75273)) % 19.23/19.04 [7529]~P98(x75291)+P85(f341(f341(f241(x75291),x75292),x75293))+~P85(f341(f341(f241(x75291),f341(f341(f110(x75291),x75294),x75292)),x75293)) % 19.23/19.04 [7531]~P98(x75311)+P85(f341(f341(f241(x75311),x75312),x75313))+~P85(f341(f341(f241(x75311),f341(f341(f110(x75311),x75312),x75314)),x75313)) % 19.23/19.04 [7532]~P86(x75321)+P85(f341(f341(f288(x75321),x75322),x75323))+~P85(f341(f341(f288(x75321),f341(f341(f90(x75321),x75324),x75322)),x75323)) % 19.23/19.04 [7533]~P86(x75331)+P85(f341(f341(f288(x75331),x75332),x75333))+~P85(f341(f341(f288(x75331),f341(f341(f90(x75331),x75332),x75334)),x75333)) % 19.23/19.04 [7611]~P85(f341(f341(f343(x76111),x76112),x76114))+P85(f341(f341(f343(x76111),x76112),x76113))+P85(f341(f341(f343(x76111),x76112),f341(f341(f3(f864(x76111,a850)),x76114),x76113))) % 19.23/19.04 [7691]P85(f341(x76911,x76912))+P85(f341(x76913,x76912))+~P85(f341(f341(f341(f110(f864(x76914,a850)),x76913),x76911),x76912)) % 19.23/19.04 [7701]~P85(f341(f341(f343(x77011),x77012),x77014))+~P85(f341(f341(f343(x77011),x77012),x77013))+P85(f341(f341(f343(x77011),x77012),f341(f341(f111(f864(x77011,a850)),x77013),x77014))) % 19.23/19.04 [7757]~P101(x77571)+~P85(f341(f71(x77571),x77574))+E(f341(f341(f74(x77571,x77571,f245(x77571)),x77572),f341(f341(f311(x77571),x77573),x77574)),f341(f341(f245(x77571),x77573),f341(f341(f74(x77571,x77571,f245(x77571)),x77572),x77574))) % 19.23/19.04 [7758]~P101(x77581)+~P85(f341(f71(x77581),x77584))+E(f341(f341(f74(x77581,x77581,f240(x77581)),x77582),f341(f341(f311(x77581),x77583),x77584)),f341(f341(f240(x77581),x77583),f341(f341(f74(x77581,x77581,f240(x77581)),x77582),x77584))) % 19.23/19.04 [7759]~P98(x77591)+~P85(f341(f71(x77591),x77594))+E(f341(f341(f74(x77591,x77591,f110(x77591)),x77592),f341(f341(f311(x77591),x77593),x77594)),f341(f341(f110(x77591),x77593),f341(f341(f74(x77591,x77591,f110(x77591)),x77592),x77594))) % 19.23/19.04 [7760]~P99(x77601)+~P85(f341(f71(x77601),x77604))+E(f341(f341(f74(x77601,x77601,f111(x77601)),x77602),f341(f341(f311(x77601),x77603),x77604)),f341(f341(f111(x77601),x77603),f341(f341(f74(x77601,x77601,f111(x77601)),x77602),x77604))) % 19.23/19.04 [7762]~P138(x77621)+~P90(x77621)+E(f341(f341(f89(x77621),f341(f341(f90(x77621),f341(f113(x77621),x77622)),x77623)),f341(f341(f90(x77621),f341(f113(x77621),x77622)),x77624)),f341(f341(f90(x77621),f341(f113(x77621),x77622)),f341(f341(f89(x77621),x77623),x77624))) % 19.23/19.04 [7763]~P123(x77631)+~P90(x77631)+E(f341(f341(f3(x77631),f341(f341(f90(x77631),f341(f113(x77631),x77632)),x77633)),f341(f341(f90(x77631),f341(f113(x77631),x77632)),x77634)),f341(f341(f90(x77631),f341(f113(x77631),x77632)),f341(f341(f3(x77631),x77633),x77634))) % 19.23/19.04 [7876]E(x78761,x78762)+P85(f341(f341(f343(x78763),x78761),f341(f163(x78763),x78764)))+~P85(f341(f341(f343(x78763),x78761),f341(f163(x78763),f341(f341(f146(x78763),x78762),x78764)))) % 19.23/19.04 [8046]P52(x80461,x80462,x80463)+~P52(x80461,x80462,x80464)+~P85(f341(f341(f241(f864(f863(x80461,x80462),a850)),x80463),x80464)) % 19.23/19.04 [8089]P85(f341(f341(f343(x80891),x80892),x80893))+P85(f341(f341(f343(x80891),x80892),x80894))+~P85(f341(f341(f343(x80891),x80892),f341(f341(f110(f864(x80891,a850)),x80894),x80893))) % 19.23/19.04 [8100]~P46(x81001,x81004,x81003)+~P85(f341(f341(f343(x81001),x81002),x81004))+P85(f341(f341(f343(f863(x81001,x81001)),f341(f341(f250(x81001,x81001),x81002),x81002)),x81003)) % 19.23/19.04 [8112]~P85(f341(f71(x81122),x81124))+~P85(f341(f71(x81121),x81123))+P85(f341(f71(f863(x81121,x81122)),f341(f341(f257(x81121,x81122),x81123),f341(f18(f864(x81122,a850),x81121),x81124)))) % 19.23/19.04 [8113]~P85(f341(f341(f343(x81131),x81132),x81134))+~P85(f341(f341(f241(f864(x81131,a850)),x81133),x81134))+P85(f341(f341(f241(f864(x81131,a850)),f341(f341(f311(x81131),x81132),x81133)),x81134)) % 19.23/19.04 [8121]~P112(x81212)+~P71(x81212)+E(f341(f341(f11(x81211,x81212),f341(f341(f10(a857,x81212,x81211),f109(x81212)),x81213)),x81214),f341(f109(x81212),f341(f341(f11(x81211,a857),x81213),x81214))) % 19.23/19.04 [8122]~P136(x81222)+~P71(x81222)+E(f341(f341(f11(x81221,x81222),f341(f341(f10(a1,x81222,x81221),f112(x81222)),x81223)),x81224),f341(f112(x81222),f341(f341(f11(x81221,a1),x81223),x81224))) % 19.23/19.04 [8146]E(f341(f341(f3(f864(x81461,a850)),x81462),f341(f341(f3(f864(x81461,a850)),x81463),x81464)),x81464)+~P85(f341(f341(f241(f864(x81461,a850)),x81462),x81463))+~P85(f341(f341(f241(f864(x81461,a850)),x81464),x81462)) % 19.23/19.04 [8238]~P85(f341(f71(x82381),x82384))+E(f341(f341(f3(a857),f341(f341(f8(x82381,a857),x82382),x82383)),f341(f341(f8(x82381,a857),x82382),x82384)),f341(f341(f8(x82381,a857),x82382),f341(f341(f3(f864(x82381,a850)),x82383),x82384)))+~P85(f341(f341(f241(f864(x82381,a850)),x82384),x82383)) % 19.23/19.04 [8396]~P9(x83961,x83964,x83963)+~P85(f341(f341(f343(x83961),x83962),x83964))+P85(f341(f341(f343(x83961),x83962),f341(f286(x83961,x83961,x83963),f341(f341(f311(x83961),x83962),f185(f864(x83961,a850)))))) % 19.23/19.04 [8458]~P85(f341(f341(f241(f864(x84581,a850)),x84582),x84583))+~P85(f341(f341(f241(f864(x84581,a850)),x84582),x84584))+P85(f341(f341(f241(f864(x84581,a850)),x84582),f341(f341(f111(f864(x84581,a850)),x84583),x84584))) % 19.23/19.04 [8549]E(x85491,f185(f864(x85492,a850)))+P85(f341(f71(x85493),x85494))+~P85(f341(f71(f863(x85493,x85492)),f341(f341(f257(x85493,x85492),x85494),f341(f18(f864(x85492,a850),x85493),x85491)))) % 19.23/19.04 [8550]E(x85501,f185(f864(x85502,a850)))+P85(f341(f71(x85503),x85504))+~P85(f341(f71(f863(x85502,x85503)),f341(f341(f257(x85502,x85503),x85501),f341(f18(f864(x85503,a850),x85502),x85504)))) % 19.23/19.04 [8609]P85(f341(f341(f343(x86091),x86092),f331(x86091,x86093)))+~P85(f341(f341(f343(x86091),x86094),f331(x86091,x86093)))+~P85(f341(f341(f343(f863(x86091,x86091)),f341(f341(f250(x86091,x86091),x86092),x86094)),x86093)) % 19.23/19.04 [8661]~P35(x86611,x86614)+P85(f341(f341(f343(f863(x86611,x86611)),f341(f341(f250(x86611,x86611),x86613),x86612)),f309(x86611,x86614)))+P35(x86611,f341(f341(f311(f863(x86611,x86611)),f341(f341(f250(x86611,x86611),x86612),x86613)),x86614)) % 19.23/19.04 [8662]~P55(x86621,x86624)+P85(f341(f341(f343(f863(x86621,x86621)),f341(f341(f250(x86621,x86621),x86623),x86622)),f309(x86621,x86624)))+P55(x86621,f341(f341(f311(f863(x86621,x86621)),f341(f341(f250(x86621,x86621),x86622),x86623)),x86624)) % 19.23/19.04 [8733]~E(x87332,x87333)+~P85(f341(f341(f343(x87331),x87332),f341(f163(x87331),x87334)))+P85(f341(f341(f343(f863(x87331,x87331)),f341(f341(f250(x87331,x87331),x87332),x87333)),f341(f163(f863(x87331,x87331)),f341(f341(f172(x87331,x87331),x87334),x87334)))) % 19.23/19.04 [8805]~E(x88053,x88054)+P85(f341(f341(f260(x88051,x88051,a850),a338),x88052))+~P85(f341(f341(f343(f863(x88051,x88051)),x88052),f341(f163(f863(x88051,x88051)),f341(f341(f172(x88051,x88051),x88053),x88054)))) % 19.23/19.04 [8843]P85(f341(f341(f343(f863(f858(x88431),f858(x88431))),f341(f341(f250(f858(x88431),f858(x88431)),x88432),x88433)),f143(x88431,x88434)))+~E(f341(f341(f164(x88431),f341(f186(f858(x88431)),x88432)),x88433),x88432)+~P85(f341(f341(f242(a857),f341(f186(f858(x88431)),x88432)),f341(f186(f858(x88431)),x88433))) % 19.23/19.04 [8937]~P85(f341(f71(x89371),x89374))+P85(f341(f341(f343(x89371),f414(x89372,x89373,x89374,x89371)),x89374))+P85(f341(f71(x89373),f341(f341(f54(x89371,f864(x89373,a850)),x89374),x89372))) % 19.23/19.04 [8938]~P85(f341(f71(x89381),x89384))+P85(f341(f341(f343(x89381),f611(x89382,x89383,x89384,x89381)),x89384))+P85(f341(f71(x89383),f341(f341(f54(x89381,f864(x89383,a850)),x89384),x89382))) % 19.23/19.04 [9018]P85(f341(f341(f343(f863(x90181,x90181)),x90182),f341(f341(f290(x90181,x90181,x90181),x90183),f309(x90181,x90183))))+~P85(f341(f341(f242(a857),f2(a857)),x90184))+~P85(f341(f341(f343(f863(x90181,x90181)),x90182),f341(f341(f179(f863(x90181,x90181),a850),x90184),x90183))) % 19.23/19.04 [9026]~P35(x90261,x90262)+~P85(f341(f341(f343(f863(x90261,x90261)),f341(f341(f250(x90261,x90261),x90264),x90263)),x90262))+~P85(f341(f341(f343(f863(x90261,x90261)),f341(f341(f250(x90261,x90261),x90263),x90264)),x90262)) % 19.23/19.04 [9144]~P85(f341(f71(x91441),x91444))+E(f341(f341(f8(x91441,a857),f341(f341(f10(f864(x91442,a850),a857,x91441),f50(x91442)),x91443)),x91444),f341(f50(f863(x91441,x91442)),f341(f341(f257(x91441,x91442),x91444),x91443)))+P85(f341(f341(f343(x91441),f557(x91443,x91442,x91444,x91441)),x91444)) % 19.23/19.04 [9146]~P85(f341(f134(x91461),x91462))+P85(f341(f134(x91461),f341(f341(f154(x91461,x91462),x91463),x91464)))+P85(f341(f341(f343(x91461),x91464),f341(f341(f3(f864(x91461,a850)),f341(f163(x91461),x91462)),f341(f341(f311(x91461),f341(f341(f158(x91461),x91462),x91463)),f185(f864(x91461,a850)))))) % 19.23/19.04 [9155]~P85(f341(f71(x91552),x91553))+~P85(f341(f71(x91551),f341(x91554,f414(x91554,x91551,x91553,x91552))))+P85(f341(f71(x91551),f341(f341(f54(x91552,f864(x91551,a850)),x91553),x91554))) % 19.23/19.04 [9156]~P85(f341(f71(x91562),x91563))+~P85(f341(f71(x91561),f341(x91564,f611(x91564,x91561,x91563,x91562))))+P85(f341(f71(x91561),f341(f341(f54(x91562,f864(x91561,a850)),x91563),x91564))) % 19.23/19.04 [9219]~P85(f341(f341(f343(f863(x92191,x92191)),x92192),f341(f341(f290(x92191,x92191,x92191),x92194),f309(x92191,x92194))))+P85(f341(f341(f343(f863(x92191,x92191)),x92192),f341(f341(f290(x92191,x92191,x92191),x92193),f309(x92191,x92193))))+~P85(f341(f341(f241(f864(f863(x92191,x92191),a850)),x92194),x92193)) % 19.23/19.04 [9227]E(f341(f341(f164(x92271),f743(x92274,x92273,x92272,x92271)),x92273),f341(f341(f164(x92271),f743(x92274,x92273,x92272,x92271)),x92272))+~P85(f341(f341(f343(f863(f858(x92271),f858(x92271))),f341(f341(f250(f858(x92271),f858(x92271)),x92272),x92273)),f143(x92271,x92274)))+E(f341(f341(f164(x92271),f341(f186(f858(x92271)),x92272)),x92273),x92272) % 19.23/19.04 [9243]~P85(f341(f71(x92431),x92434))+E(f341(f341(f8(x92431,a857),f341(f341(f10(f864(x92432,a850),a857,x92431),f50(x92432)),x92433)),x92434),f341(f50(f863(x92431,x92432)),f341(f341(f257(x92431,x92432),x92434),x92433)))+~P85(f341(f71(x92432),f341(x92433,f557(x92433,x92432,x92434,x92431)))) % 19.23/19.04 [9247]~E(f341(f186(f858(x92471)),x92473),f341(f186(f858(x92471)),x92472))+P85(f341(f341(f343(f863(f858(x92471),f858(x92471))),f341(f341(f250(f858(x92471),f858(x92471)),x92472),x92473)),f153(x92471,x92474)))+P85(f341(f341(f343(f863(x92471,x92471)),f726(x92474,x92473,x92472,x92471)),f341(f163(f863(x92471,x92471)),f341(f341(f172(x92471,x92471),x92472),x92473)))) % 19.23/19.04 [9329]~P85(f341(f341(f343(f863(f858(x93291),f858(x93291))),f341(f341(f250(f858(x93291),f858(x93291)),x93292),x93293)),f143(x93291,x93294)))+E(f341(f341(f164(x93291),f341(f186(f858(x93291)),x93292)),x93293),x93292)+P85(f341(f341(f242(a857),f743(x93294,x93293,x93292,x93291)),f341(f341(f245(a857),f341(f186(f858(x93291)),x93292)),f341(f186(f858(x93291)),x93293)))) % 19.23/19.04 [9349]~P85(f341(f341(f343(f863(f858(x93491),f858(x93491))),f341(f341(f250(f858(x93491),f858(x93491)),x93492),x93493)),f143(x93491,x93494)))+P85(f341(f341(f242(a857),f341(f186(f858(x93491)),x93492)),f341(f186(f858(x93491)),x93493)))+P85(f341(f341(f242(a857),f743(x93494,x93493,x93492,x93491)),f341(f341(f245(a857),f341(f186(f858(x93491)),x93492)),f341(f186(f858(x93491)),x93493)))) % 19.23/19.04 [9635]~P85(f341(f341(f341(x96351,f716(x96351,x96354,x96353,x96352)),f719(x96351,x96354,x96353,x96352)),f720(x96351,x96354,x96353,x96352)))+P85(f341(f341(f341(x96351,x96352),x96353),x96354))+~P85(f341(f330(f863(f864(a1,f861(f858(a849))),f863(a1,a1)),a320),f341(f341(f250(f864(a1,f861(f858(a849))),f863(a1,a1)),x96352),f341(f341(f250(a1,a1),x96353),x96354)))) % 19.23/19.04 [9694]P85(f341(f341(f341(x96941,x96942),x96943),x96944))+P85(f341(f330(f863(f864(a1,f861(f858(a849))),f863(a1,a1)),a320),f341(f341(f250(f864(a1,f861(f858(a849))),f863(a1,a1)),f716(x96941,x96944,x96943,x96942)),f341(f341(f250(a1,a1),f719(x96941,x96944,x96943,x96942)),f720(x96941,x96944,x96943,x96942)))))+~P85(f341(f330(f863(f864(a1,f861(f858(a849))),f863(a1,a1)),a320),f341(f341(f250(f864(a1,f861(f858(a849))),f863(a1,a1)),x96942),f341(f341(f250(a1,a1),x96943),x96944)))) % 19.23/19.04 [9732]~P85(f341(f341(f343(f863(f858(x97321),f858(x97321))),f341(f341(f250(f858(x97321),f858(x97321)),x97322),x97323)),f143(x97321,x97324)))+E(f341(f341(f164(x97321),f341(f186(f858(x97321)),x97322)),x97323),x97322)+P85(f341(f341(f343(f863(x97321,x97321)),f341(f341(f250(x97321,x97321),f341(f341(f158(x97321),x97322),f743(x97324,x97323,x97322,x97321))),f341(f341(f158(x97321),x97323),f743(x97324,x97323,x97322,x97321)))),x97324)) % 19.23/19.04 [9735]~P85(f341(f341(f343(f863(f858(x97351),f858(x97351))),f341(f341(f250(f858(x97351),f858(x97351)),x97352),x97353)),f143(x97351,x97354)))+P85(f341(f341(f242(a857),f341(f186(f858(x97351)),x97352)),f341(f186(f858(x97351)),x97353)))+P85(f341(f341(f343(f863(x97351,x97351)),f341(f341(f250(x97351,x97351),f341(f341(f158(x97351),x97352),f743(x97354,x97353,x97352,x97351))),f341(f341(f158(x97351),x97353),f743(x97354,x97353,x97352,x97351)))),x97354)) % 19.23/19.04 [9805]~E(f341(f186(f858(x98051)),x98052),f341(f186(f858(x98051)),x98053))+P85(f341(f341(f343(f863(f858(x98051),f858(x98051))),f341(f341(f250(f858(x98051),f858(x98051)),x98052),x98053)),f153(x98051,x98054)))+~P85(f341(f341(f343(f863(x98051,x98051)),f341(f341(f250(x98051,x98051),f341(f341(f158(x98051),x98052),f742(x98054,x98053,x98052,x98051))),f341(f341(f158(x98051),x98053),f742(x98054,x98053,x98052,x98051)))),x98054)) % 19.23/19.04 [9945]~P68(x99451)+~P85(f341(f71(x99452),x99454))+E(f341(f160(x99451),f341(f341(f149(x99452,x99451),x99453),f99(f858(x99452),f341(f341(f20(f858(x99452),a850,a850),f341(f341(f10(a850,f864(a850,a850),f858(x99452)),a339),f341(f341(f9(f858(x99452),f864(x99452,a850),a850),f341(f341(f10(f864(x99452,a850),f864(f864(x99452,a850),a850),f858(x99452)),a338),f163(x99452))),x99454))),f134(x99452))))),f233(x99452,x99451,x99453,x99454)) % 19.23/19.04 [7331]~P59(x73312)+E(x73311,f2(x73312))+E(f341(f341(f292(x73312),f341(f341(f89(x73312),x73313),f341(f341(f90(x73312),x73314),x73311))),x73311),f341(f341(f89(x73312),x73314),f341(f341(f292(x73312),x73313),x73311))) % 19.23/19.04 [7332]~P4(x73322)+E(x73321,f2(x73322))+E(f341(f341(f51(x73322),f341(f341(f89(x73322),x73323),f341(f341(f90(x73322),x73324),x73321))),x73321),f341(f341(f89(x73322),x73324),f341(f341(f51(x73322),x73323),x73321))) % 19.23/19.04 [7333]~P4(x73332)+E(x73331,f2(x73332))+E(f341(f341(f51(x73332),f341(f341(f89(x73332),x73333),f341(f341(f90(x73332),x73331),x73334))),x73331),f341(f341(f89(x73332),x73334),f341(f341(f51(x73332),x73333),x73331))) % 19.23/19.04 [7573]~P59(x75732)+E(x75731,f2(x75732))+E(f341(f341(f292(x75732),f341(f341(f89(x75732),x75733),f341(f341(f90(x75732),x75734),x75731))),x75731),f341(f341(f89(x75732),f341(f341(f292(x75732),x75733),x75731)),x75734)) % 19.23/19.04 [7574]~P60(x75742)+E(x75741,f2(x75742))+E(f341(f341(f292(x75742),f341(f341(f89(x75742),x75743),f341(f341(f90(x75742),x75741),x75744))),x75741),f341(f341(f89(x75742),f341(f341(f292(x75742),x75743),x75741)),x75744)) % 19.23/19.04 [7575]~P60(x75752)+E(x75751,f2(x75752))+E(f341(f341(f292(x75752),f341(f341(f3(x75752),x75753),f341(f341(f90(x75752),x75751),x75754))),x75751),f341(f341(f3(x75752),f341(f341(f292(x75752),x75753),x75751)),x75754)) % 19.23/19.04 [8623]~E(f341(f341(f290(x86231,x86231,x86231),x86232),x86234),f185(f864(f863(x86231,x86231),a850)))+~E(f341(f341(f290(x86231,x86231,x86231),x86232),x86233),f185(f864(f863(x86231,x86231),a850)))+E(f341(f341(f290(x86231,x86231,x86231),x86232),f341(f341(f110(f864(f863(x86231,x86231),a850)),x86233),x86234)),f185(f864(f863(x86231,x86231),a850))) % 19.23/19.04 [8734]~P85(f341(f341(f241(f864(x87341,a850)),x87343),x87344))+~P85(f341(f341(f241(f864(x87341,a850)),x87342),x87344))+P85(f341(f341(f241(f864(x87341,a850)),f341(f341(f110(f864(x87341,a850)),x87342),x87343)),x87344)) % 19.23/19.04 [9078]~P85(f341(f71(x90781),x90784))+~P85(f341(f71(x90781),x90783))+E(f341(f341(f3(a857),f341(f341(f89(a857),f341(f341(f8(x90781,a857),x90782),x90783)),f341(f341(f8(x90781,a857),x90782),x90784))),f341(f341(f8(x90781,a857),x90782),f341(f341(f111(f864(x90781,a850)),x90783),x90784))),f341(f341(f8(x90781,a857),x90782),f341(f341(f110(f864(x90781,a850)),x90783),x90784))) % 19.23/19.04 [9153]~P85(f341(f341(f343(x91531),x91533),x91532))+~P85(f341(f341(f241(f864(x91531,a850)),x91532),f341(f341(f311(x91531),x91533),x91534)))+P85(f341(f341(f241(f864(x91531,a850)),f341(f341(f3(f864(x91531,a850)),x91532),f341(f341(f311(x91531),x91533),f185(f864(x91531,a850))))),x91534)) % 19.23/19.04 [9303]~P85(f341(f341(f343(x93031),x93033),x93032))+P85(f341(f341(f241(f864(x93031,a850)),x93032),f341(f341(f311(x93031),x93033),x93034)))+~P85(f341(f341(f241(f864(x93031,a850)),f341(f341(f3(f864(x93031,a850)),x93032),f341(f341(f311(x93031),x93033),f185(f864(x93031,a850))))),x93034)) % 19.23/19.04 [9386]~P85(f341(f341(f242(a857),x93862),x93864))+~P85(f341(f341(f241(a857),x93861),x93863))+P85(f341(f341(f343(f863(f863(a857,a857),f863(a857,a857))),f341(f341(f250(f863(a857,a857),f863(a857,a857)),f341(f341(f250(a857,a857),x93861),x93862)),f341(f341(f250(a857,a857),x93863),x93864))),a47)) % 19.23/19.04 [9387]~P85(f341(f341(f241(a857),x93872),x93874))+~P85(f341(f341(f241(a857),x93871),x93873))+P85(f341(f341(f343(f863(f863(a857,a857),f863(a857,a857))),f341(f341(f250(f863(a857,a857),f863(a857,a857)),f341(f341(f250(a857,a857),x93871),x93872)),f341(f341(f250(a857,a857),x93873),x93874))),a79)) % 19.23/19.04 [9770]~P26(x97701,f864(f864(x97701,a850),a850),f341(f341(f9(x97701,f864(f863(x97701,x97701),a850),f864(f864(x97701,a850),a850)),f341(f341(f10(f864(x97701,a850),f864(f864(f863(x97701,x97701),a850),f864(f864(x97701,a850),a850)),x97701),f69(x97701)),f341(f341(f9(x97701,f864(x97701,a850),f864(x97701,a850)),f311(x97701)),f185(f864(x97701,a850))))),x97703),x97702)+~P85(f341(f341(f343(x97701),x97704),x97702))+E(f341(f341(f3(f864(f864(x97701,a850),a850)),f341(f341(f69(x97701),x97702),x97703)),f341(f341(f69(x97701),f341(f341(f311(x97701),x97704),f185(f864(x97701,a850)))),x97703)),f341(f341(f69(x97701),f341(f341(f3(f864(x97701,a850)),x97702),f341(f341(f311(x97701),x97704),f185(f864(x97701,a850))))),x97703)) % 19.23/19.04 [9911]~P46(x99111,x99112,x99114)+~P85(f341(f341(f343(f863(x99111,x99111)),x99113),x99114))+P85(f341(f341(f260(x99111,x99111,a850),f341(f341(f9(x99111,f864(x99111,a850),f864(x99111,a850)),f341(f341(f10(f864(a850,a850),f864(f864(x99111,a850),f864(x99111,a850)),x99111),f10(a850,a850,x99111)),f341(f341(f10(a850,f864(a850,a850),x99111),a339),f341(f341(f9(x99111,f864(x99111,a850),a850),f343(x99111)),x99112)))),f341(f341(f9(x99111,f864(x99111,a850),a850),f343(x99111)),x99112))),x99113)) % 19.23/19.04 [9919]P85(f341(f71(x99191),x99192))+~P85(f341(f71(x99193),f341(f312(x99191,x99193,x99194),x99192)))+~P85(f341(f71(x99191),f341(f265(x99191),f341(f341(f20(x99191,a850,a850),f341(f341(f10(a850,f864(a850,a850),x99191),a339),f341(f341(f9(x99191,f864(x99191,a850),a850),f343(x99191)),x99192))),f341(f341(f9(x99191,x99193,a850),f341(f341(f10(x99193,f864(x99193,a850),x99191),a338),x99194)),f341(x99194,f602(x99194,x99193,x99192,x99191))))))) % 19.23/19.04 [8029]~P60(x80292)+E(x80291,f2(x80292))+E(f341(f341(f292(x80292),f341(f341(f89(x80292),f341(f341(f90(x80292),x80291),x80293)),x80294)),x80291),f341(f341(f89(x80292),x80293),f341(f341(f292(x80292),x80294),x80291))) % 19.23/19.04 [8030]~P60(x80302)+E(x80301,f2(x80302))+E(f341(f341(f292(x80302),f341(f341(f3(x80302),f341(f341(f90(x80302),x80301),x80303)),x80304)),x80301),f341(f341(f3(x80302),x80303),f341(f341(f292(x80302),x80304),x80301))) % 19.23/19.04 [8870]~E(f341(f341(f290(x88701,x88701,x88701),x88703),x88704),f185(f864(f863(x88701,x88701),a850)))+~E(f341(f341(f290(x88701,x88701,x88701),x88702),x88704),f185(f864(f863(x88701,x88701),a850)))+E(f341(f341(f290(x88701,x88701,x88701),f341(f341(f110(f864(f863(x88701,x88701),a850)),x88702),x88703)),x88704),f185(f864(f863(x88701,x88701),a850))) % 19.23/19.04 [9857]~P141(x98571)+~P141(x98572)+E(f341(f341(f319(x98571),f341(f341(f9(x98571,a108,f861(f858(a849))),f341(f341(f10(f864(x98572,f861(f858(a849))),f864(a108,f861(f858(a849))),x98571),f319(x98572)),f341(f341(f10(f864(x98572,f863(x98571,x98572)),f864(x98572,f861(f858(a849))),x98571),f341(f10(f863(x98571,x98572),f861(f858(a849)),x98572),x98573)),f250(x98571,x98572)))),x98574)),x98574),f341(f341(f319(f863(x98571,x98572)),x98573),x98574)) % 19.23/19.04 [9849]P85(f341(x98491,f583(x98492,x98493,x98491,x98494)))+~P85(f341(f71(x98494),f341(f265(x98494),x98491)))+P85(f341(f71(x98493),f341(f265(x98493),f341(f341(f10(f864(x98494,a850),a850,x98493),f96(x98494)),f341(f341(f10(f864(x98494,a850),f864(x98494,a850),x98493),f341(f20(x98494,a850,a850),f341(f341(f10(a850,f864(a850,a850),x98494),a339),x98491))),x98492))))) % 19.23/19.04 [9870]~P85(f341(f71(x98702),f341(f265(x98702),x98703)))+~P85(f341(f71(x98701),f341(f265(x98701),f341(f341(f9(x98701,x98702,a850),x98704),f583(x98704,x98701,x98703,x98702)))))+P85(f341(f71(x98701),f341(f265(x98701),f341(f341(f10(f864(x98702,a850),a850,x98701),f96(x98702)),f341(f341(f10(f864(x98702,a850),f864(x98702,a850),x98701),f341(f20(x98702,a850,a850),f341(f341(f10(a850,f864(a850,a850),x98702),a339),x98703))),x98704))))) % 19.23/19.04 [5722]~E(x57225,x57222)+P38(f37(x57221,x57223),x57222,x57224,x57225)+P85(f341(x57221,x57222)) % 19.23/19.04 [6288]E(x62881,x62882)+~P38(f37(x62883,x62884),x62881,x62885,x62882)+P85(f341(x62883,x62881)) % 19.23/19.04 [7836]~P38(x78362,x78363,x78364,x78365)+~P38(f37(x78361,x78362),x78365,x78364,x78363)+P38(f37(x78361,x78362),x78363,x78364,x78363) % 19.23/19.04 [8991]E(x89911,x89912)+~P38(f37(x89915,x89913),x89911,x89914,x89912)+P38(x89913,x89911,x89914,f442(x89912,x89914,x89911,x89913,x89915)) % 19.23/19.04 [8992]E(x89921,x89922)+~P38(f37(x89925,x89923),x89921,x89924,x89922)+P38(x89923,x89921,x89924,f603(x89922,x89924,x89921,x89923,x89925)) % 19.23/19.04 [8994]E(x89941,x89942)+P38(f37(x89943,x89944),f442(x89941,x89945,x89942,x89944,x89943),x89945,x89941)+~P38(f37(x89943,x89944),x89942,x89945,x89941) % 19.23/19.04 [8995]E(x89951,x89952)+P38(f37(x89953,x89954),f603(x89951,x89955,x89952,x89954,x89953),x89955,x89951)+~P38(f37(x89953,x89954),x89952,x89955,x89951) % 19.23/19.04 [8997]~P38(f37(x89975,x89971),x89972,x89973,x89974)+P38(x89971,x89972,x89973,f442(x89974,x89973,x89972,x89971,x89975))+~P85(f341(x89975,x89972)) % 19.23/19.04 [8998]~P38(f37(x89985,x89981),x89982,x89983,x89984)+P38(x89981,x89982,x89983,f603(x89984,x89983,x89982,x89981,x89985))+~P85(f341(x89985,x89982)) % 19.23/19.04 [9002]~P38(f37(x90021,x90022),x90025,x90024,x90023)+P38(f37(x90021,x90022),f442(x90023,x90024,x90025,x90022,x90021),x90024,x90023)+~P85(f341(x90021,x90025)) % 19.23/19.04 [9003]~P38(f37(x90031,x90032),x90035,x90034,x90033)+P38(f37(x90031,x90032),f603(x90033,x90034,x90035,x90032,x90031),x90034,x90033)+~P85(f341(x90031,x90035)) % 19.23/19.04 [6438]E(x64381,x64382)+~E(f341(x64383,x64381),f341(x64383,x64382))+~P26(x64384,x64385,x64383,f248(f864(x64384,a850))) % 19.23/19.04 [6601]~E(f341(x66013,x66015),f188(x66012))+~E(f341(x66014,x66015),f188(x66012))+E(f341(f175(x66011,x66012,x66013,x66014),x66015),f188(x66012)) % 19.23/19.04 [7372]E(x73721,x73722)+~P26(x73723,x73724,x73725,f248(f864(x73723,a850)))+~E(f341(f312(x73723,x73724,x73725),x73721),f341(f312(x73723,x73724,x73725),x73722)) % 19.23/19.04 [7629]P26(x76292,x76293,f450(x76294,x76293,x76292,x76291),x76291)+~E(f341(f312(x76293,x76292,x76295),x76294),x76291)+E(x76291,f185(f864(x76292,a850))) % 19.23/19.04 [8157]~P85(f341(f341(x81573,x81572),x81575))+~P85(f341(f341(x81573,x81574),x81572))+P85(f341(f341(f343(x81571),x81572),f300(x81571,x81573,x81574,x81575))) % 19.23/19.04 [8158]~P85(f341(f341(x81583,x81582),x81585))+~P85(f341(f341(x81583,x81584),x81582))+P85(f341(f341(f343(x81581),x81582),f291(x81581,x81583,x81584,x81585))) % 19.23/19.04 [8696]~P26(x86961,x86963,x86965,f248(f864(x86961,a850)))+~P26(x86963,x86962,x86964,f248(f864(x86963,a850)))+P26(x86961,x86962,f341(f82(x86963,x86962,x86961,x86964),x86965),f248(f864(x86961,a850))) % 19.23/19.04 [9197]P85(f341(f341(f343(f863(x91971,x91971)),f341(f341(f250(x91971,x91971),x91972),x91973)),f309(x91971,x91974)))+~P85(f341(f341(f343(f863(x91971,x91971)),f341(f341(f250(x91971,x91971),x91972),x91975)),f309(x91971,x91974)))+~P85(f341(f341(f343(f863(x91971,x91971)),f341(f341(f250(x91971,x91971),x91975),x91973)),f309(x91971,x91974))) % 19.23/19.04 [9234]~P101(x92342)+~P85(f341(f134(x92341),x92345))+P85(f341(f134(x92341),f145(x92341,x92342,x92343,x92344,x92345))) % 19.23/19.04 [5253]~E(x52532,f122(x52531))+E(f341(f341(f132(x52531),x52532),x52533),f341(f341(f146(x52531),x52534),x52535))+~E(x52533,f341(f341(f146(x52531),x52534),x52535)) % 19.23/19.04 [5254]~E(x52542,f122(x52541))+E(f341(f341(f132(x52541),x52542),x52543),f341(f341(f146(x52541),x52544),x52545))+~E(f341(f341(f146(x52541),x52544),x52545),x52543) % 19.23/19.04 [6394]~E(f341(f186(f858(x63941)),x63945),f341(f186(f858(x63942)),x63944))+E(f341(f341(f149(f863(x63941,x63942),x63942),f259(x63941,x63942)),x63943),x63944)+~E(f341(f341(f172(x63941,x63942),x63945),x63944),x63943) % 19.23/19.04 [6395]~E(f341(f186(f858(x63951)),x63954),f341(f186(f858(x63952)),x63955))+E(f341(f341(f149(f863(x63951,x63952),x63951),f249(x63951,x63952)),x63953),x63954)+~E(f341(f341(f172(x63951,x63952),x63954),x63955),x63953) % 19.23/19.04 [6889]~P101(x68891)+~P15(x68891,f341(f341(f149(x68892,x68891),x68893),x68895))+P15(x68891,f341(f341(f149(x68892,x68891),x68893),f341(f133(x68892,x68894),x68895))) % 19.23/19.04 [6934]~P85(f341(x69343,x69345))+~P85(f341(f341(x69342,x69344),x69345))+P85(f341(f341(f101(x69341,x69342,x69343),x69344),x69345)) % 19.23/19.04 [7031]~P101(x70311)+P15(x70311,f341(f341(f149(x70312,x70311),x70313),f157(x70312,x70314,x70315)))+~P15(x70311,f341(f341(f149(x70312,x70311),x70313),x70315)) % 19.23/19.04 [7054]~P52(x70543,x70542,x70545)+~P52(x70541,x70543,x70544)+P52(x70541,x70542,f341(f341(f290(x70541,x70543,x70542),x70544),x70545)) % 19.23/19.04 [7144]E(x71441,x71442)+~P26(x71443,x71444,x71445,f248(f864(x71443,a850)))+~E(f341(f341(f149(x71443,x71444),x71445),x71441),f341(f341(f149(x71443,x71444),x71445),x71442)) % 19.23/19.04 [7227]P38(x72271,x72272,x72273,x72274)+~P38(x72271,x72272,x72275,x72274)+~P85(f341(f341(f241(a857),x72275),x72273)) % 19.23/19.04 [7317]~P85(f341(f341(f242(a857),x73171),f341(x73173,x73175)))+P85(f341(f341(f242(a857),x73171),f150(x73172,x73173,x73174)))+~P85(f341(f341(f343(x73172),x73175),f341(f163(x73172),x73174))) % 19.23/19.04 [7318]~P85(f341(f341(f241(a857),x73181),f341(x73183,x73185)))+P85(f341(f341(f241(a857),x73181),f150(x73182,x73183,x73184)))+~P85(f341(f341(f343(x73182),x73185),f341(f163(x73182),x73184))) % 19.23/19.04 [7728]~P100(x77281)+P85(f341(f341(f241(f864(x77281,a850)),f304(x77281,x77282,x77283)),f304(x77281,x77284,x77285)))+P85(f341(f341(f241(x77281),x77282),x77283)) % 19.23/19.04 [7755]~P6(x77551)+P85(f341(f341(f241(x77551),f341(f341(f55(x77552,x77551),x77553),x77554)),f341(x77554,x77555)))+~P85(f341(f341(f343(x77552),x77555),x77553)) % 19.23/19.04 [7823]~P26(x78231,x78232,x78234,x78233)+E(f341(f86(x78231,x78232,x78233,x78234),f341(x78234,x78235)),x78235)+~P85(f341(f341(f343(x78231),x78235),x78233)) % 19.23/19.04 [8018]~P85(f341(x80181,x80185))+P85(f341(x80181,f358(x80181,x80182,x80183,x80184)))+~P85(f341(f341(f343(x80184),x80185),x80183)) % 19.23/19.04 [8019]~P85(f341(x80191,x80195))+P85(f341(x80191,f358(x80191,x80192,x80193,x80194)))+~P85(f341(f341(f343(x80194),x80195),x80192)) % 19.23/19.04 [8110]P85(f341(f71(x81101),x81102))+~P85(f341(f71(x81103),x81104))+~P85(f341(f341(f241(f864(x81101,a850)),x81102),f341(f312(x81103,x81101,x81105),x81104))) % 19.23/19.04 [8270]E(x82701,x82702)+~P26(x82703,x82704,x82705,f341(f341(f110(f864(x82703,a850)),f341(f163(x82703),x82701)),f341(f163(x82703),x82702)))+~E(f341(f341(f149(x82703,x82704),x82705),x82701),f341(f341(f149(x82703,x82704),x82705),x82702)) % 19.23/19.04 [8327]~P100(x83271)+~P85(f341(f341(f242(f864(x83271,a850)),f304(x83271,x83274,x83275)),f304(x83271,x83272,x83273)))+P85(f341(f341(f241(x83271),x83272),x83273)) % 19.23/19.04 [8395]~P26(x83951,x83954,x83955,f248(f864(x83951,a850)))+~P85(f341(f341(f343(x83954),f341(x83955,x83952)),f341(f312(x83951,x83954,x83955),x83953)))+P85(f341(f341(f343(x83951),x83952),x83953)) % 19.23/19.04 [8473]P85(f341(x84731,x84732))+~P85(f341(x84731,f359(x84731,x84733,x84734,x84735)))+~P85(f341(f341(f343(x84735),x84732),x84734)) % 19.23/19.04 [8474]P85(f341(x84741,x84742))+~P85(f341(x84741,f359(x84741,x84743,x84744,x84745)))+~P85(f341(f341(f343(x84745),x84742),x84743)) % 19.23/19.04 [8731]~P26(x87312,x87313,x87311,x87314)+E(f341(x87311,f341(f86(x87312,x87313,x87314,x87311),x87315)),x87315)+~P85(f341(f341(f343(x87313),x87315),f341(f312(x87312,x87313,x87311),x87314))) % 19.23/19.04 [8818]E(x88181,f122(x88182))+E(f341(f341(f146(x88182),x88183),f745(x88184,x88183,x88185,x88181,x88182)),x88181)+~E(f341(f341(f132(x88182),x88181),x88185),f341(f341(f146(x88182),x88183),x88184)) % 19.23/19.04 [8819]E(x88191,f122(x88192))+E(f341(f341(f146(x88192),x88193),f746(x88194,x88191,x88195,x88193,x88192)),x88191)+~E(f341(f341(f132(x88192),x88191),x88194),f341(f341(f146(x88192),x88193),x88195)) % 19.23/19.04 [8834]E(f341(f341(f146(x88342),x88343),f745(x88344,x88343,x88341,x88345,x88342)),x88345)+~E(f341(f341(f132(x88342),x88345),x88341),f341(f341(f146(x88342),x88343),x88344))+E(x88341,f341(f341(f146(x88342),x88343),x88344)) % 19.23/19.04 [8835]E(f341(f341(f146(x88351),x88352),f746(x88354,x88355,x88353,x88352,x88351)),x88355)+~E(f341(f341(f132(x88351),x88355),x88354),f341(f341(f146(x88351),x88352),x88353))+E(f341(f341(f146(x88351),x88352),x88353),x88354) % 19.23/19.04 [8910]~E(f341(f312(x89103,x89102,x89104),f248(f864(x89103,a850))),f248(f864(x89102,a850)))+~E(f341(f312(x89101,x89103,x89105),f248(f864(x89101,a850))),f248(f864(x89103,a850)))+E(f341(f312(x89101,x89102,f341(f82(x89103,x89102,x89101,x89104),x89105)),f248(f864(x89101,a850))),f248(f864(x89102,a850))) % 19.23/19.04 [9240]E(x92401,f122(x92402))+~E(f341(f341(f132(x92402),x92401),x92403),f341(f341(f146(x92402),x92405),x92404))+E(f341(f341(f132(x92402),f746(x92403,x92401,x92404,x92405,x92402)),x92403),x92404) % 19.23/19.04 [9241]E(x92411,f122(x92412))+~E(f341(f341(f132(x92412),x92411),x92415),f341(f341(f146(x92412),x92414),x92413))+E(f341(f341(f132(x92412),f745(x92413,x92414,x92415,x92411,x92412)),x92415),x92413) % 19.23/19.04 [9248]E(f341(f341(f132(x92482),f745(x92484,x92483,x92481,x92485,x92482)),x92481),x92484)+~E(f341(f341(f132(x92482),x92485),x92481),f341(f341(f146(x92482),x92483),x92484))+E(x92481,f341(f341(f146(x92482),x92483),x92484)) % 19.23/19.04 [9249]~E(f341(f341(f132(x92491),x92495),x92494),f341(f341(f146(x92491),x92492),x92493))+E(f341(f341(f132(x92491),f746(x92494,x92495,x92493,x92492,x92491)),x92494),x92493)+E(f341(f341(f146(x92491),x92492),x92493),x92494) % 19.23/19.04 [9250]E(f341(f341(f132(x92501),x92505),f750(x92503,x92502,x92504,x92505,x92501)),x92502)+E(f341(f341(f132(x92501),x92502),f749(x92503,x92502,x92504,x92505,x92501)),x92505)+~E(f341(f341(f132(x92501),x92505),x92504),f341(f341(f132(x92501),x92502),x92503)) % 19.23/19.04 [9282]~P101(x92821)+P15(x92821,f341(f341(f149(x92822,x92821),x92823),f145(x92822,x92821,x92823,x92824,x92825)))+~P15(x92821,f341(f341(f149(x92822,x92821),x92823),x92825)) % 19.23/19.04 [9298]~P56(x92985,x92981,x92984,x92983)+P85(f341(f341(x92981,x92982),f544(x92983,x92984,x92981,x92985,x92982)))+~P85(f341(f341(f343(x92985),x92982),x92984)) % 19.23/19.04 [9395]~P85(f341(f341(f343(f863(x93951,x93951)),f341(f341(f250(x93951,x93951),x93955),x93953)),f309(x93951,x93954)))+P85(f341(f341(f343(f863(x93951,x93951)),f341(f341(f250(x93951,x93951),x93952),x93953)),f341(f341(f290(x93951,x93951,x93951),x93954),f309(x93951,x93954))))+~P85(f341(f341(f343(f863(x93951,x93951)),f341(f341(f250(x93951,x93951),x93952),x93955)),f341(f341(f290(x93951,x93951,x93951),x93954),f309(x93951,x93954)))) % 19.23/19.04 [9396]~P85(f341(f341(f343(f863(x93961,x93961)),f341(f341(f250(x93961,x93961),x93962),x93965)),f309(x93961,x93964)))+P85(f341(f341(f343(f863(x93961,x93961)),f341(f341(f250(x93961,x93961),x93962),x93963)),f341(f341(f290(x93961,x93961,x93961),x93964),f309(x93961,x93964))))+~P85(f341(f341(f343(f863(x93961,x93961)),f341(f341(f250(x93961,x93961),x93965),x93963)),f341(f341(f290(x93961,x93961,x93961),x93964),f309(x93961,x93964)))) % 19.23/19.04 [9398]P85(f341(f341(f343(f863(f858(x93981),f858(x93981))),f341(f341(f250(f858(x93981),f858(x93981)),x93982),x93983)),f153(x93981,f309(x93981,x93984))))+~P85(f341(f341(f343(f863(f858(x93981),f858(x93981))),f341(f341(f250(f858(x93981),f858(x93981)),x93982),x93985)),f153(x93981,f309(x93981,x93984))))+~P85(f341(f341(f343(f863(f858(x93981),f858(x93981))),f341(f341(f250(f858(x93981),f858(x93981)),x93985),x93983)),f153(x93981,f309(x93981,x93984)))) % 19.23/19.04 [9403]E(f341(f341(f132(x94031),x94032),f749(x94033,x94032,x94034,x94035,x94031)),x94035)+E(f341(f341(f132(x94031),f750(x94033,x94032,x94034,x94035,x94031)),x94033),x94034)+~E(f341(f341(f132(x94031),x94032),x94033),f341(f341(f132(x94031),x94035),x94034)) % 19.23/19.04 [9404]E(f341(f341(f132(x94041),x94042),f750(x94043,x94044,x94045,x94042,x94041)),x94044)+E(f341(f341(f132(x94041),f749(x94043,x94044,x94045,x94042,x94041)),x94045),x94043)+~E(f341(f341(f132(x94041),x94042),x94045),f341(f341(f132(x94041),x94044),x94043)) % 19.23/19.04 [9461]P85(f341(f341(f343(f863(x94611,x94611)),f341(f341(f250(x94611,x94611),x94612),x94613)),f341(f341(f290(x94611,x94611,x94611),x94614),f309(x94611,x94614))))+~P85(f341(f341(f343(f863(x94611,x94611)),f341(f341(f250(x94611,x94611),x94612),x94615)),f341(f341(f290(x94611,x94611,x94611),x94614),f309(x94611,x94614))))+~P85(f341(f341(f343(f863(x94611,x94611)),f341(f341(f250(x94611,x94611),x94615),x94613)),f341(f341(f290(x94611,x94611,x94611),x94614),f309(x94611,x94614)))) % 19.23/19.04 [9495]E(f341(f341(f132(x94951),f749(x94952,x94953,x94954,x94955,x94951)),x94954),x94952)+~E(f341(f341(f132(x94951),x94953),x94952),f341(f341(f132(x94951),x94955),x94954))+E(f341(f341(f132(x94951),f750(x94952,x94953,x94954,x94955,x94951)),x94952),x94954) % 19.23/19.04 [9510]~P56(x95101,x95104,x95103,x95102)+~P85(f341(f341(f343(x95101),x95105),x95103))+P85(f341(f341(f343(x95101),f544(x95102,x95103,x95104,x95101,x95105)),x95102)) % 19.23/19.04 [9626]~P85(f341(f341(f343(f863(f864(x96261,a850),f864(x96261,a850))),f341(f341(f250(f864(x96261,a850),f864(x96261,a850)),x96264),x96263)),f334(x96261,x96262)))+~P85(f341(f341(f343(x96261),x96265),x96264))+P85(f341(f341(f343(x96261),f633(x96262,x96263,x96264,x96261,x96265)),x96263)) % 19.23/19.04 [6470]~P18(x64702,x64705,x64701)+~P85(f341(f71(x64702),x64704))+E(f341(x64701,f341(f341(f311(x64702),x64703),x64704)),f341(f341(f74(x64702,x64702,x64705),x64703),x64704)) % 19.23/19.04 [6471]~E(x64713,x64714)+~E(x64712,x64715)+E(f341(f341(f311(x64711),x64712),f341(f341(f311(x64711),x64713),f185(f864(x64711,a850)))),f341(f341(f311(x64711),x64714),f341(f341(f311(x64711),x64715),f185(f864(x64711,a850))))) % 19.23/19.04 [6519]E(f341(x65191,x65192),f185(f864(x65193,a850)))+~E(f341(f341(f54(x65194,f864(x65193,a850)),x65195),x65191),f185(f864(x65193,a850)))+~P85(f341(f341(f343(x65194),x65192),x65195)) % 19.23/19.04 [6520]E(f341(x65201,x65202),f248(f864(x65203,a850)))+~E(f341(f341(f55(x65204,f864(x65203,a850)),x65205),x65201),f248(f864(x65203,a850)))+~P85(f341(f341(f343(x65204),x65202),x65205)) % 19.23/19.04 [6838]~P85(f341(f341(f192(x68381),x68383),x68385))+~P85(f341(f341(f192(x68382),x68385),x68384))+P85(f341(f341(f192(f38(x68381,x68382)),x68383),x68384)) % 19.23/19.04 [7041]~E(x70412,x70414)+~P111(x70411)+E(f341(f341(f89(x70411),f341(f341(f90(x70411),x70412),x70413)),f341(f341(f90(x70411),x70414),x70415)),f341(f341(f89(x70411),f341(f341(f90(x70411),x70412),x70415)),f341(f341(f90(x70411),x70414),x70413))) % 19.23/19.04 [7101]~P6(x71011)+~P85(f341(f341(f343(x71014),x71013),x71015))+P85(f341(f341(f241(x71011),f341(x71012,x71013)),f341(f341(f54(x71014,x71011),x71015),x71012))) % 19.23/19.04 [7149]~P103(x71491)+P85(f341(f341(f241(x71491),f341(x71492,x71493)),f341(x71494,x71493)))+~P85(f341(f341(f241(f864(x71495,x71491)),x71492),x71494)) % 19.23/19.04 [7285]E(x72851,x72852)+E(x72853,x72851)+~E(f341(f341(f311(x72854),x72851),f341(f341(f311(x72854),x72855),f185(f864(x72854,a850)))),f341(f341(f311(x72854),x72852),f341(f341(f311(x72854),x72853),f185(f864(x72854,a850))))) % 19.23/19.04 [7286]E(x72861,x72862)+E(x72863,x72861)+~E(f341(f341(f311(x72864),x72863),f341(f341(f311(x72864),x72862),f185(f864(x72864,a850)))),f341(f341(f311(x72864),x72865),f341(f341(f311(x72864),x72861),f185(f864(x72864,a850))))) % 19.23/19.04 [7287]E(x72871,x72872)+E(x72871,x72873)+~E(f341(f341(f311(x72874),x72873),f341(f341(f311(x72874),x72872),f185(f864(x72874,a850)))),f341(f341(f311(x72874),x72875),f341(f341(f311(x72874),x72871),f185(f864(x72874,a850))))) % 19.23/19.04 [7288]E(x72881,x72882)+E(x72881,x72883)+~E(f341(f341(f311(x72884),x72881),f341(f341(f311(x72884),x72885),f185(f864(x72884,a850)))),f341(f341(f311(x72884),x72882),f341(f341(f311(x72884),x72883),f185(f864(x72884,a850))))) % 19.23/19.04 [7833]P26(x78331,x78332,x78333,x78334)+~P26(x78331,x78332,x78333,x78335)+~P85(f341(f341(f241(f864(x78331,a850)),x78334),x78335)) % 19.23/19.04 [7936]P85(f341(x79361,x79362))+~P85(f341(f341(f192(x79364),x79362),x79365))+P85(f341(f341(f192(f35(x79361,x79363,x79364)),x79362),x79365)) % 19.23/19.04 [7964]~P85(f341(x79641,x79644))+~P85(f341(f341(f192(x79642),x79644),x79645))+P85(f341(f341(f192(f35(x79641,x79642,x79643)),x79644),x79645)) % 19.23/19.04 [8009]E(x80091,x80092)+~E(f341(f312(x80093,x80094,x80095),x80091),f341(f312(x80093,x80094,x80095),x80092))+~P26(x80093,x80094,x80095,f341(f341(f110(f864(x80093,a850)),x80091),x80092)) % 19.23/19.04 [8108]~P26(x81081,x81082,x81083,x81085)+~P26(x81081,x81082,x81083,x81084)+P26(x81081,x81082,x81083,f341(f341(f111(f864(x81081,a850)),x81084),x81085)) % 19.23/19.04 [8211]~P68(x82111)+E(f341(f341(f89(x82111),f341(x82112,x82113)),f341(f160(x82111),f341(f341(f149(x82114,x82111),x82112),f157(x82114,x82113,x82115)))),f341(f160(x82111),f341(f341(f149(x82114,x82111),x82112),x82115)))+~P85(f341(f341(f343(x82114),x82113),f341(f163(x82114),x82115))) % 19.23/19.04 [8299]~P101(x82991)+~P15(x82991,f341(f341(f149(x82992,x82991),x82993),x82995))+P15(x82991,f341(f341(f149(x82992,x82991),x82993),f341(f341(f144(x82992,x82991,x82993),x82994),x82995))) % 19.23/19.04 [8380]P85(f341(x83801,x83802))+P85(f341(f341(f192(x83803),x83802),x83804))+~P85(f341(f341(f192(f35(x83801,x83805,x83803)),x83802),x83804)) % 19.23/19.04 [8391]~P6(x83911)+P85(f341(f341(f241(x83911),f341(f341(f54(x83912,x83911),x83913),x83914)),f341(f341(f54(x83912,x83911),x83915),x83914)))+~P85(f341(f341(f241(f864(x83912,a850)),x83913),x83915)) % 19.23/19.04 [8392]~P6(x83921)+P85(f341(f341(f241(x83921),f341(f341(f55(x83922,x83921),x83923),x83924)),f341(f341(f55(x83922,x83921),x83925),x83924)))+~P85(f341(f341(f241(f864(x83922,a850)),x83925),x83923)) % 19.23/19.04 [8401]~P85(f341(x84014,x84012))+P85(f341(f341(f192(x84011),x84012),x84013))+~P85(f341(f341(f192(f35(x84014,x84011,x84015)),x84012),x84013)) % 19.23/19.04 [8424]~P101(x84243)+P85(f341(f134(x84241),x84242))+~P85(f341(f134(x84241),f341(f341(f144(x84241,x84243,x84244),x84245),x84242))) % 19.23/19.04 [8434]P85(f341(f341(f192(x84341),x84342),x84343))+P85(f341(f341(f192(x84344),x84342),x84343))+~P85(f341(f341(f192(f35(x84345,x84341,x84344)),x84342),x84343)) % 19.23/19.04 [8557]~P101(x85571)+~P85(f341(f341(f343(x85572),x85573),f341(f163(x85572),x85574)))+~P85(f341(f134(x85572),f341(f341(f144(x85572,x85571,x85575),x85573),x85574))) % 19.23/19.04 [8633]~P101(x86331)+P15(x86331,f341(f341(f149(x86332,x86331),x86333),x86334))+~P15(x86331,f341(f341(f149(x86332,x86331),x86333),f341(f341(f144(x86332,x86331,x86333),x86335),x86334))) % 19.23/19.04 [8718]~P101(x87182)+E(f341(f341(f144(x87181,x87182,x87183),x87184),x87185),f145(x87181,x87182,x87183,x87184,x87185))+P85(f341(f341(f343(x87182),f341(x87183,x87184)),f341(f312(x87181,x87182,x87183),f341(f163(x87181),x87185)))) % 19.23/19.04 [8785]~P101(x87852)+E(f145(x87851,x87852,x87853,x87854,x87855),x87855)+~P85(f341(f341(f343(x87852),f341(x87853,x87854)),f341(f312(x87851,x87852,x87853),f341(f163(x87851),x87855)))) % 19.23/19.04 [8799]~P26(x87992,x87991,x87993,x87995)+P85(f341(f341(f242(f864(x87991,a850)),f341(f312(x87992,x87991,x87993),x87994)),f341(f312(x87992,x87991,x87993),x87995)))+~P85(f341(f341(f242(f864(x87992,a850)),x87994),x87995)) % 19.23/19.04 [8948]~P26(x89481,x89482,x89483,f248(f864(x89481,a850)))+~P85(f341(f341(f241(f864(x89482,a850)),x89484),f341(f312(x89481,x89482,x89483),x89485)))+P85(f341(f341(f241(f864(x89481,a850)),f341(f314(x89481,x89482,x89483),x89484)),x89485)) % 19.23/19.04 [8966]~E(f341(f312(x89663,x89661,x89664),f248(f864(x89663,a850))),f248(f864(x89661,a850)))+P85(f341(f341(f241(f864(x89661,a850)),x89662),f341(f312(x89663,x89661,x89664),x89665)))+~P85(f341(f341(f241(f864(x89663,a850)),f341(f314(x89663,x89661,x89664),x89662)),x89665)) % 19.23/19.04 [9004]~E(f341(f235(x90042),x90044),f341(f171(x90041,x90042,x90045),x90043))+~P85(f341(f134(x90041),f341(f341(f149(f863(x90041,x90042),x90041),f249(x90041,x90042)),x90045)))+P85(f341(f341(f343(f863(x90041,x90042)),f341(f341(f250(x90041,x90042),x90043),x90044)),f341(f163(f863(x90041,x90042)),x90045))) % 19.23/19.04 [9070]~P26(x90701,x90704,x90705,f248(f864(x90701,a850)))+~P85(f341(f341(f241(f864(x90704,a850)),f341(f312(x90701,x90704,x90705),x90702)),f341(f312(x90701,x90704,x90705),x90703)))+P85(f341(f341(f241(f864(x90701,a850)),x90702),x90703)) % 19.23/19.04 [9136]E(f341(f235(x91361),x91362),f341(f171(x91363,x91361,x91364),x91365))+~P85(f341(f134(x91363),f341(f341(f149(f863(x91363,x91361),x91363),f249(x91363,x91361)),x91364)))+~P85(f341(f341(f343(f863(x91363,x91361)),f341(f341(f250(x91363,x91361),x91365),x91362)),f341(f163(f863(x91363,x91361)),x91364))) % 19.23/19.04 [9138]E(f341(f171(x91381,x91382,x91383),x91384),f341(f235(x91382),x91385))+~P85(f341(f134(x91381),f341(f341(f149(f863(x91381,x91382),x91381),f249(x91381,x91382)),x91383)))+~P85(f341(f341(f343(f863(x91381,x91382)),f341(f341(f250(x91381,x91382),x91384),x91385)),f341(f163(f863(x91381,x91382)),x91383))) % 19.23/19.04 [9344]~P17(x93441,x93442,x93443)+~P85(f341(f71(x93441),x93445))+P85(f341(f76(x93441,x93442,x93443,x93444,x93445),f341(f341(f74(x93441,x93442,x93443),x93444),x93445))) % 19.23/19.04 [9418]P85(f341(x94181,f708(x94182,x94181,x94183,x94184,x94185)))+~P85(f341(f341(f241(f864(x94185,a850)),x94184),x94183))+P85(f341(f341(f241(f864(x94185,a850)),f341(f341(f111(f864(x94185,a850)),x94184),f341(f265(x94185),x94181))),f341(f341(f111(f864(x94185,a850)),x94183),f341(f265(x94185),x94182)))) % 19.23/19.04 [9508]~P6(x95085)+P85(f341(f341(f343(x95081),f675(x95082,x95083,x95081,x95084,x95085)),x95083))+P85(f341(f341(f241(x95085),x95084),f341(f341(f55(x95081,x95085),x95083),x95082))) % 19.23/19.04 [9520]~P85(f341(x95205,f708(x95205,x95203,x95204,x95202,x95201)))+~P85(f341(f341(f241(f864(x95201,a850)),x95202),x95204))+P85(f341(f341(f241(f864(x95201,a850)),f341(f341(f111(f864(x95201,a850)),x95202),f341(f265(x95201),x95203))),f341(f341(f111(f864(x95201,a850)),x95204),f341(f265(x95201),x95205)))) % 19.23/19.04 [9588]P85(f341(f341(f343(x95881),f708(x95882,x95883,x95884,x95885,x95881)),x95885))+~P85(f341(f341(f241(f864(x95881,a850)),x95885),x95884))+P85(f341(f341(f241(f864(x95881,a850)),f341(f341(f111(f864(x95881,a850)),x95885),f341(f265(x95881),x95883))),f341(f341(f111(f864(x95881,a850)),x95884),f341(f265(x95881),x95882)))) % 19.23/19.04 [9637]~P6(x96371)+~P85(f341(f341(f241(x96371),x96372),f341(x96375,f675(x96375,x96374,x96373,x96372,x96371))))+P85(f341(f341(f241(x96371),x96372),f341(f341(f55(x96373,x96371),x96374),x96375))) % 19.23/19.04 [9667]~P71(x96671)+~P85(f341(f71(x96672),x96675))+E(f341(f341(f341(f75(x96671,x96672,f90(x96671)),f341(f341(f20(x96672,x96671,x96671),f341(f341(f10(x96671,f864(x96671,x96671),x96672),f90(x96671)),x96673)),x96674)),f87(x96671)),x96675),f341(f341(f90(x96671),f341(f341(f341(f75(x96671,x96672,f90(x96671)),x96673),f87(x96671)),x96675)),f341(f341(f341(f75(x96671,x96672,f90(x96671)),x96674),f87(x96671)),x96675))) % 19.23/19.04 [9715]~P85(f341(f341(f343(f863(f864(x97151,a850),f864(x97151,a850))),f341(f341(f250(f864(x97151,a850),f864(x97151,a850)),x97155),x97154)),f334(x97151,x97153)))+~P85(f341(f341(f343(x97151),x97152),x97155))+P85(f341(f341(f343(f863(x97151,x97151)),f341(f341(f250(x97151,x97151),x97152),f633(x97153,x97154,x97155,x97151,x97152))),x97153)) % 19.23/19.04 [9867]~P85(f341(f341(f343(f863(f858(x98671),f858(x98671))),f341(f341(f250(f858(x98671),f858(x98671)),f341(f341(f132(x98671),x98675),x98672)),f341(f341(f132(x98671),x98675),x98673))),f143(x98671,x98674)))+P85(f341(f341(f343(f863(f858(x98671),f858(x98671))),f341(f341(f250(f858(x98671),f858(x98671)),x98672),x98673)),f143(x98671,x98674)))+P85(f341(f341(f343(f863(x98671,x98671)),f341(f341(f250(x98671,x98671),f751(x98674,x98673,x98672,x98675,x98671)),f751(x98674,x98673,x98672,x98675,x98671))),x98674)) % 19.23/19.04 [7152]~E(x71523,x71525)+E(f341(f341(f158(x71521),f341(f341(f154(x71521,x71522),x71523),x71524)),x71525),x71524)+~P85(f341(f341(f242(a857),x71523),f341(f186(f858(x71521)),x71522))) % 19.23/19.04 [7161]~E(f341(f186(f858(x71611)),x71613),f341(f186(f858(x71612)),x71614))+E(f341(f171(x71611,x71612,f341(f341(f172(x71611,x71612),x71613),x71614)),x71615),f188(x71612))+P85(f341(f341(f343(x71611),x71615),f341(f163(x71611),x71613))) % 19.23/19.04 [7281]~E(f341(f341(f132(x72811),x72812),x72814),f341(f341(f132(x72811),x72813),x72815))+E(f341(f341(f164(x72811),f341(f186(f858(x72811)),x72812)),x72813),x72812)+P85(f341(f341(f241(a857),f341(f186(f858(x72811)),x72813)),f341(f186(f858(x72811)),x72812))) % 19.23/19.04 [7794]~E(f341(f341(f132(x77941),x77942),x77944),f341(f341(f132(x77941),x77943),x77945))+E(f341(f341(f164(x77941),f341(f186(f858(x77941)),x77942)),x77943),x77942)+~P85(f341(f341(f241(a857),f341(f186(f858(x77941)),x77942)),f341(f186(f858(x77941)),x77943))) % 19.23/19.04 [7818]~P85(f341(f71(x78181),f341(x78184,x78185)))+~P85(f341(f341(f343(x78182),x78185),x78183))+P85(f341(f71(x78181),f341(f341(f55(x78182,f864(x78181,a850)),x78183),x78184))) % 19.23/19.04 [7930]~E(f341(f186(f858(x79301)),x79302),f341(f186(f858(x79303)),x79304))+~E(f341(f171(x79301,x79303,f341(f341(f172(x79301,x79303),x79302),x79304)),x79305),f188(x79303))+~P85(f341(f341(f343(x79301),x79305),f341(f163(x79301),x79302))) % 19.23/19.04 [7996]~P46(x79961,x79963,x79965)+~P46(x79961,x79962,x79964)+P46(x79961,f341(f341(f110(f864(x79961,a850)),x79962),x79963),f341(f341(f110(f864(f863(x79961,x79961),a850)),x79964),x79965)) % 19.23/19.04 [7997]~P46(x79971,x79973,x79975)+~P46(x79971,x79972,x79974)+P46(x79971,f341(f341(f111(f864(x79971,a850)),x79972),x79973),f341(f341(f111(f864(f863(x79971,x79971),a850)),x79974),x79975)) % 19.23/19.04 [8343]E(f341(f341(f250(x83431,x83432),f341(f341(f158(x83431),x83433),x83434)),f341(f341(f158(x83432),x83435),x83434)),f341(f341(f158(f863(x83431,x83432)),f341(f341(f172(x83431,x83432),x83433),x83435)),x83434))+~P85(f341(f341(f242(a857),x83434),f341(f186(f858(x83431)),x83433)))+~P85(f341(f341(f242(a857),x83434),f341(f186(f858(x83432)),x83435))) % 19.23/19.04 [8501]~P46(x85011,x85013,x85014)+P85(f341(f341(f343(x85011),x85012),x85013))+~P85(f341(f341(f343(f863(x85011,x85011)),f341(f341(f250(x85011,x85011),x85015),x85012)),x85014)) % 19.23/19.04 [8502]~P46(x85021,x85023,x85024)+P85(f341(f341(f343(x85021),x85022),x85023))+~P85(f341(f341(f343(f863(x85021,x85021)),f341(f341(f250(x85021,x85021),x85022),x85025)),x85024)) % 19.23/19.04 [8503]~P9(x85031,x85033,x85034)+P85(f341(f341(f343(x85031),x85032),x85033))+~P85(f341(f341(f343(f863(x85031,x85031)),f341(f341(f250(x85031,x85031),x85035),x85032)),x85034)) % 19.23/19.04 [8504]~P9(x85041,x85043,x85044)+P85(f341(f341(f343(x85041),x85042),x85043))+~P85(f341(f341(f343(f863(x85041,x85041)),f341(f341(f250(x85041,x85041),x85042),x85045)),x85044)) % 19.23/19.04 [8741]~P9(x87411,x87415,x87412)+E(f341(f286(x87411,x87411,x87412),f341(f341(f311(x87411),x87413),f185(f864(x87411,a850)))),f341(f286(x87411,x87411,x87412),f341(f341(f311(x87411),x87414),f185(f864(x87411,a850)))))+~P85(f341(f341(f343(f863(x87411,x87411)),f341(f341(f250(x87411,x87411),x87413),x87414)),x87412)) % 19.23/19.04 [8907]P85(f341(x89071,x89072))+~P85(f341(f341(f343(x89073),x89072),x89075))+P85(f341(f341(f343(x89073),f359(x89071,x89074,x89075,x89073)),f341(f341(f110(f864(x89073,a850)),x89075),x89074))) % 19.23/19.04 [8908]P85(f341(x89081,x89082))+~P85(f341(f341(f343(x89083),x89082),x89084))+P85(f341(f341(f343(x89083),f359(x89081,x89084,x89085,x89083)),f341(f341(f110(f864(x89083,a850)),x89085),x89084))) % 19.23/19.04 [8916]~P85(f341(x89162,x89165))+~P85(f341(f341(f343(x89161),x89165),x89164))+P85(f341(f341(f343(x89161),f358(x89162,x89163,x89164,x89161)),f341(f341(f110(f864(x89161,a850)),x89164),x89163))) % 19.23/19.04 [8917]~P85(f341(x89172,x89175))+~P85(f341(f341(f343(x89171),x89175),x89173))+P85(f341(f341(f343(x89171),f358(x89172,x89173,x89174,x89171)),f341(f341(f110(f864(x89171,a850)),x89174),x89173))) % 19.23/19.04 [8930]~P85(f341(f341(f241(f864(x89301,a850)),x89305),x89303))+~P85(f341(f341(f241(f864(x89301,a850)),x89302),x89304))+P85(f341(f341(f241(f864(x89301,a850)),f341(f341(f3(f864(x89301,a850)),x89302),x89303)),f341(f341(f3(f864(x89301,a850)),x89304),x89305))) % 19.23/19.04 [8931]~P85(f341(f341(f241(f864(x89311,a850)),x89313),x89315))+~P85(f341(f341(f241(f864(x89311,a850)),x89312),x89314))+P85(f341(f341(f241(f864(x89311,a850)),f341(f341(f110(f864(x89311,a850)),x89312),x89313)),f341(f341(f110(f864(x89311,a850)),x89314),x89315))) % 19.23/19.04 [8932]~P85(f341(f341(f241(f864(x89321,a850)),x89323),x89325))+~P85(f341(f341(f241(f864(x89321,a850)),x89322),x89324))+P85(f341(f341(f241(f864(x89321,a850)),f341(f341(f111(f864(x89321,a850)),x89322),x89323)),f341(f341(f111(f864(x89321,a850)),x89324),x89325))) % 19.23/19.04 [9021]P85(f341(f341(f343(f863(x90211,x90211)),f341(f341(f250(x90211,x90211),x90212),x90213)),f336(x90211,x90214,x90215)))+~P85(f341(f341(f241(a857),f341(x90214,x90212)),f341(x90214,x90213)))+~P85(f341(f341(f343(f863(x90211,x90211)),f341(f341(f250(x90211,x90211),x90212),x90213)),x90215)) % 19.23/19.04 [9028]~E(f341(f186(f858(x90281)),x90283),f341(f186(f858(x90282)),x90284))+E(f341(f171(x90281,x90282,f341(f341(f172(x90281,x90282),x90283),x90284)),x90285),f341(f235(x90282),f725(x90285,x90284,x90282,x90283,x90281)))+~P85(f341(f341(f343(x90281),x90285),f341(f163(x90281),x90283))) % 19.23/19.04 [9178]P85(f341(f341(f343(f863(x91781,x91781)),f341(f341(f250(x91781,x91781),x91782),x91783)),f309(x91781,x91784)))+~P85(f341(f341(f343(f863(x91781,x91781)),f341(f341(f250(x91781,x91781),x91782),x91785)),f309(x91781,x91784)))+~P85(f341(f341(f343(f863(x91781,x91781)),f341(f341(f250(x91781,x91781),x91785),x91783)),x91784)) % 19.23/19.04 [9179]P85(f341(f341(f343(f863(x91791,x91791)),f341(f341(f250(x91791,x91791),x91792),x91793)),f309(x91791,x91794)))+~P85(f341(f341(f343(f863(x91791,x91791)),f341(f341(f250(x91791,x91791),x91795),x91793)),f309(x91791,x91794)))+~P85(f341(f341(f343(f863(x91791,x91791)),f341(f341(f250(x91791,x91791),x91792),x91795)),x91794)) % 19.23/19.04 [9272]E(x92721,x92722)+E(f341(a121,f653(x92723,x92724,x92721,x92722,x92725)),x92724)+~P85(f341(f341(f343(f863(x92725,x92725)),f341(f341(f250(x92725,x92725),x92722),x92721)),f341(f341(f179(f863(x92725,x92725),a850),x92724),x92723))) % 19.23/19.04 [9273]E(x92731,x92732)+E(f341(a121,f655(x92733,x92734,x92731,x92732,x92735)),x92734)+~P85(f341(f341(f343(f863(x92735,x92735)),f341(f341(f250(x92735,x92735),x92732),x92731)),f341(f341(f179(f863(x92735,x92735),a850),x92734),x92733))) % 19.23/19.04 [9274]E(x92741,f2(a857))+E(f341(a121,f653(x92742,x92741,x92743,x92744,x92745)),x92741)+~P85(f341(f341(f343(f863(x92745,x92745)),f341(f341(f250(x92745,x92745),x92744),x92743)),f341(f341(f179(f863(x92745,x92745),a850),x92741),x92742))) % 19.23/19.04 [9275]E(x92751,f2(a857))+E(f341(a121,f655(x92752,x92751,x92753,x92754,x92755)),x92751)+~P85(f341(f341(f343(f863(x92755,x92755)),f341(f341(f250(x92755,x92755),x92754),x92753)),f341(f341(f179(f863(x92755,x92755),a850),x92751),x92752))) % 19.23/19.04 [9294]P85(f341(f341(f343(f863(x92941,x92941)),f341(f341(f250(x92941,x92941),x92942),x92943)),f341(f341(f290(x92941,x92941,x92941),x92944),f309(x92941,x92944))))+~P85(f341(f341(f343(f863(x92941,x92941)),f341(f341(f250(x92941,x92941),x92942),x92945)),x92944))+~P85(f341(f341(f343(f863(x92941,x92941)),f341(f341(f250(x92941,x92941),x92945),x92943)),x92944)) % 19.23/19.04 [9304]~P85(f341(f341(f343(f863(x93041,x93041)),f341(f341(f250(x93041,x93041),x93042),x93045)),f309(x93041,x93044)))+P85(f341(f341(f343(f863(x93041,x93041)),f341(f341(f250(x93041,x93041),x93042),x93043)),f341(f341(f290(x93041,x93041,x93041),x93044),f309(x93041,x93044))))+~P85(f341(f341(f343(f863(x93041,x93041)),f341(f341(f250(x93041,x93041),x93045),x93043)),x93044)) % 19.23/19.04 [9340]~P9(x93401,x93405,x93402)+~P85(f341(f341(f343(f863(x93401,x93401)),f341(f341(f250(x93401,x93401),x93403),x93404)),x93402))+P85(f341(f341(f241(f864(x93401,a850)),f341(f286(x93401,x93401,x93402),f341(f341(f311(x93401),x93403),f185(f864(x93401,a850))))),f341(f286(x93401,x93401,x93402),f341(f341(f311(x93401),x93404),f185(f864(x93401,a850)))))) % 19.23/19.04 [9391]P85(f341(f341(f343(f863(x93911,x93911)),f341(f341(f250(x93911,x93911),x93912),x93913)),f341(f341(f290(x93911,x93911,x93911),x93914),f309(x93911,x93914))))+~P85(f341(f341(f343(f863(x93911,x93911)),f341(f341(f250(x93911,x93911),x93912),x93915)),f341(f341(f290(x93911,x93911,x93911),x93914),f309(x93911,x93914))))+~P85(f341(f341(f343(f863(x93911,x93911)),f341(f341(f250(x93911,x93911),x93915),x93913)),x93914)) % 19.23/19.04 [9392]P85(f341(f341(f343(f863(x93921,x93921)),f341(f341(f250(x93921,x93921),x93922),x93923)),f341(f341(f290(x93921,x93921,x93921),x93924),f309(x93921,x93924))))+~P85(f341(f341(f343(f863(x93921,x93921)),f341(f341(f250(x93921,x93921),x93925),x93923)),f341(f341(f290(x93921,x93921,x93921),x93924),f309(x93921,x93924))))+~P85(f341(f341(f343(f863(x93921,x93921)),f341(f341(f250(x93921,x93921),x93922),x93925)),x93924)) % 19.23/19.04 [9438]~P85(f341(f76(x94381,x94381,x94384,x94382,x94383),x94385))+P85(f341(f341(f343(x94381),x94382),x94383))+P85(f341(f72(x94381,x94384,f341(f341(f311(x94381),x94382),x94383)),x94385)) % 19.23/19.04 [9483]~E(f341(f312(x94833,x94832,x94835),x94834),x94831)+E(x94831,f185(f864(x94832,a850)))+P85(f341(f341(f241(f864(x94833,a850)),f341(f312(x94832,x94833,f450(x94834,x94833,x94832,x94831)),x94831)),x94834)) % 19.23/19.04 [9523]~P6(x95235)+P85(f341(f341(f343(x95231),f421(x95232,x95233,x95234,x95231,x95235)),x95234))+P85(f341(f341(f241(x95235),f341(f341(f54(x95231,x95235),x95234),x95233)),x95232)) % 19.23/19.04 [9692]E(x96921,x96922)+P85(f341(f341(f343(f863(x96923,x96923)),f341(f341(f250(x96923,x96923),x96921),f654(x96924,x96925,x96922,x96921,x96923))),x96924))+~P85(f341(f341(f343(f863(x96923,x96923)),f341(f341(f250(x96923,x96923),x96921),x96922)),f341(f341(f179(f863(x96923,x96923),a850),x96925),x96924))) % 19.23/19.04 [9693]E(x96931,f2(a857))+P85(f341(f341(f343(f863(x96932,x96932)),f341(f341(f250(x96932,x96932),x96933),f654(x96934,x96931,x96935,x96933,x96932))),x96934))+~P85(f341(f341(f343(f863(x96932,x96932)),f341(f341(f250(x96932,x96932),x96933),x96935)),f341(f341(f179(f863(x96932,x96932),a850),x96931),x96934))) % 19.23/19.04 [9737]~P6(x97371)+~P85(f341(f341(f241(x97371),f341(x97374,f421(x97375,x97374,x97373,x97372,x97371))),x97375))+P85(f341(f341(f241(x97371),f341(f341(f54(x97372,x97371),x97373),x97374)),x97375)) % 19.23/19.04 [9792]E(x97921,x97922)+P85(f341(f341(f343(f863(x97923,x97923)),f341(f341(f250(x97923,x97923),f656(x97924,x97925,x97921,x97922,x97923)),x97921)),x97924))+~P85(f341(f341(f343(f863(x97923,x97923)),f341(f341(f250(x97923,x97923),x97922),x97921)),f341(f341(f179(f863(x97923,x97923),a850),x97925),x97924))) % 19.23/19.04 [9793]E(x97931,f2(a857))+P85(f341(f341(f343(f863(x97932,x97932)),f341(f341(f250(x97932,x97932),f656(x97933,x97931,x97934,x97935,x97932)),x97934)),x97933))+~P85(f341(f341(f343(f863(x97932,x97932)),f341(f341(f250(x97932,x97932),x97935),x97934)),f341(f341(f179(f863(x97932,x97932),a850),x97931),x97933))) % 19.23/19.04 [9797]E(x97971,x97972)+P85(f341(f341(f343(f863(x97973,x97973)),f341(f341(f250(x97973,x97973),x97971),f656(x97974,x97975,x97972,x97971,x97973))),f341(f341(f179(f863(x97973,x97973),a850),f655(x97974,x97975,x97972,x97971,x97973)),x97974)))+~P85(f341(f341(f343(f863(x97973,x97973)),f341(f341(f250(x97973,x97973),x97971),x97972)),f341(f341(f179(f863(x97973,x97973),a850),x97975),x97974))) % 19.23/19.04 [9798]E(x97981,f2(a857))+P85(f341(f341(f343(f863(x97982,x97982)),f341(f341(f250(x97982,x97982),x97983),f656(x97984,x97981,x97985,x97983,x97982))),f341(f341(f179(f863(x97982,x97982),a850),f655(x97984,x97981,x97985,x97983,x97982)),x97984)))+~P85(f341(f341(f343(f863(x97982,x97982)),f341(f341(f250(x97982,x97982),x97983),x97985)),f341(f341(f179(f863(x97982,x97982),a850),x97981),x97984))) % 19.23/19.04 [9858]E(x98581,x98582)+P85(f341(f341(f343(f863(x98583,x98583)),f341(f341(f250(x98583,x98583),f654(x98584,x98585,x98581,x98582,x98583)),x98581)),f341(f341(f179(f863(x98583,x98583),a850),f653(x98584,x98585,x98581,x98582,x98583)),x98584)))+~P85(f341(f341(f343(f863(x98583,x98583)),f341(f341(f250(x98583,x98583),x98582),x98581)),f341(f341(f179(f863(x98583,x98583),a850),x98585),x98584))) % 19.23/19.04 [9859]E(x98591,f2(a857))+P85(f341(f341(f343(f863(x98592,x98592)),f341(f341(f250(x98592,x98592),f654(x98593,x98591,x98594,x98595,x98592)),x98594)),f341(f341(f179(f863(x98592,x98592),a850),f653(x98593,x98591,x98594,x98595,x98592)),x98593)))+~P85(f341(f341(f343(f863(x98592,x98592)),f341(f341(f250(x98592,x98592),x98595),x98594)),f341(f341(f179(f863(x98592,x98592),a850),x98591),x98593))) % 19.23/19.04 [9890]~P68(x98902)+~P85(f341(f71(x98901),x98905))+E(f341(f341(f8(x98901,x98902),f341(f341(f9(x98901,x98902,x98902),f341(f341(f20(x98901,x98902,f864(x98902,x98902)),f341(f341(f10(a850,f864(x98902,f864(x98902,x98902)),x98901),f105(x98902)),f341(f341(f9(x98901,f864(x98901,a850),a850),f343(x98901)),x98903))),x98904)),f2(x98902))),x98905),f341(f341(f8(x98901,x98902),x98904),f341(f341(f111(f864(x98901,a850)),x98905),x98903))) % 19.23/19.04 [8555]~P71(x85551)+~P85(f341(f71(x85554),x85555))+E(f341(f341(f90(x85551),f341(x85552,x85553)),f341(f341(f11(x85554,x85551),x85552),f341(f341(f3(f864(x85554,a850)),x85555),f341(f341(f311(x85554),x85553),f185(f864(x85554,a850)))))),f341(f341(f11(x85554,x85551),x85552),f341(f341(f311(x85554),x85553),x85555))) % 19.23/19.04 [8556]~P68(x85561)+~P85(f341(f71(x85564),x85565))+E(f341(f341(f89(x85561),f341(x85562,x85563)),f341(f341(f8(x85564,x85561),x85562),f341(f341(f3(f864(x85564,a850)),x85565),f341(f341(f311(x85564),x85563),f185(f864(x85564,a850)))))),f341(f341(f8(x85564,x85561),x85562),f341(f341(f311(x85564),x85563),x85565))) % 19.23/19.04 [8860]~P68(x88601)+E(f341(f341(f89(x88601),f341(f341(f8(a857,x88601),x88602),f304(a857,x88603,x88604))),f341(f341(f8(a857,x88601),x88602),f304(a857,f341(f341(f89(a857),x88604),f87(a857)),f341(f341(f89(a857),x88604),x88605)))),f341(f341(f8(a857,x88601),x88602),f304(a857,x88603,f341(f341(f89(a857),x88604),x88605))))+~P85(f341(f341(f241(a857),x88603),f341(f341(f89(a857),x88604),f87(a857)))) % 19.23/19.04 [8861]~P85(f341(f341(f343(x88611),x88614),x88615))+~P85(f341(f341(f241(f864(x88611,a850)),f341(f163(x88611),x88612)),x88615))+P85(f341(f341(f241(f864(x88611,a850)),f341(f163(x88611),f341(f341(f154(x88611,x88612),x88613),x88614))),x88615)) % 19.23/19.04 [9080]~P6(x90802)+~P85(f341(f71(x90801),x90805))+E(f341(f341(f74(x90801,x90802,f341(f341(f10(x90802,f864(x90802,x90802),x90801),f110(x90802)),x90803)),x90804),x90805),f341(f341(f110(x90802),x90804),f341(f341(f54(x90801,x90802),x90805),x90803))) % 19.23/19.04 [9081]~P6(x90812)+~P85(f341(f71(x90811),x90815))+E(f341(f341(f74(x90811,x90812,f341(f341(f10(x90812,f864(x90812,x90812),x90811),f111(x90812)),x90813)),x90814),x90815),f341(f341(f111(x90812),x90814),f341(f341(f55(x90811,x90812),x90815),x90813))) % 19.23/19.04 [9165]~P26(x91651,x91652,x91653,x91655)+P26(x91651,x91652,x91653,f341(f341(f311(x91651),x91654),x91655))+P85(f341(f341(f343(x91652),f341(x91653,x91654)),f341(f312(x91651,x91652,x91653),f341(f341(f3(f864(x91651,a850)),x91655),f341(f341(f311(x91651),x91654),f185(f864(x91651,a850))))))) % 19.23/19.04 [9365]~P85(f341(f341(f343(f863(f858(x93651),f858(x93651))),f341(f341(f250(f858(x93651),f858(x93651)),x93652),x93654)),f153(x93651,x93655)))+~P85(f341(f341(f242(a857),x93653),f341(f186(f858(x93651)),x93652)))+P85(f341(f341(f343(f863(x93651,x93651)),f341(f341(f250(x93651,x93651),f341(f341(f158(x93651),x93652),x93653)),f341(f341(f158(x93651),x93654),x93653))),x93655)) % 19.23/19.04 [9599]E(x95991,f2(a1))+~P85(f341(f64(x95993,x95991),f341(f341(f250(a1,a1),x95994),x95995)))+P85(f341(f64(f341(f341(f90(a1),x95992),x95993),x95991),f341(f341(f250(a1,a1),f341(f341(f89(a1),f341(f341(f90(a1),x95992),x95994)),f341(f341(f51(a1),f341(f341(f90(a1),x95992),x95995)),x95991))),f60(a1,f341(f341(f90(a1),x95992),x95995),x95991)))) % 19.23/19.04 [9604]~P85(f341(f341(f242(a857),f2(a857)),x96043))+~P85(f341(f63(x96042,x96043),f341(f341(f250(a857,a857),x96044),x96045)))+P85(f341(f63(f341(f341(f90(a857),x96041),x96042),x96043),f341(f341(f250(a857,a857),f341(f341(f89(a857),f341(f341(f90(a857),x96041),x96044)),f341(f341(f51(a857),f341(f341(f90(a857),x96041),x96045)),x96043))),f60(a857,f341(f341(f90(a857),x96041),x96045),x96043)))) % 19.23/19.04 [9912]~P68(x99122)+~P85(f341(f71(x99121),x99124))+E(f341(f341(f8(x99121,x99122),x99123),f341(f265(x99121),f341(f341(f20(x99121,a850,a850),f341(f341(f10(a850,f864(a850,a850),x99121),a339),f341(f341(f9(x99121,f864(x99121,a850),a850),f343(x99121)),x99124))),f341(f341(f9(x99121,f864(x99121,a850),a850),f343(x99121)),x99125)))),f341(f341(f8(x99121,x99122),f341(f341(f9(x99121,x99122,x99122),f341(f341(f20(x99121,x99122,f864(x99122,x99122)),f341(f341(f10(a850,f864(x99122,f864(x99122,x99122)),x99121),f105(x99122)),f341(f341(f9(x99121,f864(x99121,a850),a850),f343(x99121)),x99125))),x99123)),f2(x99122))),x99124)) % 19.23/19.04 [8194]~E(f341(f341(f132(x81941),x81942),x81945),f341(f341(f132(x81941),x81943),x81944))+E(f341(f341(f132(x81941),f341(f341(f135(x81941),f341(f186(f858(x81941)),x81942)),x81943)),x81944),x81945)+P85(f341(f341(f241(a857),f341(f186(f858(x81941)),x81943)),f341(f186(f858(x81941)),x81942))) % 19.23/19.04 [8394]~E(f341(f341(f132(x83942),x83943),x83941),f341(f341(f132(x83942),x83944),x83945))+E(x83941,f341(f341(f132(x83942),f341(f341(f135(x83942),f341(f186(f858(x83942)),x83943)),x83944)),x83945))+~P85(f341(f341(f241(a857),f341(f186(f858(x83942)),x83943)),f341(f186(f858(x83942)),x83944))) % 19.23/19.04 [8484]~E(f341(f341(f89(a857),f341(f341(f90(a857),x84843),x84844)),x84841),f341(f341(f89(a857),f341(f341(f90(a857),x84842),x84844)),x84845))+~P85(f341(f341(f241(a857),x84843),x84842))+E(x84841,f341(f341(f89(a857),f341(f341(f90(a857),f341(f341(f3(a857),x84842),x84843)),x84844)),x84845)) % 19.23/19.04 [8485]~E(f341(f341(f89(a857),f341(f341(f90(a857),x84851),x84853)),x84854),f341(f341(f89(a857),f341(f341(f90(a857),x84852),x84853)),x84855))+~P85(f341(f341(f241(a857),x84852),x84851))+E(f341(f341(f89(a857),f341(f341(f90(a857),f341(f341(f3(a857),x84851),x84852)),x84853)),x84854),x84855) % 19.23/19.04 [8626]E(f341(f341(f89(a857),f341(f341(f90(a857),x86261),x86262)),x86263),f341(f341(f89(a857),f341(f341(f90(a857),x86264),x86262)),x86265))+~P85(f341(f341(f241(a857),x86264),x86261))+~E(x86265,f341(f341(f89(a857),f341(f341(f90(a857),f341(f341(f3(a857),x86261),x86264)),x86262)),x86263)) % 19.23/19.04 [8627]E(f341(f341(f89(a857),f341(f341(f90(a857),x86271),x86272)),x86273),f341(f341(f89(a857),f341(f341(f90(a857),x86274),x86272)),x86275))+~P85(f341(f341(f241(a857),x86274),x86271))+~E(f341(f341(f89(a857),f341(f341(f90(a857),f341(f341(f3(a857),x86271),x86274)),x86272)),x86273),x86275) % 19.23/19.04 [8962]~P85(f341(f341(f288(a1),x89621),x89624))+~P85(f341(f341(f288(a1),x89621),f341(f341(f89(a1),x89622),x89625)))+P85(f341(f341(f288(a1),x89621),f341(f341(f89(a1),f341(f341(f89(a1),x89622),f341(f341(f90(a1),x89623),x89624))),x89625))) % 19.23/19.04 [9166]~P85(f341(f341(f288(a1),x91661),x91664))+P85(f341(f341(f288(a1),x91661),f341(f341(f89(a1),x91662),x91663)))+~P85(f341(f341(f288(a1),x91661),f341(f341(f89(a1),f341(f341(f89(a1),x91662),f341(f341(f90(a1),x91665),x91664))),x91663))) % 19.23/19.04 [9415]~P59(x94152)+~P85(f341(f71(x94151),x94155))+E(f341(f341(f11(x94151,x94152),f341(f341(f20(x94151,x94152,x94152),f341(f341(f10(x94152,f864(x94152,x94152),x94151),f292(x94152)),x94153)),x94154)),x94155),f341(f341(f292(x94152),f341(f341(f11(x94151,x94152),x94153),x94155)),f341(f341(f11(x94151,x94152),x94154),x94155))) % 19.23/19.04 [9538]~E(f658(x95385,x95384,x95383,x95382,x95381),f659(x95385,x95384,x95383,x95382,x95381))+P85(f341(f341(f343(f863(x95381,x95381)),f341(f341(f250(x95381,x95381),x95382),x95383)),f309(x95381,x95384)))+~P85(f341(f341(f343(f863(x95381,x95381)),f341(f341(f250(x95381,x95381),x95382),x95383)),f309(x95381,f341(f341(f110(f864(f863(x95381,x95381),a850)),x95384),x95385)))) % 19.23/19.04 [9539]~E(f663(x95395,x95394,x95393,x95392,x95391),f664(x95395,x95394,x95393,x95392,x95391))+P85(f341(f341(f343(f863(x95391,x95391)),f341(f341(f250(x95391,x95391),x95392),x95393)),f309(x95391,x95394)))+~P85(f341(f341(f343(f863(x95391,x95391)),f341(f341(f250(x95391,x95391),x95392),x95393)),f309(x95391,f341(f341(f110(f864(f863(x95391,x95391),a850)),x95394),x95395)))) % 19.23/19.04 [9725]P85(f341(f341(f343(f863(x97251,x97251)),f341(f341(f250(x97251,x97251),x97252),f659(x97255,x97254,x97253,x97252,x97251))),f309(x97251,x97254)))+P85(f341(f341(f343(f863(x97251,x97251)),f341(f341(f250(x97251,x97251),x97252),x97253)),f309(x97251,x97254)))+~P85(f341(f341(f343(f863(x97251,x97251)),f341(f341(f250(x97251,x97251),x97252),x97253)),f309(x97251,f341(f341(f110(f864(f863(x97251,x97251),a850)),x97254),x97255)))) % 19.23/19.04 [9819]P85(f341(f341(f343(f863(x98191,x98191)),f341(f341(f250(x98191,x98191),f664(x98195,x98194,x98193,x98192,x98191)),x98193)),f309(x98191,x98194)))+P85(f341(f341(f343(f863(x98191,x98191)),f341(f341(f250(x98191,x98191),x98192),x98193)),f309(x98191,x98194)))+~P85(f341(f341(f343(f863(x98191,x98191)),f341(f341(f250(x98191,x98191),x98192),x98193)),f309(x98191,f341(f341(f110(f864(f863(x98191,x98191),a850)),x98194),x98195)))) % 19.23/19.04 [9865]P85(f341(f341(f343(f863(x98651,x98651)),f341(f341(f250(x98651,x98651),x98652),x98653)),f309(x98651,x98654)))+P85(f341(f341(f343(f863(x98651,x98651)),f341(f341(f250(x98651,x98651),f659(x98655,x98654,x98653,x98652,x98651)),f658(x98655,x98654,x98653,x98652,x98651))),x98655))+~P85(f341(f341(f343(f863(x98651,x98651)),f341(f341(f250(x98651,x98651),x98652),x98653)),f309(x98651,f341(f341(f110(f864(f863(x98651,x98651),a850)),x98654),x98655)))) % 19.23/19.04 [9866]P85(f341(f341(f343(f863(x98661,x98661)),f341(f341(f250(x98661,x98661),x98662),x98663)),f309(x98661,x98664)))+P85(f341(f341(f343(f863(x98661,x98661)),f341(f341(f250(x98661,x98661),f663(x98665,x98664,x98663,x98662,x98661)),f664(x98665,x98664,x98663,x98662,x98661))),x98665))+~P85(f341(f341(f343(f863(x98661,x98661)),f341(f341(f250(x98661,x98661),x98662),x98663)),f309(x98661,f341(f341(f110(f864(f863(x98661,x98661),a850)),x98664),x98665)))) % 19.23/19.04 [9989]~P85(f341(f341(f343(f863(f858(x99891),f858(x99891))),f341(f341(f250(f858(x99891),f858(x99891)),x99894),x99895)),f153(x99891,x99892)))+~P85(f341(f341(f343(f863(x99891,x99891)),x99893),f341(f163(f863(x99891,x99891)),f341(f341(f172(x99891,x99891),x99894),x99895))))+P85(f341(f341(f260(x99891,x99891,a850),f341(f341(f9(x99891,f864(f863(x99891,x99891),a850),f864(x99891,a850)),f341(f341(f10(f864(x99891,f864(f864(f863(x99891,x99891),a850),a850)),f864(f864(f863(x99891,x99891),a850),f864(x99891,a850)),x99891),f9(x99891,f864(f863(x99891,x99891),a850),a850)),f341(f341(f10(f864(x99891,f863(x99891,x99891)),f864(x99891,f864(f864(f863(x99891,x99891),a850),a850)),x99891),f341(f10(f863(x99891,x99891),f864(f864(f863(x99891,x99891),a850),a850),x99891),f343(f863(x99891,x99891)))),f250(x99891,x99891)))),x99892)),x99893)) % 19.23/19.04 [9442]~P85(f341(f341(f241(a857),x94423),x94422))+~P85(f341(f341(f242(a857),f341(f341(f89(a857),f341(f341(f90(a857),x94423),x94424)),x94421)),f341(f341(f89(a857),f341(f341(f90(a857),x94422),x94424)),x94425)))+P85(f341(f341(f242(a857),x94421),f341(f341(f89(a857),f341(f341(f90(a857),f341(f341(f3(a857),x94422),x94423)),x94424)),x94425))) % 19.23/19.04 [9443]~P85(f341(f341(f241(a857),x94433),x94432))+~P85(f341(f341(f241(a857),f341(f341(f89(a857),f341(f341(f90(a857),x94433),x94434)),x94431)),f341(f341(f89(a857),f341(f341(f90(a857),x94432),x94434)),x94435)))+P85(f341(f341(f241(a857),x94431),f341(f341(f89(a857),f341(f341(f90(a857),f341(f341(f3(a857),x94432),x94433)),x94434)),x94435))) % 19.23/19.04 [9465]~P85(f341(f341(f241(a857),x94651),x94654))+P85(f341(f341(f242(a857),f341(f341(f89(a857),f341(f341(f90(a857),x94651),x94652)),x94653)),f341(f341(f89(a857),f341(f341(f90(a857),x94654),x94652)),x94655)))+~P85(f341(f341(f242(a857),x94653),f341(f341(f89(a857),f341(f341(f90(a857),f341(f341(f3(a857),x94654),x94651)),x94652)),x94655))) % 19.23/19.04 [9466]~P85(f341(f341(f241(a857),x94661),x94664))+P85(f341(f341(f241(a857),f341(f341(f89(a857),f341(f341(f90(a857),x94661),x94662)),x94663)),f341(f341(f89(a857),f341(f341(f90(a857),x94664),x94662)),x94665)))+~P85(f341(f341(f241(a857),x94663),f341(f341(f89(a857),f341(f341(f90(a857),f341(f341(f3(a857),x94664),x94661)),x94662)),x94665))) % 19.23/19.04 [9576]~P85(f341(f341(f241(a857),x95762),x95761))+~P85(f341(f341(f242(a857),f341(f341(f89(a857),f341(f341(f90(a857),x95761),x95763)),x95764)),f341(f341(f89(a857),f341(f341(f90(a857),x95762),x95763)),x95765)))+P85(f341(f341(f242(a857),f341(f341(f89(a857),f341(f341(f90(a857),f341(f341(f3(a857),x95761),x95762)),x95763)),x95764)),x95765)) % 19.23/19.04 [9577]~P85(f341(f341(f241(a857),x95772),x95771))+~P85(f341(f341(f241(a857),f341(f341(f89(a857),f341(f341(f90(a857),x95771),x95773)),x95774)),f341(f341(f89(a857),f341(f341(f90(a857),x95772),x95773)),x95775)))+P85(f341(f341(f241(a857),f341(f341(f89(a857),f341(f341(f90(a857),f341(f341(f3(a857),x95771),x95772)),x95773)),x95774)),x95775)) % 19.23/19.04 [9623]~P85(f341(f341(f241(a857),x96234),x96231))+P85(f341(f341(f242(a857),f341(f341(f89(a857),f341(f341(f90(a857),x96231),x96232)),x96233)),f341(f341(f89(a857),f341(f341(f90(a857),x96234),x96232)),x96235)))+~P85(f341(f341(f242(a857),f341(f341(f89(a857),f341(f341(f90(a857),f341(f341(f3(a857),x96231),x96234)),x96232)),x96233)),x96235)) % 19.23/19.04 [9624]~P85(f341(f341(f241(a857),x96244),x96241))+P85(f341(f341(f241(a857),f341(f341(f89(a857),f341(f341(f90(a857),x96241),x96242)),x96243)),f341(f341(f89(a857),f341(f341(f90(a857),x96244),x96242)),x96245)))+~P85(f341(f341(f241(a857),f341(f341(f89(a857),f341(f341(f90(a857),f341(f341(f3(a857),x96241),x96244)),x96242)),x96243)),x96245)) % 19.23/19.04 [9850]~P13(x98501,x98502,x98505,x98503)+~P85(f341(f341(f343(f863(x98501,x98501)),x98504),x98505))+P85(f341(f341(f260(x98501,x98501,a850),f341(f341(f9(x98501,f864(x98501,x98502),f864(x98501,a850)),f341(f341(f10(f864(x98502,a850),f864(f864(x98501,x98502),f864(x98501,a850)),x98501),f10(x98502,a850,x98501)),f341(f341(f10(x98502,f864(x98502,a850),x98501),a338),x98503))),x98503)),x98504)) % 19.23/19.04 [7167]~P38(x71674,x71672,x71675,x71676)+P38(f35(x71671,x71673,x71674),x71672,x71675,x71676)+P85(f341(x71671,x71672)) % 19.23/19.04 [7247]~P38(x72472,x72474,x72475,x72476)+P38(f35(x72471,x72472,x72473),x72474,x72475,x72476)+~P85(f341(x72471,x72474)) % 19.23/19.04 [7338]P38(x73383,x73382,x73384,x73385)+~P38(f35(x73381,x73386,x73383),x73382,x73384,x73385)+P85(f341(x73381,x73382)) % 19.23/19.04 [7371]P38(x73711,x73712,x73713,x73714)+~P38(f35(x73715,x73711,x73716),x73712,x73713,x73714)+~P85(f341(x73715,x73712)) % 19.23/19.04 [7742]~P38(x77421,x77423,x77424,x77426)+~P38(x77422,x77426,x77424,x77425)+P38(f38(x77421,x77422),x77423,x77424,x77425) % 19.23/19.04 [7745]P38(x77451,x77452,x77453,x77454)+P38(x77455,x77452,x77453,x77454)+~P38(f35(x77456,x77451,x77455),x77452,x77453,x77454) % 19.23/19.04 [6720]~E(f341(x67204,x67205),f188(x67202))+E(f341(f175(x67201,x67202,x67203,x67204),x67205),f341(f235(x67202),x67206))+~E(f341(x67203,x67205),f341(f235(x67202),x67206)) % 19.23/19.04 [6826]~E(f341(x68263,x68266),f188(x68261))+E(f341(f237(f861(x68261),x68262,f188(x68261),x68263),f341(x68264,x68265)),f188(x68261))+~E(f341(x68264,x68265),f341(f235(x68262),x68266)) % 19.23/19.04 [7429]E(f341(x74291,x74292),f188(x74293))+~E(f341(f175(x74295,x74293,x74296,x74291),x74292),f341(f235(x74293),x74294))+E(f341(x74291,x74292),f341(f235(x74293),x74294)) % 19.23/19.04 [7466]~E(f341(f175(x74666,x74663,x74665,x74661),x74662),f341(f235(x74663),x74664))+E(f341(x74661,x74662),f341(f235(x74663),x74664))+E(f341(x74665,x74662),f341(f235(x74663),x74664)) % 19.23/19.04 [8355]~P20(x83556,x83551,x83552,x83554)+E(f341(f82(x83551,x83551,x83551,f341(x83552,x83553)),f341(x83554,x83555)),f341(f82(x83551,x83551,x83551,f341(x83554,x83555)),f341(x83552,x83553)))+~P85(f341(f71(x83556),x83555)) % 19.23/19.04 [8751]~P26(x87511,x87513,x87515,x87516)+~P26(x87513,x87512,x87514,f341(f312(x87511,x87513,x87515),x87516))+P26(x87511,x87512,f341(f82(x87513,x87512,x87511,x87514),x87515),x87516) % 19.23/19.04 [9256]~P85(f341(f341(x92563,x92562),x92566))+~P85(f341(f341(x92564,x92565),x92562))+P85(f341(f341(f343(x92561),x92562),f301(x92561,x92563,x92564,x92565,x92566))) % 19.23/19.04 [9257]~P85(f341(f341(x92574,x92572),x92576))+~P85(f341(f341(x92573,x92575),x92572))+P85(f341(f341(f343(x92571),x92572),f298(x92571,x92573,x92574,x92575,x92576))) % 19.23/19.04 [9366]E(x93661,x93662)+E(x93663,x93664)+~P85(f341(f341(f343(f863(f858(x93665),f858(x93665))),f341(f341(f250(f858(x93665),f858(x93665)),f341(f341(f146(x93665),x93663),x93661)),f341(f341(f146(x93665),x93664),x93662))),f152(x93665,x93666))) % 19.23/19.04 [9375]~E(x93752,x93754)+P85(f341(f341(f343(f863(f858(x93751),f858(x93751))),f341(f341(f250(f858(x93751),f858(x93751)),f341(f341(f146(x93751),x93752),x93753)),f341(f341(f146(x93751),x93754),x93755))),f141(x93751,x93756)))+~P85(f341(f341(f343(f863(f858(x93751),f858(x93751))),f341(f341(f250(f858(x93751),f858(x93751)),x93753),x93755)),f141(x93751,x93756))) % 19.23/19.04 [9376]~E(x93762,x93764)+P85(f341(f341(f343(f863(f858(x93761),f858(x93761))),f341(f341(f250(f858(x93761),f858(x93761)),f341(f341(f146(x93761),x93762),x93763)),f341(f341(f146(x93761),x93764),x93765))),f143(x93761,x93766)))+~P85(f341(f341(f343(f863(f858(x93761),f858(x93761))),f341(f341(f250(f858(x93761),f858(x93761)),x93763),x93765)),f143(x93761,x93766))) % 19.23/19.04 [9377]~E(x93772,x93774)+P85(f341(f341(f343(f863(f858(x93771),f858(x93771))),f341(f341(f250(f858(x93771),f858(x93771)),f341(f341(f146(x93771),x93772),x93773)),f341(f341(f146(x93771),x93774),x93775))),f152(x93771,x93776)))+~P85(f341(f341(f343(f863(f858(x93771),f858(x93771))),f341(f341(f250(f858(x93771),f858(x93771)),x93773),x93775)),f152(x93771,x93776))) % 19.23/19.04 [9378]~E(x93782,x93784)+P85(f341(f341(f343(f863(f858(x93781),f858(x93781))),f341(f341(f250(f858(x93781),f858(x93781)),f341(f341(f132(x93781),x93782),x93783)),f341(f341(f132(x93781),x93784),x93785))),f152(x93781,x93786)))+~P85(f341(f341(f343(f863(f858(x93781),f858(x93781))),f341(f341(f250(f858(x93781),f858(x93781)),x93783),x93785)),f152(x93781,x93786))) % 19.23/19.04 [9379]~E(x93793,x93795)+P85(f341(f341(f343(f863(f858(x93791),f858(x93791))),f341(f341(f250(f858(x93791),f858(x93791)),f341(f341(f132(x93791),x93792),x93793)),f341(f341(f132(x93791),x93794),x93795))),f152(x93791,x93796)))+~P85(f341(f341(f343(f863(f858(x93791),f858(x93791))),f341(f341(f250(f858(x93791),f858(x93791)),x93792),x93794)),f152(x93791,x93796))) % 19.23/19.04 [9431]E(x94311,x94312)+P85(f341(f341(f343(f863(f858(x94313),f858(x94313))),f341(f341(f250(f858(x94313),f858(x94313)),x94311),x94312)),f152(x94313,x94314)))+~P85(f341(f341(f343(f863(f858(x94313),f858(x94313))),f341(f341(f250(f858(x94313),f858(x94313)),f341(f341(f146(x94313),x94315),x94311)),f341(f341(f146(x94313),x94316),x94312))),f152(x94313,x94314))) % 19.23/19.04 [9578]~E(x95783,x95785)+P85(f341(f341(f343(f863(f858(x95781),f858(x95781))),f341(f341(f250(f858(x95781),f858(x95781)),f341(f341(f132(x95781),x95782),f341(f341(f146(x95781),x95783),f122(x95781)))),f341(f341(f132(x95781),x95784),f341(f341(f146(x95781),x95785),f122(x95781))))),f152(x95781,x95786)))+~P85(f341(f341(f343(f863(f858(x95781),f858(x95781))),f341(f341(f250(f858(x95781),f858(x95781)),x95782),x95784)),f152(x95781,x95786))) % 19.23/19.04 [9591]E(f341(x95911,x95912),f188(x95913))+~E(f341(f237(f861(x95916),x95913,f188(x95916),x95914),f341(x95911,x95912)),f188(x95916))+E(f341(x95914,f715(x95912,x95911,x95914,x95915,x95916,x95913)),f188(x95916)) % 19.23/19.04 [9592]E(f341(x95921,x95922),f188(x95923))+~E(f341(f237(f861(x95926),x95923,f188(x95926),x95924),f341(x95921,x95922)),f188(x95926))+E(f341(f235(x95923),f715(x95922,x95921,x95924,x95925,x95926,x95923)),f341(x95921,x95922)) % 19.23/19.04 [9627]E(x96271,x96272)+E(x96273,x96274)+~P85(f341(f341(f343(f863(f858(x96275),f858(x96275))),f341(f341(f250(f858(x96275),f858(x96275)),f341(f341(f132(x96275),x96273),f341(f341(f146(x96275),x96271),f122(x96275)))),f341(f341(f132(x96275),x96274),f341(f341(f146(x96275),x96272),f122(x96275))))),f152(x96275,x96276))) % 19.23/19.04 [9649]E(x96491,x96492)+~P85(f341(f341(f343(f863(f858(x96493),f858(x96493))),f341(f341(f250(f858(x96493),f858(x96493)),f341(f341(f132(x96493),x96491),f341(f341(f146(x96493),x96495),f122(x96493)))),f341(f341(f132(x96493),x96492),f341(f341(f146(x96493),x96496),f122(x96493))))),f152(x96493,x96494)))+P85(f341(f341(f343(f863(f858(x96493),f858(x96493))),f341(f341(f250(f858(x96493),f858(x96493)),x96491),x96492)),f152(x96493,x96494))) % 19.23/19.04 [9677]~P85(f341(f341(f343(f863(f864(x96771,a850),f864(x96771,a850))),f341(f341(f250(f864(x96771,a850),f864(x96771,a850)),x96772),x96774)),f334(x96771,x96776)))+~P85(f341(f341(f343(f863(f864(x96771,a850),f864(x96771,a850))),f341(f341(f250(f864(x96771,a850),f864(x96771,a850)),x96773),x96775)),f334(x96771,x96776)))+P85(f341(f341(f343(f863(f864(x96771,a850),f864(x96771,a850))),f341(f341(f250(f864(x96771,a850),f864(x96771,a850)),f341(f341(f110(f864(x96771,a850)),x96772),x96773)),f341(f341(f110(f864(x96771,a850)),x96774),x96775))),f334(x96771,x96776))) % 19.23/19.04 [5148]~E(f341(x51483,x51486),x51485)+~E(x51484,f341(f235(x51481),x51486))+E(f341(f341(f204(x51481,x51482),x51483),x51484),f341(f235(x51482),x51485)) % 19.23/19.04 [5545]~E(f341(f341(f132(x55451),x55456),x55453),x55455)+E(f341(f341(f132(x55451),x55452),x55453),f341(f341(f146(x55451),x55454),x55455))+~E(x55452,f341(f341(f146(x55451),x55454),x55456)) % 19.23/19.04 [5546]~E(f341(f341(f132(x55461),x55466),x55463),x55465)+E(f341(f341(f132(x55461),x55462),x55463),f341(f341(f132(x55461),x55464),x55465))+~E(x55462,f341(f341(f132(x55461),x55464),x55466)) % 19.23/19.04 [5548]E(f341(f341(f132(x55481),x55482),x55483),f341(f341(f146(x55481),x55484),x55485))+~E(f341(f341(f146(x55481),x55484),x55486),x55482)+~E(x55485,f341(f341(f132(x55481),x55486),x55483)) % 19.23/19.04 [5550]~E(f341(f341(f132(x55501),x55502),x55506),x55504)+E(f341(f341(f132(x55501),x55502),x55503),f341(f341(f132(x55501),x55504),x55505))+~E(x55503,f341(f341(f132(x55501),x55506),x55505)) % 19.23/19.04 [6713]E(f341(x67131,x67132),f341(x67133,x67132))+~E(f341(f341(f149(x67134,x67135),x67131),x67136),f341(f341(f149(x67134,x67135),x67133),x67136))+~P85(f341(f341(f343(x67134),x67132),f341(f163(x67134),x67136))) % 19.23/19.04 [7103]~P20(x71034,x71035,x71036,x71031)+E(f341(f341(x71031,x71032),x71033),f341(f341(f74(x71034,x71035,x71036),x71033),x71032))+~P85(f341(f71(x71034),x71032)) % 19.23/19.04 [7172]~E(x71722,f341(x71724,x71726))+~P85(f341(f341(f343(x71723),x71726),x71725))+P85(f341(f341(f343(x71721),x71722),f341(f312(x71723,x71721,x71724),x71725))) % 19.23/19.04 [7173]~E(f341(x71734,x71732),x71736)+~P85(f341(f341(f343(x71733),x71736),x71735))+P85(f341(f341(f343(x71731),x71732),f341(f314(x71731,x71733,x71734),x71735))) % 19.23/19.04 [7648]~P33(x76481,x76482,x76484,x76486)+P33(x76481,x76482,f341(f341(f146(x76481),x76483),x76484),f341(f341(f146(x76481),x76485),x76486))+~P85(f341(f341(x76482,x76483),x76485)) % 19.23/19.04 [8634]~P54(x86344,x86345,x86341,x86342,x86346)+E(f341(x86341,f341(x86342,x86343)),x86343)+~P85(f341(f341(f343(x86345),x86343),x86346)) % 19.23/19.04 [9368]E(x93681,x93682)+E(f341(f186(f858(x93683)),x93684),f341(f186(f858(x93683)),x93685))+~P85(f341(f341(f343(f863(f858(x93683),f858(x93683))),f341(f341(f250(f858(x93683),f858(x93683)),f341(f341(f146(x93683),x93681),x93684)),f341(f341(f146(x93683),x93682),x93685))),f141(x93683,x93686))) % 19.23/19.04 [9428]~P17(x94281,x94282,x94283)+E(f341(f341(f74(x94281,x94282,x94283),x94284),x94285),x94286)+~P85(f341(f76(x94281,x94282,x94283,x94284,x94285),x94286)) % 19.23/19.04 [9434]E(f341(f186(f858(x94341)),x94342),f341(f186(f858(x94341)),x94343))+P85(f341(f341(f343(f863(f858(x94341),f858(x94341))),f341(f341(f250(f858(x94341),f858(x94341)),x94342),x94343)),f141(x94341,x94344)))+~P85(f341(f341(f343(f863(f858(x94341),f858(x94341))),f341(f341(f250(f858(x94341),f858(x94341)),f341(f341(f146(x94341),x94345),x94342)),f341(f341(f146(x94341),x94346),x94343))),f141(x94341,x94344))) % 19.23/19.04 [9456]~P85(f341(f341(f343(f863(x94561,x94561)),f341(f341(f250(x94561,x94561),x94562),x94564)),f309(x94561,x94566)))+P85(f341(f341(f343(f863(f858(x94561),f858(x94561))),f341(f341(f250(f858(x94561),f858(x94561)),f341(f341(f146(x94561),x94562),x94563)),f341(f341(f146(x94561),x94564),x94565))),f309(f858(x94561),f152(x94561,x94566))))+~P85(f341(f341(f343(f863(f858(x94561),f858(x94561))),f341(f341(f250(f858(x94561),f858(x94561)),x94563),x94565)),f309(f858(x94561),f152(x94561,x94566)))) % 19.23/19.04 [9938]~P68(x99382)+E(f341(f341(f8(x99381,x99382),f341(f341(f10(f864(x99383,a850),x99382,x99381),f341(f8(x99383,x99382),x99384)),f341(f341(f10(f864(x99383,a850),f864(x99383,a850),x99381),f265(x99383)),f341(f341(f10(f864(x99383,a850),f864(x99383,a850),x99381),f341(f20(x99383,a850,a850),f341(f341(f10(a850,f864(a850,a850),x99383),a339),f341(f341(f9(x99383,f864(x99383,a850),a850),f343(x99383)),x99385)))),f341(f9(x99383,x99381,a850),f341(f341(f10(x99381,f864(x99381,a850),x99383),a338),x99386)))))),f341(f312(x99383,x99381,x99386),x99385)),f341(f341(f8(x99383,x99382),x99384),x99385))+~P85(f341(f71(x99383),x99385)) % 19.23/19.04 [6773]~P101(x67733)+P85(f341(x67732,x67735))+E(f341(f133(x67731,x67732),f341(f341(f144(x67731,x67733,x67734),x67735),x67736)),f341(f133(x67731,x67732),x67736)) % 19.23/19.04 [6775]P85(f341(x67751,x67752))+~E(f161(x67753,x67751,x67754),f341(f341(f250(f858(x67753),f858(x67753)),x67755),x67756))+~P85(f341(f341(f343(x67753),x67752),f341(f163(x67753),x67755))) % 19.23/19.04 [6823]~P85(f341(x68232,x68236))+~E(f161(x68231,x68232,x68233),f341(f341(f250(f858(x68231),f858(x68231)),x68234),x68235))+~P85(f341(f341(f343(x68231),x68236),f341(f163(x68231),x68235))) % 19.23/19.04 [7511]~P16(x75111,x75112,x75113)+~P85(f341(f71(x75111),x75116))+E(f341(f341(f74(x75111,x75112,x75113),x75114),f341(f341(f311(x75111),x75115),x75116)),f341(f341(f74(x75111,x75112,x75113),f341(f341(x75113,x75115),x75114)),x75116)) % 19.23/19.04 [7563]~P101(x75632)+~P85(f341(f341(f241(x75632),f341(x75633,x75634)),f341(x75633,x75635)))+E(f341(f341(f144(x75631,x75632,x75633),x75634),f341(f341(f146(x75631),x75635),x75636)),f341(f341(f146(x75631),x75634),f341(f341(f146(x75631),x75635),x75636))) % 19.23/19.04 [7679]E(x76791,x76792)+~E(f341(f341(f257(x76793,x76794),x76791),f341(f18(f864(x76794,a850),x76793),x76795)),f341(f341(f257(x76793,x76794),x76792),f341(f18(f864(x76794,a850),x76793),x76795)))+~P85(f341(f341(f343(x76794),x76796),x76795)) % 19.23/19.04 [7747]~P16(x77471,x77472,x77473)+~P85(f341(f71(x77471),x77476))+E(f341(f341(f74(x77471,x77472,x77473),x77474),f341(f341(f311(x77471),x77475),x77476)),f341(f341(x77473,x77475),f341(f341(f74(x77471,x77472,x77473),x77474),x77476))) % 19.23/19.04 [7863]~P17(x78631,x78632,x78633)+~P85(f341(f71(x78631),x78636))+E(f341(f341(f74(x78631,x78632,x78633),f341(f341(x78633,x78634),x78635)),x78636),f341(f341(x78633,x78634),f341(f341(f74(x78631,x78632,x78633),x78635),x78636))) % 19.23/19.04 [7931]~P21(x79312,x79315,x79316,x79311)+~P85(f341(f71(x79312),x79314))+E(f341(x79311,f341(f341(f311(x79312),x79313),x79314)),f341(f82(x79315,x79315,x79315,f341(x79311,x79314)),f341(x79316,x79313))) % 19.23/19.04 [7969]~P101(x79692)+P85(f341(f341(f241(x79692),f341(x79693,x79694)),f341(x79693,x79695)))+E(f341(f341(f144(x79691,x79692,x79693),x79694),f341(f341(f146(x79691),x79695),x79696)),f341(f341(f146(x79691),x79695),f341(f341(f144(x79691,x79692,x79693),x79694),x79696))) % 19.23/19.04 [8101]~E(f341(f186(f858(x81011)),x81015),f341(f186(f858(x81012)),x81016))+~E(f341(f186(f858(x81011)),x81013),f341(f186(f858(x81012)),x81014))+E(f341(f341(f132(f863(x81011,x81012)),f341(f341(f172(x81011,x81012),x81013),x81014)),f341(f341(f172(x81011,x81012),x81015),x81016)),f341(f341(f172(x81011,x81012),f341(f341(f132(x81011),x81013),x81015)),f341(f341(f132(x81012),x81014),x81016))) % 19.23/19.04 [8208]~E(x82082,f341(f312(x82083,x82081,x82084),x82086))+P85(f341(f341(f241(f864(x82081,a850)),x82082),f341(f312(x82083,x82081,x82084),x82085)))+~P85(f341(f341(f241(f864(x82083,a850)),x82086),x82085)) % 19.23/19.04 [8311]~P101(x83115)+E(f341(x83111,x83112),f341(x83111,x83113))+E(f341(f341(f144(x83114,x83115,x83111),x83112),f341(f341(f144(x83114,x83115,x83111),x83113),x83116)),f341(f341(f144(x83114,x83115,x83111),x83113),f341(f341(f144(x83114,x83115,x83111),x83112),x83116))) % 19.23/19.04 [8348]~P26(x83483,x83481,x83484,x83485)+P26(x83483,x83481,f341(f341(f341(f81(x83483,x83481),x83484),x83486),x83482),x83485)+P85(f341(f341(f343(x83481),x83482),f341(f312(x83483,x83481,x83484),x83485))) % 19.23/19.04 [8493]~P85(f341(f341(f343(x84932),x84934),f341(x84936,x84933)))+~P85(f341(f341(f343(x84931),x84933),x84935))+P85(f341(f341(f343(f863(x84931,x84932)),f341(f341(f250(x84931,x84932),x84933),x84934)),f341(f341(f257(x84931,x84932),x84935),x84936))) % 19.23/19.04 [8905]~P71(x89052)+~P26(x89054,x89051,x89055,x89056)+E(f341(f341(f11(x89051,x89052),x89053),f341(f312(x89054,x89051,x89055),x89056)),f341(f341(f11(x89054,x89052),f341(f82(x89051,x89052,x89054,x89053),x89055)),x89056)) % 19.23/19.04 [8906]~P68(x89062)+~P26(x89064,x89061,x89065,x89066)+E(f341(f341(f8(x89061,x89062),x89063),f341(f312(x89064,x89061,x89065),x89066)),f341(f341(f8(x89064,x89062),f341(f82(x89061,x89062,x89064,x89063),x89065)),x89066)) % 19.23/19.05 [9143]~E(f341(f341(f341(a194,x91435),f42(x91431)),f341(f341(a195,x91434),x91431)),f341(f341(f341(a194,x91436),f42(x91431)),f341(f341(a195,x91434),x91431)))+~P85(f341(f341(f192(x91433),f341(f341(f341(a194,x91434),f42(x91431)),f341(x91432,x91434))),x91436))+P85(f341(f341(f192(f34(x91431,x91432,x91433)),x91434),f341(f341(f341(a194,x91435),f42(x91431)),f341(f341(a195,x91434),x91431)))) % 19.23/19.05 [9147]~P20(x91473,x91471,x91476,x91472)+~P85(f341(f71(x91473),x91474))+E(f341(f82(x91471,x91471,x91471,f341(x91472,f341(f341(f3(f864(x91473,a850)),x91474),f341(f341(f311(x91473),x91475),f185(f864(x91473,a850)))))),f341(x91476,x91475)),f341(x91472,f341(f341(f311(x91473),x91475),x91474))) % 19.23/19.05 [9532]~E(f341(f341(f341(a194,f341(f341(a196,x95325),f341(a195,x95324))),x95321),f341(f341(a195,x95325),a27)),f341(f341(f341(a194,f341(f341(a196,x95326),f341(a195,x95324))),x95321),f341(f341(a195,x95326),a27)))+~P85(f341(f341(f192(f341(a29,x95322)),f341(f341(f341(a194,f341(f341(a196,x95324),a197)),f42(a28)),f341(x95323,x95324))),x95326))+P85(f341(f341(f192(f33(x95321,x95322,x95323)),x95324),f341(f341(f341(a194,f341(f341(a196,x95325),f341(a195,x95324))),x95321),f341(f341(a195,x95325),a27)))) % 19.23/19.05 [9706]~E(f341(f312(x97062,x97064,x97066),f248(f864(x97062,a850))),f248(f864(x97064,a850)))+~E(f341(f312(x97061,x97063,x97065),f248(f864(x97061,a850))),f248(f864(x97063,a850)))+E(f341(f312(f863(x97061,x97062),f863(x97063,x97064),f261(x97061,x97063,x97062,x97064,x97065,x97066)),f248(f864(f863(x97061,x97062),a850))),f248(f864(f863(x97063,x97064),a850))) % 19.23/19.05 [9768]~P26(x97683,x97684,x97685,f341(x97686,f697(x97686,x97685,x97684,x97683,x97682,x97681)))+P26(x97683,x97684,x97685,f341(f341(f55(x97682,f864(x97683,a850)),x97681),x97686))+E(x97681,f185(f864(x97682,a850))) % 19.23/19.05 [9826]P26(x98266,x98265,x98264,f341(f341(f55(x98262,f864(x98266,a850)),x98261),x98263))+E(x98261,f185(f864(x98262,a850)))+P85(f341(f341(f343(x98262),f697(x98263,x98264,x98265,x98266,x98262,x98261)),x98261)) % 19.23/19.05 [9834]P85(f341(f341(f343(x98341),f629(x98342,x98343,x98344,x98345,x98346,x98341)),x98346))+P85(f341(f341(f241(f864(f863(x98341,x98344),a850)),f341(f341(f257(x98341,x98344),x98346),x98343)),f341(f341(f257(x98341,x98344),x98345),x98342)))+~P85(f341(f341(f241(f864(x98341,a850)),x98346),x98345)) % 19.23/19.05 [9955]~P85(f341(f341(f241(f864(x99552,a850)),f341(x99554,f629(x99556,x99554,x99552,x99555,x99553,x99551))),f341(x99556,f629(x99556,x99554,x99552,x99555,x99553,x99551))))+~P85(f341(f341(f241(f864(x99551,a850)),x99553),x99555))+P85(f341(f341(f241(f864(f863(x99551,x99552),a850)),f341(f341(f257(x99551,x99552),x99553),x99554)),f341(f341(f257(x99551,x99552),x99555),x99556))) % 19.23/19.05 [7696]~P85(f341(x76961,x76965))+~P85(f341(x76966,x76964))+P85(f341(x76961,f341(f259(x76962,x76963),f341(f341(f250(x76962,x76963),x76964),x76965)))) % 19.23/19.05 [7697]~P85(f341(x76971,x76974))+~P85(f341(x76976,x76975))+P85(f341(x76971,f341(f249(x76972,x76973),f341(f341(f250(x76972,x76973),x76974),x76975)))) % 19.23/19.05 [7752]~P85(f341(f341(x77524,x77526),x77525))+~P85(f341(f341(f343(x77521),x77526),x77523))+P85(f341(f341(f341(f54(x77521,f864(x77522,a850)),x77523),x77524),x77525)) % 19.23/19.05 [7785]~E(f341(f186(f858(x77851)),x77853),f341(f186(f858(x77854)),x77855))+~E(f341(f171(x77851,x77854,f341(f341(f172(x77851,x77854),x77853),x77855)),x77852),f341(f235(x77854),x77856))+P85(f341(f341(f343(x77851),x77852),f341(f163(x77851),x77853))) % 19.23/19.05 [8054]~P85(f341(f341(f343(x80541),x80542),f341(x80545,x80546)))+~P85(f341(f341(f343(x80543),x80546),x80544))+P85(f341(f341(f343(x80541),x80542),f341(f341(f54(x80543,f864(x80541,a850)),x80544),x80545))) % 19.23/19.05 [8094]P85(f341(f341(x80941,x80942),x80943))+~P85(f341(f341(x80944,x80942),x80943))+~P85(f341(f341(f241(f864(x80945,f864(x80946,a850))),x80944),x80941)) % 19.23/19.05 [8232]P85(f341(f341(x82321,x82322),x82323))+~P85(f341(f341(f343(x82324),x82322),x82325))+~P85(f341(f341(f341(f55(x82324,f864(x82326,a850)),x82325),x82321),x82323)) % 19.23/19.05 [8371]P85(f341(f341(f343(x83711),x83712),f341(x83713,x83714)))+~P85(f341(f341(f343(x83715),x83714),x83716))+~P85(f341(f341(f343(x83711),x83712),f341(f341(f55(x83715,f864(x83711,a850)),x83716),x83713))) % 19.23/19.05 [8616]~P13(x86164,x86165,x86166,x86161)+E(f341(x86161,x86162),f341(x86161,x86163))+~P85(f341(f341(f343(f863(x86164,x86164)),f341(f341(f250(x86164,x86164),x86162),x86163)),x86166)) % 19.23/19.05 [8647]P85(f341(f341(f241(f864(x86471,a850)),x86472),f341(x86473,x86474)))+~P85(f341(f341(f343(x86475),x86474),x86476))+~P85(f341(f341(f241(f864(x86471,a850)),x86472),f341(f341(f55(x86475,f864(x86471,a850)),x86476),x86473))) % 19.23/19.05 [8672]~P52(x86723,x86724,f341(f287(x86724,x86723),x86725))+E(x86721,f185(f864(x86722,a850)))+E(f341(f341(f55(x86722,f864(x86723,a850)),x86721),f341(f341(f10(f864(x86724,a850),f864(x86723,a850),x86722),f286(x86724,x86723,x86725)),x86726)),f341(f286(x86724,x86723,x86725),f341(f341(f55(x86722,f864(x86724,a850)),x86721),x86726))) % 19.23/19.05 [8744]P85(f341(f341(f343(x87441),x87442),f341(f286(x87443,x87441,x87444),x87445)))+~P85(f341(f341(f343(x87443),x87446),x87445))+~P85(f341(f341(f343(f863(x87443,x87441)),f341(f341(f250(x87443,x87441),x87446),x87442)),x87444)) % 19.23/19.05 [9023]P85(f341(f341(f241(f864(x90231,a850)),f341(f286(x90232,x90231,x90233),x90234)),f341(f286(x90232,x90231,x90235),x90236)))+~P85(f341(f341(f241(f864(x90232,a850)),x90234),x90236))+~P85(f341(f341(f241(f864(f863(x90232,x90231),a850)),x90233),x90235)) % 19.23/19.05 [9180]~P85(f341(f341(f343(x91802),x91806),x91804))+~P85(f341(f341(f241(f864(x91801,a850)),x91803),x91805))+P85(f341(f341(f241(f864(f863(x91801,x91802),a850)),f341(f341(f257(x91801,x91802),x91803),f341(f18(f864(x91802,a850),x91801),x91804))),f341(f341(f257(x91801,x91802),x91805),f341(f18(f864(x91802,a850),x91801),x91804)))) % 19.23/19.05 [9327]~E(x93273,x93275)+P85(f341(f341(f343(f863(f858(x93271),f858(x93271))),f341(f341(f250(f858(x93271),f858(x93271)),f341(f341(f146(x93271),x93272),x93273)),f341(f341(f146(x93271),x93274),x93275))),f152(x93271,x93276)))+~P85(f341(f341(f343(f863(x93271,x93271)),f341(f341(f250(x93271,x93271),x93272),x93274)),x93276)) % 19.23/19.05 [9332]~E(f341(f186(f858(x93321)),x93325),f341(f186(f858(x93322)),x93326))+E(f177(x93321,x93322,f178(x93321,x93322,x93323,f341(f341(f3(f864(x93321,a850)),x93324),f341(f163(x93321),x93325))),x93325,x93326),f178(x93321,x93322,f177(x93321,x93322,x93323,x93325,x93326),x93324))+~P85(f341(f341(f241(f864(x93321,a850)),f341(f163(x93321),x93325)),x93324)) % 19.23/19.05 [9333]~E(f341(f186(f858(x93331)),x93333),f341(f186(f858(x93331)),x93335))+P85(f341(f341(f343(f863(f858(x93331),f858(x93331))),f341(f341(f250(f858(x93331),f858(x93331)),f341(f341(f146(x93331),x93332),x93333)),f341(f341(f146(x93331),x93334),x93335))),f141(x93331,x93336)))+~P85(f341(f341(f343(f863(x93331,x93331)),f341(f341(f250(x93331,x93331),x93332),x93334)),x93336)) % 19.23/19.05 [9360]P85(f341(f341(f343(f863(x93601,x93601)),f341(f341(f250(x93601,x93601),x93602),x93603)),f341(f341(f179(f863(x93601,x93601),a850),f341(a121,x93604)),x93605)))+~P85(f341(f341(f343(f863(x93601,x93601)),f341(f341(f250(x93601,x93601),x93606),x93603)),x93605))+~P85(f341(f341(f343(f863(x93601,x93601)),f341(f341(f250(x93601,x93601),x93602),x93606)),f341(f341(f179(f863(x93601,x93601),a850),x93604),x93605))) % 19.23/19.05 [9361]P85(f341(f341(f343(f863(x93611,x93611)),f341(f341(f250(x93611,x93611),x93612),x93613)),f341(f341(f179(f863(x93611,x93611),a850),f341(a121,x93614)),x93615)))+~P85(f341(f341(f343(f863(x93611,x93611)),f341(f341(f250(x93611,x93611),x93612),x93616)),x93615))+~P85(f341(f341(f343(f863(x93611,x93611)),f341(f341(f250(x93611,x93611),x93616),x93613)),f341(f341(f179(f863(x93611,x93611),a850),x93614),x93615))) % 19.23/19.05 [9364]~P85(f341(f341(f343(x93644),x93645),x93646))+P85(f341(f341(f241(f864(x93641,a850)),x93642),x93643))+~P85(f341(f341(f241(f864(f863(x93641,x93644),a850)),f341(f341(f257(x93641,x93644),x93642),f341(f18(f864(x93644,a850),x93641),x93646))),f341(f341(f257(x93641,x93644),x93643),f341(f18(f864(x93644,a850),x93641),x93646)))) % 19.23/19.05 [9405]E(x94051,x94052)+~P85(f341(f341(f343(f863(f858(x94053),f858(x94053))),f341(f341(f250(f858(x94053),f858(x94053)),f341(f341(f146(x94053),x94051),x94055)),f341(f341(f146(x94053),x94052),x94056))),f141(x94053,x94054)))+P85(f341(f341(f343(f863(x94053,x94053)),f341(f341(f250(x94053,x94053),x94051),x94052)),x94054)) % 19.23/19.05 [9406]E(x94061,x94062)+~P85(f341(f341(f343(f863(f858(x94063),f858(x94063))),f341(f341(f250(f858(x94063),f858(x94063)),f341(f341(f146(x94063),x94061),x94065)),f341(f341(f146(x94063),x94062),x94066))),f143(x94063,x94064)))+P85(f341(f341(f343(f863(x94063,x94063)),f341(f341(f250(x94063,x94063),x94061),x94062)),x94064)) % 19.23/19.05 [9407]E(x94071,x94072)+~P85(f341(f341(f343(f863(f858(x94073),f858(x94073))),f341(f341(f250(f858(x94073),f858(x94073)),f341(f341(f146(x94073),x94071),x94075)),f341(f341(f146(x94073),x94072),x94076))),f152(x94073,x94074)))+P85(f341(f341(f343(f863(x94073,x94073)),f341(f341(f250(x94073,x94073),x94071),x94072)),x94074)) % 19.23/19.05 [9441]P85(f341(f341(f343(f863(f858(x94411),f858(x94411))),f341(f341(f250(f858(x94411),f858(x94411)),f341(f341(f146(x94411),x94412),x94413)),f341(f341(f146(x94411),x94414),x94415))),f153(x94411,x94416)))+~P85(f341(f341(f343(f863(f858(x94411),f858(x94411))),f341(f341(f250(f858(x94411),f858(x94411)),x94413),x94415)),f153(x94411,x94416)))+~P85(f341(f341(f343(f863(x94411,x94411)),f341(f341(f250(x94411,x94411),x94412),x94414)),x94416)) % 19.23/19.05 [9463]P85(f341(x94631,x94632))+~P85(f341(x94631,f418(x94631,x94633,x94634,x94635,x94636)))+~P85(f341(f341(f343(x94636),x94632),f341(f341(f54(x94635,f864(x94636,a850)),x94634),x94633))) % 19.23/19.05 [9468]~P85(f341(f341(f343(f863(f858(x94681),f858(x94681))),f341(f341(f250(f858(x94681),f858(x94681)),f341(f341(f146(x94681),x94682),x94685)),f341(f341(f146(x94681),x94683),x94686))),f141(x94681,x94684)))+P85(f341(f341(f343(f863(f858(x94681),f858(x94681))),f341(f341(f250(f858(x94681),f858(x94681)),x94685),x94686)),f141(x94681,x94684)))+P85(f341(f341(f343(f863(x94681,x94681)),f341(f341(f250(x94681,x94681),x94682),x94683)),x94684)) % 19.23/19.05 [9469]~P85(f341(f341(f343(f863(f858(x94691),f858(x94691))),f341(f341(f250(f858(x94691),f858(x94691)),f341(f341(f146(x94691),x94692),x94695)),f341(f341(f146(x94691),x94693),x94696))),f143(x94691,x94694)))+P85(f341(f341(f343(f863(f858(x94691),f858(x94691))),f341(f341(f250(f858(x94691),f858(x94691)),x94695),x94696)),f143(x94691,x94694)))+P85(f341(f341(f343(f863(x94691,x94691)),f341(f341(f250(x94691,x94691),x94692),x94693)),x94694)) % 19.23/19.05 [9470]~P85(f341(f341(f343(f863(f858(x94701),f858(x94701))),f341(f341(f250(f858(x94701),f858(x94701)),f341(f341(f146(x94701),x94702),x94705)),f341(f341(f146(x94701),x94703),x94706))),f152(x94701,x94704)))+P85(f341(f341(f343(f863(f858(x94701),f858(x94701))),f341(f341(f250(f858(x94701),f858(x94701)),x94705),x94706)),f152(x94701,x94704)))+P85(f341(f341(f343(f863(x94701,x94701)),f341(f341(f250(x94701,x94701),x94702),x94703)),x94704)) % 19.23/19.05 [9548]P85(f341(x95481,x95482))+P85(f341(f341(f343(x95483),f419(x95481,x95484,x95485,x95483,x95486)),x95485))+~P85(f341(f341(f343(x95486),x95482),f341(f341(f54(x95483,f864(x95486,a850)),x95485),x95484))) % 19.23/19.05 [9554]~E(x95542,x95544)+P85(f341(f341(f343(f863(f858(x95541),f858(x95541))),f341(f341(f250(f858(x95541),f858(x95541)),f341(f341(f132(x95541),x95542),f341(f341(f146(x95541),x95543),f122(x95541)))),f341(f341(f132(x95541),x95544),f341(f341(f146(x95541),x95545),f122(x95541))))),f152(x95541,x95546)))+~P85(f341(f341(f343(f863(x95541,x95541)),f341(f341(f250(x95541,x95541),x95543),x95545)),x95546)) % 19.23/19.05 [9641]E(x96411,x96412)+~P85(f341(f341(f343(f863(f858(x96413),f858(x96413))),f341(f341(f250(f858(x96413),f858(x96413)),f341(f341(f132(x96413),x96415),f341(f341(f146(x96413),x96411),f122(x96413)))),f341(f341(f132(x96413),x96416),f341(f341(f146(x96413),x96412),f122(x96413))))),f152(x96413,x96414)))+P85(f341(f341(f343(f863(x96413,x96413)),f341(f341(f250(x96413,x96413),x96411),x96412)),x96414)) % 19.23/19.05 [9666]~P85(f341(f341(f343(f863(f858(x96661),f858(x96661))),f341(f341(f250(f858(x96661),f858(x96661)),f341(f341(f132(x96661),x96665),f341(f341(f146(x96661),x96662),f122(x96661)))),f341(f341(f132(x96661),x96666),f341(f341(f146(x96661),x96663),f122(x96661))))),f152(x96661,x96664)))+P85(f341(f341(f343(f863(f858(x96661),f858(x96661))),f341(f341(f250(f858(x96661),f858(x96661)),x96665),x96666)),f152(x96661,x96664)))+P85(f341(f341(f343(f863(x96661,x96661)),f341(f341(f250(x96661,x96661),x96662),x96663)),x96664)) % 19.23/19.05 [9678]P85(f341(x96781,x96782))+P85(f341(f341(f343(x96783),f418(x96781,x96784,x96785,x96786,x96783)),f341(x96784,f419(x96781,x96784,x96785,x96786,x96783))))+~P85(f341(f341(f343(x96783),x96782),f341(f341(f54(x96786,f864(x96783,a850)),x96785),x96784))) % 19.23/19.05 [8757]~P17(x87573,x87574,x87571)+~P85(f341(f71(x87573),x87576))+E(f341(f341(x87571,x87572),f341(f341(f74(x87573,x87574,x87571),x87575),f341(f341(f3(f864(x87573,a850)),x87576),f341(f341(f311(x87573),x87572),f185(f864(x87573,a850)))))),f341(f341(f74(x87573,x87574,x87571),x87575),f341(f341(f311(x87573),x87572),x87576))) % 19.23/19.05 [8856]~E(f341(f171(x88561,x88562,x88564),x88565),f341(f235(x88562),x88566))+~P85(f341(f341(x88563,x88565),x88566))+E(f341(f171(x88561,x88562,f341(f133(f863(x88561,x88562),f341(f260(x88561,x88562,a850),x88563)),x88564)),x88565),f341(f235(x88562),x88566)) % 19.23/19.05 [9029]~P85(f341(f341(f343(x90295),x90293),x90296))+P85(f341(f341(f241(f864(x90291,a850)),f341(x90292,x90293)),x90294))+~P85(f341(f341(f241(f864(x90291,a850)),f341(f341(f54(x90295,f864(x90291,a850)),x90296),x90292)),x90294)) % 19.23/19.05 [9617]~P9(x96171,x96175,x96174)+P85(f341(f341(f343(f863(x96171,x96171)),f341(f341(f250(x96171,x96171),x96172),x96173)),x96174))+~P85(f341(f341(f343(x96171),x96176),f341(f341(f111(f864(x96171,a850)),f341(f286(x96171,x96171,x96174),f341(f341(f311(x96171),x96172),f185(f864(x96171,a850))))),f341(f286(x96171,x96171,x96174),f341(f341(f311(x96171),x96173),f185(f864(x96171,a850))))))) % 19.23/19.05 [8526]~P123(x85262)+~E(f341(f341(f89(x85262),f341(f341(f90(x85262),x85264),x85265)),x85261),f341(f341(f89(x85262),f341(f341(f90(x85262),x85263),x85265)),x85266))+E(x85261,f341(f341(f89(x85262),f341(f341(f90(x85262),f341(f341(f3(x85262),x85263),x85264)),x85265)),x85266)) % 19.23/19.05 [8527]~P123(x85271)+~E(f341(f341(f89(x85271),f341(f341(f90(x85271),x85272),x85274)),x85275),f341(f341(f89(x85271),f341(f341(f90(x85271),x85273),x85274)),x85276))+E(f341(f341(f89(x85271),f341(f341(f90(x85271),f341(f341(f3(x85271),x85272),x85273)),x85274)),x85275),x85276) % 19.23/19.05 [8675]~P123(x86751)+E(f341(f341(f89(x86751),f341(f341(f90(x86751),x86752),x86753)),x86754),f341(f341(f89(x86751),f341(f341(f90(x86751),x86755),x86753)),x86756))+~E(x86756,f341(f341(f89(x86751),f341(f341(f90(x86751),f341(f341(f3(x86751),x86752),x86755)),x86753)),x86754)) % 19.23/19.05 [8676]~P123(x86761)+E(f341(f341(f89(x86761),f341(f341(f90(x86761),x86762),x86763)),x86764),f341(f341(f89(x86761),f341(f341(f90(x86761),x86765),x86763)),x86766))+~E(f341(f341(f89(x86761),f341(f341(f90(x86761),f341(f341(f3(x86761),x86762),x86765)),x86763)),x86764),x86766) % 19.23/19.05 [8968]~P85(f341(f341(x89684,x89685),x89686))+~P85(f341(f341(x89683,x89685),x89686))+P85(f341(f341(f341(f341(f111(f864(x89681,f864(x89682,a850))),x89683),x89684),x89685),x89686)) % 19.23/19.05 [9198]P85(f341(f341(x91981,x91982),x91983))+P85(f341(f341(x91984,x91982),x91983))+~P85(f341(f341(f341(f341(f110(f864(x91985,f864(x91986,a850))),x91984),x91981),x91982),x91983)) % 19.23/19.05 [9485]~P131(x94851)+~P85(f341(f341(f242(x94851),f341(f341(f89(x94851),f341(f341(f90(x94851),x94854),x94855)),x94852)),f341(f341(f89(x94851),f341(f341(f90(x94851),x94853),x94855)),x94856)))+P85(f341(f341(f242(x94851),x94852),f341(f341(f89(x94851),f341(f341(f90(x94851),f341(f341(f3(x94851),x94853),x94854)),x94855)),x94856))) % 19.23/19.05 [9486]~P131(x94861)+~P85(f341(f341(f241(x94861),f341(f341(f89(x94861),f341(f341(f90(x94861),x94864),x94865)),x94862)),f341(f341(f89(x94861),f341(f341(f90(x94861),x94863),x94865)),x94866)))+P85(f341(f341(f241(x94861),x94862),f341(f341(f89(x94861),f341(f341(f90(x94861),f341(f341(f3(x94861),x94863),x94864)),x94865)),x94866))) % 19.23/19.05 [9504]~P131(x95041)+P85(f341(f341(f242(x95041),f341(f341(f89(x95041),f341(f341(f90(x95041),x95042),x95043)),x95044)),f341(f341(f89(x95041),f341(f341(f90(x95041),x95045),x95043)),x95046)))+~P85(f341(f341(f242(x95041),x95044),f341(f341(f89(x95041),f341(f341(f90(x95041),f341(f341(f3(x95041),x95045),x95042)),x95043)),x95046))) % 19.23/19.05 [9505]~P131(x95051)+P85(f341(f341(f241(x95051),f341(f341(f89(x95051),f341(f341(f90(x95051),x95052),x95053)),x95054)),f341(f341(f89(x95051),f341(f341(f90(x95051),x95055),x95053)),x95056)))+~P85(f341(f341(f241(x95051),x95054),f341(f341(f89(x95051),f341(f341(f90(x95051),f341(f341(f3(x95051),x95055),x95052)),x95053)),x95056))) % 19.23/19.05 [9610]~P131(x96101)+~P85(f341(f341(f242(x96101),f341(f341(f89(x96101),f341(f341(f90(x96101),x96102),x96104)),x96105)),f341(f341(f89(x96101),f341(f341(f90(x96101),x96103),x96104)),x96106)))+P85(f341(f341(f242(x96101),f341(f341(f89(x96101),f341(f341(f90(x96101),f341(f341(f3(x96101),x96102),x96103)),x96104)),x96105)),x96106)) % 19.23/19.05 [9611]~P131(x96111)+~P85(f341(f341(f241(x96111),f341(f341(f89(x96111),f341(f341(f90(x96111),x96112),x96114)),x96115)),f341(f341(f89(x96111),f341(f341(f90(x96111),x96113),x96114)),x96116)))+P85(f341(f341(f241(x96111),f341(f341(f89(x96111),f341(f341(f90(x96111),f341(f341(f3(x96111),x96112),x96113)),x96114)),x96115)),x96116)) % 19.23/19.05 [9651]~P131(x96511)+P85(f341(f341(f242(x96511),f341(f341(f89(x96511),f341(f341(f90(x96511),x96512),x96513)),x96514)),f341(f341(f89(x96511),f341(f341(f90(x96511),x96515),x96513)),x96516)))+~P85(f341(f341(f242(x96511),f341(f341(f89(x96511),f341(f341(f90(x96511),f341(f341(f3(x96511),x96512),x96515)),x96513)),x96514)),x96516)) % 19.23/19.05 [9652]~P131(x96521)+P85(f341(f341(f241(x96521),f341(f341(f89(x96521),f341(f341(f90(x96521),x96522),x96523)),x96524)),f341(f341(f89(x96521),f341(f341(f90(x96521),x96525),x96523)),x96526)))+~P85(f341(f341(f241(x96521),f341(f341(f89(x96521),f341(f341(f90(x96521),f341(f341(f3(x96521),x96522),x96525)),x96523)),x96524)),x96526)) % 19.23/19.05 [9820]~P68(x98202)+~P85(f341(f71(x98201),x98206))+E(f341(f341(f8(x98201,x98202),f341(f341(f20(x98201,x98202,x98202),f341(f341(f20(x98201,x98202,f864(x98202,x98202)),f341(f341(f10(a850,f864(x98202,f864(x98202,x98202)),x98201),f105(x98202)),x98203)),x98204)),x98205)),x98206),f341(f341(f89(x98202),f341(f341(f8(x98201,x98202),x98204),f341(f341(f111(f864(x98201,a850)),x98206),f341(f265(x98201),x98203)))),f341(f341(f8(x98201,x98202),x98205),f341(f341(f111(f864(x98201,a850)),x98206),f341(f88(f864(x98201,a850)),f341(f265(x98201),x98203)))))) % 19.23/19.05 [9886]P85(f341(f341(f343(x98862),x98864),x98866))+P85(f341(f341(f343(x98862),x98865),x98866))+E(f341(f314(x98861,x98862,f341(f341(f9(x98861,x98862,x98862),f341(f341(f9(x98861,x98862,f864(x98862,x98862)),f341(f341(f10(a850,f864(x98862,f864(x98862,x98862)),x98861),f105(x98862)),f341(f341(f9(x98861,f864(x98861,a850),a850),f343(x98861)),x98863))),x98864)),x98865)),x98866),f185(f864(x98861,a850))) % 19.23/19.05 [9887]P85(f341(f341(f343(x98872),x98875),x98876))+~P85(f341(f341(f343(x98872),x98874),x98876))+E(f341(f314(x98871,x98872,f341(f341(f9(x98871,x98872,x98872),f341(f341(f9(x98871,x98872,f864(x98872,x98872)),f341(f341(f10(a850,f864(x98872,f864(x98872,x98872)),x98871),f105(x98872)),f341(f341(f9(x98871,f864(x98871,a850),a850),f343(x98871)),x98873))),x98874)),x98875)),x98876),x98873) % 19.23/19.05 [9888]P85(f341(f341(f343(x98882),x98884),x98886))+~P85(f341(f341(f343(x98882),x98885),x98886))+E(f341(f314(x98881,x98882,f341(f341(f9(x98881,x98882,x98882),f341(f341(f9(x98881,x98882,f864(x98882,x98882)),f341(f341(f10(a850,f864(x98882,f864(x98882,x98882)),x98881),f105(x98882)),f341(f341(f9(x98881,f864(x98881,a850),a850),f343(x98881)),x98883))),x98884)),x98885)),x98886),f341(f88(f864(x98881,a850)),x98883)) % 19.23/19.05 [9889]~P85(f341(f341(f343(x98892),x98894),x98896))+~P85(f341(f341(f343(x98892),x98895),x98896))+E(f341(f314(x98891,x98892,f341(f341(f9(x98891,x98892,x98892),f341(f341(f9(x98891,x98892,f864(x98892,x98892)),f341(f341(f10(a850,f864(x98892,f864(x98892,x98892)),x98891),f105(x98892)),f341(f341(f9(x98891,f864(x98891,a850),a850),f343(x98891)),x98893))),x98894)),x98895)),x98896),f248(f864(x98891,a850))) % 19.23/19.05 [8551]E(x85511,x85512)+~P54(x85514,x85515,x85513,x85516,x85517)+~E(f341(x85513,x85511),f341(x85513,x85512)) % 19.23/19.05 [6932]E(f341(f237(f861(x69321),x69322,f188(x69321),x69323),f341(x69324,x69325)),f341(f235(x69321),x69326))+~E(f341(x69324,x69325),f341(f235(x69322),x69327))+~E(f341(x69323,x69327),f341(f235(x69321),x69326)) % 19.23/19.05 [8573]~P12(x85736,x85735,x85737,x85734,x85731)+E(f341(f341(x85731,x85732),x85733),x85734)+P85(f341(f71(x85735),x85733)) % 19.23/19.05 [9352]P40(x93521,x93522,x93523,x93524,x93525,f341(f341(x93523,x93526),x93527))+~E(f341(f341(x93523,x93526),x93527),x93524)+~E(x93525,f185(f864(x93521,a850))) % 19.23/19.05 [9524]~P85(f341(x95246,x95243))+~P85(f341(f341(f343(f863(x95242,x95242)),f341(f341(f250(x95242,x95242),x95244),x95245)),f341(x95247,x95243)))+P85(f341(f341(f343(f863(f863(x95241,x95242),f863(x95241,x95242))),f341(f341(f250(f863(x95241,x95242),f863(x95241,x95242)),f341(f341(f250(x95241,x95242),x95243),x95244)),f341(f341(f250(x95241,x95242),x95243),x95245))),f284(x95241,x95242,x95246,x95247))) % 19.23/19.05 [9704]~P26(x97043,x97041,x97044,f248(f864(x97043,a850)))+E(f341(f171(x97041,x97042,f341(f341(f149(f863(x97043,x97042),f863(x97041,x97042)),f341(f260(x97043,x97042,f863(x97041,x97042)),f341(f341(f10(x97041,f864(x97042,f863(x97041,x97042)),x97043),f250(x97041,x97042)),x97044))),x97045)),f341(x97044,x97046)),f341(f235(x97042),x97047))+~E(f341(f171(x97043,x97042,x97045),x97046),f341(f235(x97042),x97047)) % 19.23/19.05 [9940]~P40(x99402,x99407,x99403,x99406,x99401,f341(f341(x99403,x99405),x99404))+E(f341(f341(x99403,f357(x99404,x99405,x99401,x99406,x99403,x99407,x99402)),f360(x99404,x99405,x99401,x99406,x99403,x99407,x99402)),f341(f341(x99403,x99405),x99404))+E(x99401,f185(f864(x99402,a850))) % 19.23/19.05 [9941]~P40(x99417,x99416,x99411,x99414,x99415,f341(f341(x99411,x99412),x99413))+E(f341(f341(x99411,f357(x99413,x99412,x99415,x99414,x99411,x99416,x99417)),f360(x99413,x99412,x99415,x99414,x99411,x99416,x99417)),f341(f341(x99411,x99412),x99413))+E(f341(f341(x99411,x99412),x99413),x99414) % 19.23/19.05 [8579]~P38(x85793,f341(f341(f341(a194,x85794),f42(x85791)),f341(x85792,x85794)),x85795,x85797)+P38(f34(x85791,x85792,x85793),x85794,x85795,f341(f341(f341(a194,x85796),f42(x85791)),f341(f341(a195,x85794),x85791)))+~E(f341(f341(f341(a194,x85796),f42(x85791)),f341(f341(a195,x85794),x85791)),f341(f341(f341(a194,x85797),f42(x85791)),f341(f341(a195,x85794),x85791))) % 19.23/19.05 [9268]~P38(f341(a29,x92682),f341(f341(f341(a194,f341(f341(a196,x92684),a197)),f42(a28)),f341(x92683,x92684)),x92685,x92687)+P38(f33(x92681,x92682,x92683),x92684,x92685,f341(f341(f341(a194,f341(f341(a196,x92686),f341(a195,x92684))),x92681),f341(f341(a195,x92686),a27)))+~E(f341(f341(f341(a194,f341(f341(a196,x92686),f341(a195,x92684))),x92681),f341(f341(a195,x92686),a27)),f341(f341(f341(a194,f341(f341(a196,x92687),f341(a195,x92684))),x92681),f341(f341(a195,x92687),a27))) % 19.23/19.05 [9595]~P85(f341(f76(x95951,x95954,x95955,x95956,x95953),x95957))+P85(f341(f76(x95951,x95954,x95955,x95956,f341(f341(f311(x95951),x95952),x95953)),f341(f341(x95955,x95952),x95957)))+P85(f341(f341(f343(x95951),x95952),x95953)) % 19.23/19.05 [9967]~P40(x99672,x99677,x99676,x99675,x99671,f341(f341(x99676,x99674),x99673))+E(x99671,f185(f864(x99672,a850)))+P85(f341(f341(f343(x99672),f357(x99673,x99674,x99671,x99675,x99676,x99677,x99672)),x99671)) % 19.23/19.05 [9968]~P40(x99685,x99687,x99681,x99684,x99686,f341(f341(x99681,x99682),x99683))+E(f341(f341(x99681,x99682),x99683),x99684)+P85(f341(f341(f343(x99685),f357(x99683,x99682,x99686,x99684,x99681,x99687,x99685)),x99686)) % 19.23/19.05 [6712]~E(x67125,x67127)+~E(x67126,x67124)+E(f341(f341(f341(f341(f81(x67121,f861(x67122)),x67123),x67124),f341(f235(x67122),x67125)),x67126),f341(f235(x67122),x67127)) % 19.23/19.05 [6847]E(x68471,x68472)+~E(f341(x68475,x68471),f341(f235(x68474),x68477))+E(f341(f341(f341(f341(f81(x68473,f861(x68474)),x68475),x68472),f341(f235(x68474),x68476)),x68471),f341(f235(x68474),x68477)) % 19.23/19.05 [7589]E(x75891,x75892)+~E(x75893,x75894)+~E(f341(f341(f341(f341(f81(x75895,f861(x75896)),x75897),x75894),f341(f235(x75896),x75891)),x75893),f341(f235(x75896),x75892)) % 19.23/19.05 [7654]E(x76541,x76542)+E(f341(x76543,x76544),f341(f235(x76545),x76541))+~E(f341(f341(f341(f341(f81(x76546,f861(x76545)),x76543),x76547),f341(f235(x76545),x76542)),x76544),f341(f235(x76545),x76541)) % 19.23/19.05 [7655]E(x76551,x76552)+E(f341(x76553,x76551),f341(f235(x76554),x76555))+~E(f341(f341(f341(f341(f81(x76556,f861(x76554)),x76553),x76552),f341(f235(x76554),x76557)),x76551),f341(f235(x76554),x76555)) % 19.23/19.05 [8778]~P22(x87784,x87785,x87786,x87787,x87781)+~P85(f341(f71(x87785),x87783))+E(f341(f341(x87781,x87782),x87783),f341(f341(f341(f75(x87784,x87785,x87786),x87782),x87787),x87783)) % 19.23/19.05 [8779]~P12(x87794,x87795,x87796,x87797,x87791)+~P85(f341(f71(x87795),x87793))+E(f341(f341(x87791,x87792),x87793),f341(f341(f341(f75(x87794,x87795,x87796),x87792),x87797),x87793)) % 19.23/19.05 [9320]~P25(x93201,x93202,f341(f341(f311(f856(x93201)),f341(f341(f341(f100(x93201),x93203),x93204),x93207)),f185(f864(f856(x93201),a850))))+P25(x93201,x93202,f341(f341(f311(f856(x93201)),f341(f341(f341(f100(x93201),x93203),f38(x93204,x93205)),x93206)),f185(f864(f856(x93201),a850))))+~P25(x93201,x93202,f341(f341(f311(f856(x93201)),f341(f341(f341(f100(x93201),x93207),x93205),x93206)),f185(f864(f856(x93201),a850)))) % 19.23/19.05 [9499]~P24(x94993,x94994,x94995,x94997,x94996,x94991)+~P85(f341(f71(x94994),x94992))+E(f341(x94991,x94992),f341(f341(f341(f75(x94993,x94994,x94995),x94996),x94997),x94992)) % 19.23/19.05 [9646]P40(x96461,x96462,x96463,x96464,x96465,f341(f341(x96463,x96466),x96467))+~P40(x96461,x96462,x96463,x96464,f341(f341(f3(f864(x96461,a850)),x96465),f341(f341(f311(x96461),x96466),f185(f864(x96461,a850)))),x96467)+~P85(f341(f341(f343(x96461),x96466),x96465)) % 19.23/19.05 [9915]~P25(x99151,x99152,f341(f341(f311(f856(x99151)),f341(f341(f341(f100(x99151),f101(x99151,x99153,x99154)),x99155),x99157)),f185(f864(f856(x99151),a850))))+P25(x99151,x99152,f341(f341(f311(f856(x99151)),f341(f341(f341(f100(x99151),x99153),f35(x99154,x99155,x99156)),x99157)),f185(f864(f856(x99151),a850))))+~P25(x99151,x99152,f341(f341(f311(f856(x99151)),f341(f341(f341(f100(x99151),f101(x99151,x99153,f341(f82(a850,a850,a855,a337),x99154))),x99156),x99157)),f185(f864(f856(x99151),a850)))) % 19.23/19.05 [9985]P85(f341(f341(x99857,f846(x99854,x99855,x99851,x99856,x99853,x99852,x99857)),f847(x99854,x99855,x99851,x99856,x99853,x99852,x99857)))+~P85(f341(f341(x99857,f341(f259(x99852,x99853),x99856)),f341(f249(x99852,x99853),x99856)))+P85(f341(x99851,f341(f341(f260(x99852,x99853,x99854),x99855),x99856))) % 19.23/19.05 [9994]~P40(x99942,x99943,x99944,x99945,x99941,f341(f341(x99944,x99947),x99946))+P40(x99942,x99943,x99944,x99945,f341(f341(f3(f864(x99942,a850)),x99941),f341(f341(f311(x99942),f357(x99946,x99947,x99941,x99945,x99944,x99943,x99942)),f185(f864(x99942,a850)))),f360(x99946,x99947,x99941,x99945,x99944,x99943,x99942))+E(x99941,f185(f864(x99942,a850))) % 19.23/19.05 [9995]~P40(x99955,x99956,x99951,x99954,x99957,f341(f341(x99951,x99952),x99953))+P40(x99955,x99956,x99951,x99954,f341(f341(f3(f864(x99955,a850)),x99957),f341(f341(f311(x99955),f357(x99953,x99952,x99957,x99954,x99951,x99956,x99955)),f185(f864(x99955,a850)))),f360(x99953,x99952,x99957,x99954,x99951,x99956,x99955))+E(f341(f341(x99951,x99952),x99953),x99954) % 19.23/19.05 [10014]~P85(f341(x100141,f341(f341(x100145,f847(x100144,x100145,x100141,x100146,x100143,x100142,x100147)),f846(x100144,x100145,x100141,x100146,x100143,x100142,x100147))))+~P85(f341(f341(x100147,f341(f259(x100142,x100143),x100146)),f341(f249(x100142,x100143),x100146)))+P85(f341(x100141,f341(f341(f260(x100142,x100143,x100144),x100145),x100146))) % 19.23/19.05 [9071]E(f177(x90711,x90712,x90713,x90714,f341(f341(f154(x90712,x90715),x90716),x90717)),f177(x90711,x90712,x90713,x90714,x90715))+~P85(f341(f341(f242(a857),x90716),f341(f186(f858(x90712)),x90715)))+~P85(f341(f341(f241(a857),f341(f186(f858(x90711)),x90714)),x90716)) % 19.23/19.05 [9341]P85(f341(f341(f241(f864(f863(x93411,x93412),a850)),f341(f341(f290(x93411,x93413,x93412),x93414),x93415)),f341(f341(f290(x93411,x93413,x93412),x93416),x93417)))+~P85(f341(f341(f241(f864(f863(x93413,x93412),a850)),x93415),x93417))+~P85(f341(f341(f241(f864(f863(x93411,x93413),a850)),x93414),x93416)) % 19.23/19.05 [9657]~P85(f341(f341(f343(x96571),x96576),x96575))+P85(f341(f76(x96571,x96572,x96573,x96574,x96575),f341(f341(x96573,x96576),x96577)))+~P85(f341(f76(x96571,x96572,x96573,x96574,f341(f341(f3(f864(x96571,a850)),x96575),f341(f341(f311(x96571),x96576),f185(f864(x96571,a850))))),x96577)) % 19.23/19.05 [10045]~P139(x100451)+~P26(f863(x100452,x100453),x100451,f341(f260(x100452,x100453,x100451),f341(f341(f9(x100452,f864(x100453,x100451),f864(x100453,x100451)),f341(f341(f10(f864(x100451,x100451),f864(f864(x100453,x100451),f864(x100453,x100451)),x100452),f10(x100451,x100451,x100453)),f341(f341(f10(x100451,f864(x100451,x100451),x100452),f90(x100451)),x100454))),x100455)),f341(f341(f257(x100452,x100453),x100456),f341(f18(f864(x100453,a850),x100452),x100457)))+E(f341(f341(f8(x100451,x100451),f41(x100451)),f341(f265(x100451),f341(f341(f10(f864(x100452,a850),a850,x100451),f96(x100452)),f341(f341(f10(f864(x100452,f864(x100453,a850)),f864(x100452,a850),x100451),f341(f10(f864(x100453,a850),a850,x100452),f96(x100453))),f341(f341(f9(x100451,f864(x100452,f864(x100453,a850)),f864(x100452,f864(x100453,a850))),f341(f341(f10(f864(x100452,f864(f864(x100453,a850),f864(x100453,a850))),f864(f864(x100452,f864(x100453,a850)),f864(x100452,f864(x100453,a850))),x100451),f20(x100452,f864(x100453,a850),f864(x100453,a850))),f341(f341(f10(f864(x100452,f864(x100453,f864(a850,a850))),f864(x100452,f864(f864(x100453,a850),f864(x100453,a850))),x100451),f341(f10(f864(x100453,f864(a850,a850)),f864(f864(x100453,a850),f864(x100453,a850)),x100452),f20(x100453,a850,a850))),f341(f341(f10(f864(x100452,f864(x100453,a850)),f864(x100452,f864(x100453,f864(a850,a850))),x100451),f341(f10(f864(x100453,a850),f864(x100453,f864(a850,a850)),x100452),f341(f10(a850,f864(a850,a850),x100453),a339))),f341(f341(f9(x100451,f864(x100452,f864(x100453,x100451)),f864(x100452,f864(x100453,a850))),f341(f341(f10(f864(f864(x100453,x100451),f864(x100453,a850)),f864(f864(x100452,f864(x100453,x100451)),f864(x100452,f864(x100453,a850))),x100451),f10(f864(x100453,x100451),f864(x100453,a850),x100452)),f341(f341(f10(f864(x100451,a850),f864(f864(x100453,x100451),f864(x100453,a850)),x100451),f10(x100451,a850,x100453)),a338))),f341(f341(f9(x100452,f864(x100453,x100451),f864(x100453,x100451)),f341(f341(f10(f864(x100451,x100451),f864(f864(x100453,x100451),f864(x100453,x100451)),x100452),f10(x100451,x100451,x100453)),f341(f341(f10(x100451,f864(x100451,x100451),x100452),f90(x100451)),x100454))),x100455)))))),f341(f341(f9(x100452,f864(x100453,a850),f864(x100453,a850)),f341(f341(f10(f864(a850,a850),f864(f864(x100453,a850),f864(x100453,a850)),x100452),f10(a850,a850,x100453)),f341(f341(f10(a850,f864(a850,a850),x100452),a339),f341(f341(f9(x100452,f864(x100452,a850),a850),f343(x100452)),x100456)))),f341(f341(f9(x100453,f864(x100453,a850),a850),f343(x100453)),x100457))))))),f341(f341(f90(x100451),f341(f341(f8(x100452,x100451),x100454),x100456)),f341(f341(f8(x100453,x100451),x100455),x100457))) % 19.23/19.05 [9734]P50(x97341,x97342,x97343,x97344,x97345,x97346,x97347)+~P85(f341(f341(x97344,x97346),x97348))+~P85(f341(f341(x97345,x97348),x97347)) % 19.23/19.05 [9128]~P20(x91288,x91281,x91283,x91285)+~P85(f341(f71(x91288),x91286))+E(f341(f82(x91281,x91281,x91282,f341(x91283,x91284)),f341(f82(x91281,x91281,x91282,f341(x91285,x91286)),x91287)),f341(f82(x91281,x91281,x91282,f341(x91285,x91286)),f341(f82(x91281,x91281,x91282,f341(x91283,x91284)),x91287))) % 19.23/19.05 [9490]~P23(x94907,x94902,x94905,x94908,x94906,x94901)+~P85(f341(f71(x94902),x94904))+E(f341(x94901,f341(f341(f311(x94902),x94903),x94904)),f341(f341(x94905,f341(x94906,x94903)),f341(x94901,x94904))) % 19.23/19.05 [9606]~P26(x96062,x96064,x96066,x96068)+~P26(x96061,x96063,x96065,x96067)+P26(f863(x96061,x96062),f863(x96063,x96064),f261(x96061,x96063,x96062,x96064,x96065,x96066),f341(f341(f257(x96061,x96062),x96067),f341(f18(f864(x96062,a850),x96061),x96068))) % 19.23/19.05 [9283]P85(f341(f341(f343(f863(x92831,x92832)),f341(f341(f250(x92831,x92832),x92833),x92834)),f341(f341(f290(x92831,x92835,x92832),x92836),x92837)))+~P85(f341(f341(f343(f863(x92831,x92835)),f341(f341(f250(x92831,x92835),x92833),x92838)),x92836))+~P85(f341(f341(f343(f863(x92835,x92832)),f341(f341(f250(x92835,x92832),x92838),x92834)),x92837)) % 19.23/19.05 [9473]~P85(f341(f341(f241(f864(f863(x94733,x94732),a850)),x94735),f341(f341(f257(x94733,x94732),x94738),f341(f18(f864(x94732,a850),x94733),x94737))))+~P85(f341(f341(f241(f864(f863(x94731,x94733),a850)),x94734),f341(f341(f257(x94731,x94733),x94736),f341(f18(f864(x94733,a850),x94731),x94738))))+P85(f341(f341(f241(f864(f863(x94731,x94732),a850)),f341(f341(f290(x94731,x94733,x94732),x94734),x94735)),f341(f341(f257(x94731,x94732),x94736),f341(f18(f864(x94732,a850),x94731),x94737)))) % 19.23/19.05 [9519]~E(x95193,x95195)+P85(f341(f341(f343(f863(f863(x95191,x95192),f863(x95191,x95192))),f341(f341(f250(f863(x95191,x95192),f863(x95191,x95192)),f341(f341(f250(x95191,x95192),x95193),x95194)),f341(f341(f250(x95191,x95192),x95195),x95196))),f335(x95191,x95192,x95197,x95198)))+~P85(f341(f341(f343(f863(x95192,x95192)),f341(f341(f250(x95192,x95192),x95194),x95196)),x95198)) % 19.23/19.05 [9625]E(x96251,x96252)+~P85(f341(f341(f343(f863(f863(x96253,x96255),f863(x96253,x96255))),f341(f341(f250(f863(x96253,x96255),f863(x96253,x96255)),f341(f341(f250(x96253,x96255),x96251),x96256)),f341(f341(f250(x96253,x96255),x96252),x96257))),f335(x96253,x96255,x96254,x96258)))+P85(f341(f341(f343(f863(x96253,x96253)),f341(f341(f250(x96253,x96253),x96251),x96252)),x96254)) % 19.23/19.05 [9640]~P85(f341(f341(f343(f863(f863(x96401,x96405),f863(x96401,x96405))),f341(f341(f250(f863(x96401,x96405),f863(x96401,x96405)),f341(f341(f250(x96401,x96405),x96402),x96406)),f341(f341(f250(x96401,x96405),x96403),x96407))),f335(x96401,x96405,x96404,x96408)))+P85(f341(f341(f343(f863(x96401,x96401)),f341(f341(f250(x96401,x96401),x96402),x96403)),x96404))+P85(f341(f341(f343(f863(x96405,x96405)),f341(f341(f250(x96405,x96405),x96406),x96407)),x96408)) % 19.23/19.05 [9549]~P24(x95497,x95495,x95491,x95498,x95492,x95494)+~P85(f341(f71(x95495),x95496))+E(f341(f341(x95491,f341(x95492,x95493)),f341(x95494,f341(f341(f3(f864(x95495,a850)),x95496),f341(f341(f311(x95495),x95493),f185(f864(x95495,a850)))))),f341(x95494,f341(f341(f311(x95495),x95493),x95496))) % 19.23/19.05 [9088]~P85(f341(f341(f341(x90885,x90888),x90886),x90887))+~P85(f341(f341(f343(x90881),x90888),x90884))+P85(f341(f341(f341(f341(f54(x90881,f864(x90882,f864(x90883,a850))),x90884),x90885),x90886),x90887)) % 19.23/19.05 [9271]P85(f341(f341(f341(x92711,x92712),x92713),x92714))+~P85(f341(f341(f343(x92715),x92712),x92716))+~P85(f341(f341(f341(f341(f55(x92715,f864(x92717,f864(x92718,a850))),x92716),x92711),x92713),x92714)) % 19.23/19.05 [9464]~P22(x94643,x94642,x94644,x94648,x94641)+~P85(f341(f71(x94642),x94647))+E(f341(f341(x94641,f341(f341(f20(x94642,x94643,x94643),f341(f341(f10(x94643,f864(x94643,x94643),x94642),x94644),x94645)),x94646)),x94647),f341(f341(x94644,f341(f341(x94641,x94645),x94647)),f341(f341(x94641,x94646),x94647))) % 19.23/19.05 [9712]~E(f341(f312(x97122,x97124,x97126),x97128),x971210)+~E(f341(f312(x97121,x97123,x97125),x97127),x97129)+E(f341(f312(f863(x97121,x97122),f863(x97123,x97124),f261(x97121,x97123,x97122,x97124,x97125,x97126)),f341(f341(f257(x97121,x97122),x97127),f341(f18(f864(x97122,a850),x97121),x97128))),f341(f341(f257(x97123,x97124),x97129),f341(f18(f864(x97124,a850),x97123),x971210))) % 19.23/19.05 [4748]~P101(x47482)+~P15(x47482,x47481)+P15(x47482,f123(x47482,x47481))+E(x47481,f122(x47482)) % 19.23/19.05 [4982]~P6(x49822)+E(f12(x49822,x49821),f53(x49822,x49821))+E(x49821,f185(f864(x49822,a850)))+~P85(f341(f71(x49822),x49821)) % 19.23/19.05 [4983]~P6(x49832)+E(f15(x49832,x49831),f52(x49832,x49831))+E(x49831,f185(f864(x49832,a850)))+~P85(f341(f71(x49832),x49831)) % 19.23/19.05 [5920]~P95(x59202)+E(x59201,f185(f864(x59202,a850)))+P85(f341(f341(f241(x59202),f12(x59202,x59201)),f15(x59202,x59201)))+~P85(f341(f71(x59202),x59201)) % 19.23/19.05 [5934]~P37(x59342)+~P37(x59341)+E(x59341,x59342)+~E(f341(f312(a1,a857,a114),x59341),f341(f312(a1,a857,a114),x59342)) % 19.23/19.05 [8949]~P113(x89491)+~P85(f341(f341(f343(x89491),x89492),f119(x89491)))+P85(f341(f341(f242(x89491),f341(f341(f89(x89491),f341(f341(f89(x89491),f87(x89491)),x89492)),x89492)),f2(x89491)))+~P85(f341(f341(f242(x89491),x89492),f2(x89491))) % 19.23/19.05 [9169]~P113(x91691)+~P85(f341(f341(f343(x91691),x91692),f119(x91691)))+~P85(f341(f341(f242(x91691),f341(f341(f89(x91691),f341(f341(f89(x91691),f87(x91691)),x91692)),x91692)),f2(x91691)))+P85(f341(f341(f242(x91691),x91692),f2(x91691))) % 19.23/19.05 [4801]~P106(x48012)+~P139(x48012)+E(x48011,f2(a857))+E(f341(f341(f251(x48012),f2(x48012)),x48011),f2(x48012)) % 19.23/19.05 [4805]~P106(x48051)+~P139(x48051)+~E(x48052,f2(a857))+E(f341(f341(f251(x48051),f2(x48051)),x48052),f87(x48051)) % 19.23/19.05 [4969]~P135(x49692)+E(x49691,f87(x49692))+E(x49691,f341(f88(x49692),f87(x49692)))+~E(f341(f341(f90(x49692),x49691),x49691),f87(x49692)) % 19.23/19.05 [5210]~P82(x52102)+E(x52101,f2(x52102))+E(f91(x52102,x52101),f341(f88(x52102),f87(x52102)))+P85(f341(f341(f242(x52102),f2(x52102)),x52101)) % 19.23/19.05 [5442]~P82(x54422)+E(f91(x54422,x54421),f87(x54422))+E(x54421,f2(x54422))+~P85(f341(f341(f242(x54422),f2(x54422)),x54421)) % 19.23/19.05 [5451]E(x54511,x54512)+~E(f341(f113(a857),x54511),f341(f113(a857),x54512))+P85(f341(a191,f341(f113(a1),x54512)))+P85(f341(a191,f341(f113(a1),x54511))) % 19.23/19.05 [5497]~P88(x54971)+~E(x54972,f2(x54971))+E(f341(f341(f89(x54971),x54972),x54972),f2(x54971))+~P85(f341(f341(f343(x54971),x54972),f119(x54971))) % 19.23/19.05 [5534]E(x55341,f2(a1))+~E(f341(f341(f51(a1),x55342),x55341),f2(a1))+P85(f341(f341(f242(a1),x55341),x55342))+P85(f341(f341(f242(a1),x55342),x55341)) % 19.23/19.05 [5563]E(x55631,f2(a1))+~E(f341(f341(f51(a1),x55632),x55631),f2(a1))+P85(f341(f341(f241(a1),x55632),f2(a1)))+P85(f341(f341(f242(a1),x55632),x55631)) % 19.23/19.05 [5595]E(x55951,f2(a1))+~E(f341(f341(f51(a1),x55952),x55951),f2(a1))+P85(f341(f341(f241(a1),f2(a1)),x55952))+P85(f341(f341(f242(a1),x55951),x55952)) % 19.23/19.05 [5632]~P88(x56322)+E(x56321,f2(x56322))+~E(f341(f341(f89(x56322),x56321),x56321),f2(x56322))+~P85(f341(f341(f343(x56322),x56321),f119(x56322))) % 19.23/19.05 [5699]E(f341(f113(a857),x56991),f341(f113(a857),x56992))+~E(f341(f113(a1),x56992),f2(a1))+P85(f341(a191,f341(f113(a1),x56992)))+~P85(f341(a191,f341(f113(a1),x56991))) % 19.23/19.05 [5728]~E(f341(f113(a857),x57282),f341(f113(a857),x57281))+E(f341(f113(a1),x57281),f2(a1))+P85(f341(a191,f341(f113(a1),x57281)))+~P85(f341(a191,f341(f113(a1),x57282))) % 19.23/19.05 [5737]~P101(x57372)+E(x57371,f185(f864(x57372,a850)))+~P85(f341(f71(x57372),x57371))+P85(f341(f341(f343(x57372),f16(x57372,x57371)),x57371)) % 19.23/19.05 [5738]~P101(x57382)+E(x57381,f185(f864(x57382,a850)))+~P85(f341(f71(x57382),x57381))+P85(f341(f341(f343(x57382),f17(x57382,x57381)),x57381)) % 19.23/19.05 [5901]~P113(x59011)+~P89(x59011)+P85(f341(f341(f242(x59011),f2(x59011)),f341(f113(x59011),x59012)))+~P85(f341(f341(f242(a1),a92),x59012)) % 19.23/19.05 [5902]~P113(x59021)+~P89(x59021)+P85(f341(f341(f241(x59021),f2(x59021)),f341(f113(x59021),x59022)))+~P85(f341(f341(f241(a1),a92),x59022)) % 19.23/19.05 [5919]~P113(x59191)+~P89(x59191)+E(f341(f84(x59191),f341(f113(x59191),x59192)),f341(f113(x59191),x59192))+P85(f341(f341(f242(x59191),f341(f113(x59191),x59192)),f2(x59191))) % 19.23/19.05 [5961]E(x59611,x59612)+~E(f341(a114,x59611),f341(a114,x59612))+~P85(f341(f341(f241(a1),f2(a1)),x59612))+~P85(f341(f341(f241(a1),f2(a1)),x59611)) % 19.23/19.05 [6157]~P89(x61572)+~P113(x61572)+~P85(f341(f341(f242(x61572),f2(x61572)),f341(f113(x61572),x61571)))+P85(f341(f341(f242(a1),a92),x61571)) % 19.23/19.05 [6158]~P89(x61582)+~P113(x61582)+~P85(f341(f341(f241(x61582),f2(x61582)),f341(f113(x61582),x61581)))+P85(f341(f341(f241(a1),a92),x61581)) % 19.23/19.05 [6163]~P113(x61631)+~P89(x61631)+P85(f341(f341(f242(x61631),f341(f113(x61631),x61632)),f2(x61631)))+~P85(f341(f341(f242(a1),x61632),a92)) % 19.23/19.05 [6164]~P113(x61641)+~P89(x61641)+P85(f341(f341(f241(x61641),f341(f113(x61641),x61642)),f2(x61641)))+~P85(f341(f341(f241(a1),x61642),a92)) % 19.23/19.05 [6493]~P89(x64932)+~P113(x64932)+~P85(f341(f341(f242(x64932),f341(f113(x64932),x64931)),f2(x64932)))+P85(f341(f341(f242(a1),x64931),a92)) % 19.23/19.05 [6494]~P89(x64942)+~P113(x64942)+~P85(f341(f341(f241(x64942),f341(f113(x64942),x64941)),f2(x64942)))+P85(f341(f341(f241(a1),x64941),a92)) % 19.23/19.05 [6585]~P113(x65851)+~P89(x65851)+E(f341(f84(x65851),f341(f113(x65851),x65852)),f341(f88(x65851),f341(f113(x65851),x65852)))+~P85(f341(f341(f242(x65851),f341(f113(x65851),x65852)),f2(x65851))) % 19.23/19.05 [6602]E(f341(f113(a857),x66021),f341(f113(a857),x66022))+~E(f341(f113(a1),x66022),f2(a1))+~P85(f341(f341(f241(a1),f341(f113(a1),x66021)),f2(a1)))+~P85(f341(a191,f341(f113(a1),x66021))) % 19.23/19.05 [7012]P85(f341(f341(f288(a857),f341(a114,x70121)),f341(a114,x70122)))+~P85(f341(f341(f241(a1),f2(a1)),x70122))+~P85(f341(f341(f241(a1),f2(a1)),x70121))+~P85(f341(f341(f288(a1),x70121),x70122)) % 19.23/19.05 [7254]~P85(f341(f341(f288(a857),f341(a114,x72541)),f341(a114,x72542)))+~P85(f341(f341(f241(a1),f2(a1)),x72542))+~P85(f341(f341(f241(a1),f2(a1)),x72541))+P85(f341(f341(f288(a1),x72541),x72542)) % 19.23/19.05 [7517]~P101(x75172)+E(x75171,f185(f864(x75172,a850)))+~P85(f341(f71(x75172),x75171))+P85(f341(f341(f241(x75172),f14(x75172,f245(x75172),x75171)),f13(x75172,f240(x75172),x75171))) % 19.23/19.05 [7842]~P7(x78421)+~P37(x78422)+P85(f341(f341(f343(a1),x78421),x78422))+~P85(f341(f341(f343(a857),f341(a114,x78421)),f341(f312(a1,a857,a114),x78422))) % 19.23/19.05 [5734]~P136(x57342)+E(x57341,f2(a1))+E(f341(f88(x57342),f341(f112(x57342),f341(f88(a1),x57341))),f341(f112(x57342),x57341))+~P85(f341(f341(f242(a1),x57341),f2(a1))) % 19.23/19.05 [5810]~P88(x58101)+~P89(x58101)+~P32(x58101,f341(f113(x58101),x58102))+P32(x58101,f341(f113(x58101),f341(f341(f89(a1),x58102),x58102))) % 19.23/19.05 [6147]~P69(x61472)+E(x61471,f185(f864(x61472,a850)))+E(f17(x61472,f341(f312(x61472,x61472,f88(x61472)),x61471)),f341(f88(x61472),f16(x61472,x61471)))+~P85(f341(f71(x61472),x61471)) % 19.23/19.05 [6148]~P69(x61482)+E(x61481,f185(f864(x61482,a850)))+E(f16(x61482,f341(f312(x61482,x61482,f88(x61482)),x61481)),f341(f88(x61482),f17(x61482,x61481)))+~P85(f341(f71(x61482),x61481)) % 19.23/19.05 [6178]~P88(x61781)+~P89(x61781)+P32(x61781,f341(f113(x61781),x61782))+~P32(x61781,f341(f113(x61781),f341(f341(f89(a1),x61782),x61782))) % 19.23/19.05 [6272]E(x62721,f2(a1))+E(f341(a66,f65(f341(f88(a1),x62721),f341(f88(a1),x62722))),f61(x62721,x62722))+P85(f341(f341(f241(a1),f2(a1)),x62722))+~P85(f341(f341(f241(a1),f2(a1)),x62721)) % 19.23/19.05 [8596]~P37(x85962)+~P37(x85961)+P85(f341(f341(f242(f864(a857,a850)),f341(f312(a1,a857,a114),x85961)),f341(f312(a1,a857,a114),x85962)))+~P85(f341(f341(f242(f864(a1,a850)),x85961),x85962)) % 19.23/19.05 [8873]~P37(x88732)+~P37(x88731)+~P85(f341(f341(f242(f864(a857,a850)),f341(f312(a1,a857,a114),x88731)),f341(f312(a1,a857,a114),x88732)))+P85(f341(f341(f242(f864(a1,a850)),x88731),x88732)) % 19.23/19.05 [8874]~P37(x88742)+~P37(x88741)+~P85(f341(f341(f241(f864(a857,a850)),f341(f312(a1,a857,a114),x88741)),f341(f312(a1,a857,a114),x88742)))+P85(f341(f341(f241(f864(a1,a850)),x88741),x88742)) % 19.23/19.05 [9312]E(x93121,f2(a1))+E(x93122,f2(a1))+E(f341(f341(f95(a1,f863(a1,a1)),f341(f341(a220,x93122),x93121)),f341(f341(f20(a1,a1,f863(a1,a1)),f341(f341(f10(a1,f864(a1,f863(a1,a1)),a1),f250(a1,a1)),f341(f51(a1),x93122))),f341(f51(a1),x93121))),f218(x93122,x93121))+P85(f341(f341(f242(a1),x93121),f2(a1))) % 19.23/19.05 [8161]~P89(x81612)+~P113(x81612)+~P85(f341(f341(f242(x81612),f341(f113(x81612),x81611)),f87(x81612)))+P85(f341(f341(f242(a1),x81611),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106))) % 19.23/19.05 [8162]~P89(x81622)+~P113(x81622)+~P85(f341(f341(f241(x81622),f341(f113(x81622),x81621)),f87(x81622)))+P85(f341(f341(f241(a1),x81621),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106))) % 19.23/19.05 [8436]~P113(x84361)+~P89(x84361)+P85(f341(f341(f242(x84361),f341(f113(x84361),x84362)),f87(x84361)))+~P85(f341(f341(f242(a1),x84362),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106))) % 19.23/19.05 [8437]~P113(x84371)+~P89(x84371)+P85(f341(f341(f241(x84371),f341(f113(x84371),x84372)),f87(x84371)))+~P85(f341(f341(f241(a1),x84372),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106))) % 19.23/19.05 [8621]~P89(x86212)+~P113(x86212)+~P85(f341(f341(f242(x86212),f87(x86212)),f341(f113(x86212),x86211)))+P85(f341(f341(f242(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),x86211)) % 19.23/19.05 [8622]~P89(x86222)+~P113(x86222)+~P85(f341(f341(f241(x86222),f87(x86222)),f341(f113(x86222),x86221)))+P85(f341(f341(f241(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),x86221)) % 19.23/19.05 [8955]~P113(x89551)+~P89(x89551)+P85(f341(f341(f242(x89551),f87(x89551)),f341(f113(x89551),x89552)))+~P85(f341(f341(f242(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),x89552)) % 19.23/19.05 [8956]~P113(x89561)+~P89(x89561)+P85(f341(f341(f241(x89561),f87(x89561)),f341(f113(x89561),x89562)))+~P85(f341(f341(f241(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),x89562)) % 19.23/19.05 [9433]~P135(x94332)+E(x94331,f87(x94332))+E(x94331,f341(f88(x94332),f87(x94332)))+~E(f341(f341(f251(x94332),x94331),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),f87(x94332)) % 19.23/19.05 [9688]~P61(x96881)+~P89(x96881)+~P85(f341(f341(f242(x96881),f2(x96881)),x96882))+P85(f341(f341(f242(x96881),f2(x96881)),f341(f341(f292(x96881),x96882),f341(f113(x96881),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))))) % 19.23/19.05 [9743]~P61(x97431)+~P89(x97431)+P85(f341(f341(f242(x97431),f2(x97431)),x97432))+~P85(f341(f341(f242(x97431),f2(x97431)),f341(f341(f292(x97431),x97432),f341(f113(x97431),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))))) % 19.23/19.05 [10019]~P136(x100192)+E(x100191,f2(a1))+P85(f341(f341(f242(a1),x100191),f2(a1)))+E(f341(f341(f260(a1,a1,x100192),f341(f341(f9(a1,f864(a1,f864(x100192,x100192)),f864(a1,x100192)),f341(f341(f10(f864(f864(x100192,x100192),x100192),f864(f864(a1,f864(x100192,x100192)),f864(a1,x100192)),a1),f10(f864(x100192,x100192),x100192,a1)),f341(f341(f10(x100192,f864(f864(x100192,x100192),x100192),a1),f95(x100192,x100192)),f112(x100192)))),f341(f341(f9(a1,f864(x100192,x100192),f864(x100192,x100192)),f341(f341(f10(f864(x100192,f864(x100192,x100192)),f864(f864(x100192,x100192),f864(x100192,x100192)),a1),f20(x100192,x100192,x100192)),f341(f341(f9(a1,f864(x100192,x100192),f864(x100192,f864(x100192,x100192))),f341(f341(f10(f864(x100192,f864(x100192,x100192)),f864(f864(x100192,x100192),f864(x100192,f864(x100192,x100192))),a1),f10(x100192,f864(x100192,x100192),x100192)),f341(f341(f10(a850,f864(x100192,f864(x100192,x100192)),a1),f105(x100192)),f341(f341(f9(a1,a1,a850),a338),f2(a1))))),f341(f341(f20(x100192,x100192,x100192),f89(x100192)),f7(x100192))))),f341(f341(f9(x100192,x100192,x100192),f341(f341(f10(x100192,f864(x100192,x100192),x100192),f89(x100192)),f341(f341(f20(x100192,x100192,x100192),f89(x100192)),f7(x100192)))),f87(x100192))))),f61(x100191,f341(f113(a1),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106))))),f341(f112(x100192),x100191)) % 19.23/19.05 [4774]~P88(x47743)+~P89(x47743)+E(x47741,x47742)+~E(f341(f113(x47743),x47741),f341(f113(x47743),x47742)) % 19.23/19.05 [5910]~P85(f341(x59101,x59102))+~P85(f341(x59101,x59103))+~P85(f341(f341(f241(a857),x59103),f803(x59102,x59101)))+P85(f341(x59101,f2(a857))) % 19.23/19.05 [6339]P142(x63392,x63393,x63391)+E(x63391,f2(a1))+P85(f341(f341(f241(a1),f2(a1)),f788(x63391,x63393,x63392)))+P85(f341(f341(f242(a1),x63391),f2(a1))) % 19.23/19.05 [6340]P143(x63402,x63403,x63401)+E(x63401,f2(a1))+P85(f341(f341(f241(a1),f2(a1)),f795(x63401,x63403,x63402)))+P85(f341(f341(f242(a1),x63401),f2(a1))) % 19.23/19.05 [6472]P142(x64721,x64722,x64723)+~P85(f341(x64721,x64722))+P85(f341(f341(f241(a1),f2(a1)),f788(x64723,x64722,x64721)))+P85(f341(f341(f242(a1),x64723),f2(a1))) % 19.23/19.05 [6496]P143(x64961,x64962,x64963)+P85(f341(f341(f241(a1),f2(a1)),f795(x64963,x64962,x64961)))+~P85(f341(x64961,f2(a1)))+P85(f341(f341(f242(a1),x64963),f2(a1))) % 19.23/19.05 [6528]P142(x65282,x65283,x65281)+E(x65281,f2(a1))+~P85(f341(x65282,f788(x65281,x65283,x65282)))+P85(f341(f341(f242(a1),x65281),f2(a1))) % 19.23/19.05 [6529]P143(x65292,x65293,x65291)+E(x65291,f2(a1))+~P85(f341(x65292,f796(x65291,x65293,x65292)))+P85(f341(f341(f242(a1),x65291),f2(a1))) % 19.23/19.05 [6632]~P101(x66321)+~P6(x66321)+~P85(f341(f341(f242(x66321),x66322),f52(x66321,x66323)))+P85(f341(f341(f242(x66321),x66322),f681(x66323,x66322,x66321))) % 19.23/19.05 [6642]P142(x66421,x66422,x66423)+~P85(f341(x66421,x66422))+~P85(f341(x66421,f788(x66423,x66422,x66421)))+P85(f341(f341(f242(a1),x66423),f2(a1))) % 19.23/19.05 [6674]P143(x66741,x66742,x66743)+~P85(f341(x66741,f796(x66743,x66742,x66741)))+~P85(f341(x66741,f2(a1)))+P85(f341(f341(f242(a1),x66743),f2(a1))) % 19.23/19.05 [6935]P142(x69352,x69353,x69351)+E(x69351,f2(a1))+P85(f341(f341(f241(a1),f2(a1)),f788(x69351,x69353,x69352)))+P85(f341(f341(f242(a1),x69351),f792(x69351,x69353,x69352))) % 19.23/19.05 [6936]P143(x69362,x69363,x69361)+E(x69361,f2(a1))+P85(f341(f341(f241(a1),f2(a1)),f795(x69361,x69363,x69362)))+P85(f341(f341(f242(a1),x69361),f794(x69361,x69363,x69362))) % 19.23/19.05 [7053]P142(x70531,x70532,x70533)+~P85(f341(x70531,x70532))+P85(f341(f341(f241(a1),f2(a1)),f788(x70533,x70532,x70531)))+P85(f341(f341(f242(a1),x70533),f792(x70533,x70532,x70531))) % 19.23/19.05 [7074]P143(x70741,x70742,x70743)+P85(f341(f341(f241(a1),f2(a1)),f795(x70743,x70742,x70741)))+P85(f341(f341(f242(a1),x70743),f794(x70743,x70742,x70741)))+~P85(f341(x70741,f2(a1))) % 19.23/19.05 [7104]P142(x71042,x71043,x71041)+E(x71041,f2(a1))+~P85(f341(x71042,f788(x71041,x71043,x71042)))+P85(f341(f341(f242(a1),x71041),f792(x71041,x71043,x71042))) % 19.23/19.05 [7105]P143(x71052,x71053,x71051)+E(x71051,f2(a1))+~P85(f341(x71052,f796(x71051,x71053,x71052)))+P85(f341(f341(f242(a1),x71051),f794(x71051,x71053,x71052))) % 19.23/19.05 [7145]P142(x71452,x71453,x71451)+E(x71451,f2(a1))+P85(f341(f341(f241(a1),f2(a1)),f788(x71451,x71453,x71452)))+~P85(f341(x71452,f792(x71451,x71453,x71452))) % 19.23/19.05 [7146]P143(x71462,x71463,x71461)+E(x71461,f2(a1))+P85(f341(f341(f241(a1),f2(a1)),f795(x71461,x71463,x71462)))+~P85(f341(x71462,f797(x71461,x71463,x71462))) % 19.23/19.05 [7251]P142(x72511,x72512,x72513)+~P85(f341(x72511,x72512))+~P85(f341(x72511,f788(x72513,x72512,x72511)))+P85(f341(f341(f242(a1),x72513),f792(x72513,x72512,x72511))) % 19.23/19.05 [7267]P143(x72671,x72672,x72673)+~P85(f341(x72671,f796(x72673,x72672,x72671)))+P85(f341(f341(f242(a1),x72673),f794(x72673,x72672,x72671)))+~P85(f341(x72671,f2(a1))) % 19.23/19.05 [7273]P142(x72731,x72732,x72733)+~P85(f341(x72731,x72732))+P85(f341(f341(f241(a1),f2(a1)),f788(x72733,x72732,x72731)))+~P85(f341(x72731,f792(x72733,x72732,x72731))) % 19.23/19.05 [7291]P143(x72911,x72912,x72913)+P85(f341(f341(f241(a1),f2(a1)),f795(x72913,x72912,x72911)))+~P85(f341(x72911,f797(x72913,x72912,x72911)))+~P85(f341(x72911,f2(a1))) % 19.23/19.05 [7315]P142(x73152,x73153,x73151)+E(x73151,f2(a1))+~P85(f341(x73152,f788(x73151,x73153,x73152)))+~P85(f341(x73152,f792(x73151,x73153,x73152))) % 19.23/19.05 [7316]P143(x73162,x73163,x73161)+E(x73161,f2(a1))+~P85(f341(x73162,f796(x73161,x73163,x73162)))+~P85(f341(x73162,f797(x73161,x73163,x73162))) % 19.23/19.05 [7412]P142(x74121,x74122,x74123)+~P85(f341(x74121,x74122))+~P85(f341(x74121,f788(x74123,x74122,x74121)))+~P85(f341(x74121,f792(x74123,x74122,x74121))) % 19.23/19.05 [7427]P143(x74271,x74272,x74273)+~P85(f341(x74271,f796(x74273,x74272,x74271)))+~P85(f341(x74271,f797(x74273,x74272,x74271)))+~P85(f341(x74271,f2(a1))) % 19.23/19.05 [7477]P142(x74772,x74773,x74771)+E(x74771,f2(a1))+P85(f341(f341(f241(a1),f2(a1)),f788(x74771,x74773,x74772)))+P85(f341(f341(f241(a1),f792(x74771,x74773,x74772)),f2(a1))) % 19.23/19.05 [7478]P143(x74782,x74783,x74781)+E(x74781,f2(a1))+P85(f341(f341(f241(a1),f2(a1)),f795(x74781,x74783,x74782)))+P85(f341(f341(f241(a1),f794(x74781,x74783,x74782)),f2(a1))) % 19.23/19.05 [7479]~P81(x74791)+~P85(f341(f341(f242(x74791),x74793),f2(x74791)))+~P85(f341(f341(f242(x74791),x74792),f2(x74791)))+P85(f341(f341(f242(x74791),f341(f341(f89(x74791),x74792),x74793)),f2(x74791))) % 19.23/19.05 [7480]~P81(x74801)+~P85(f341(f341(f241(x74801),x74802),f2(x74801)))+~P85(f341(f341(f242(x74801),x74803),f2(x74801)))+P85(f341(f341(f242(x74801),f341(f341(f89(x74801),x74802),x74803)),f2(x74801))) % 19.23/19.05 [7481]~P81(x74811)+~P85(f341(f341(f241(x74811),x74813),f2(x74811)))+~P85(f341(f341(f242(x74811),x74812),f2(x74811)))+P85(f341(f341(f242(x74811),f341(f341(f89(x74811),x74812),x74813)),f2(x74811))) % 19.23/19.05 [7482]~P81(x74821)+~P85(f341(f341(f241(x74821),x74823),f2(x74821)))+~P85(f341(f341(f241(x74821),x74822),f2(x74821)))+P85(f341(f341(f241(x74821),f341(f341(f89(x74821),x74822),x74823)),f2(x74821))) % 19.23/19.05 [7483]~P112(x74831)+~P85(f341(f341(f343(x74831),x74833),f182(x74831)))+~P85(f341(f341(f343(x74831),x74832),f182(x74831)))+P85(f341(f341(f343(x74831),f341(f341(f89(x74831),x74832),x74833)),f182(x74831))) % 19.23/19.05 [7484]~P136(x74841)+~P85(f341(f341(f343(x74841),x74843),f119(x74841)))+~P85(f341(f341(f343(x74841),x74842),f119(x74841)))+P85(f341(f341(f343(x74841),f341(f341(f89(x74841),x74842),x74843)),f119(x74841))) % 19.23/19.05 [7485]~P112(x74851)+~P85(f341(f341(f343(x74851),x74853),f182(x74851)))+~P85(f341(f341(f343(x74851),x74852),f182(x74851)))+P85(f341(f341(f343(x74851),f341(f341(f90(x74851),x74852),x74853)),f182(x74851))) % 19.23/19.05 [7486]~P136(x74861)+~P85(f341(f341(f343(x74861),x74863),f119(x74861)))+~P85(f341(f341(f343(x74861),x74862),f119(x74861)))+P85(f341(f341(f343(x74861),f341(f341(f90(x74861),x74862),x74863)),f119(x74861))) % 19.23/19.05 [7487]~P136(x74871)+~P85(f341(f341(f343(x74871),x74873),f119(x74871)))+~P85(f341(f341(f343(x74871),x74872),f119(x74871)))+P85(f341(f341(f343(x74871),f341(f341(f3(x74871),x74872),x74873)),f119(x74871))) % 19.23/19.05 [7513]P142(x75133,x75132,x75131)+E(x75131,f2(a1))+E(f341(f341(f89(a1),f341(f341(f90(a1),x75131),f789(x75131,x75132,x75133))),f788(x75131,x75132,x75133)),x75132)+P85(f341(f341(f242(a1),x75131),f2(a1))) % 19.23/19.05 [7514]P143(x75143,x75142,x75141)+E(x75141,f2(a1))+E(f341(f341(f89(a1),f341(f341(f90(a1),x75141),f796(x75141,x75142,x75143))),f795(x75141,x75142,x75143)),x75142)+P85(f341(f341(f242(a1),x75141),f2(a1))) % 19.23/19.05 [7599]P142(x75991,x75992,x75993)+~P85(f341(x75991,x75992))+P85(f341(f341(f241(a1),f2(a1)),f788(x75993,x75992,x75991)))+P85(f341(f341(f241(a1),f792(x75993,x75992,x75991)),f2(a1))) % 19.23/19.05 [7630]P143(x76301,x76302,x76303)+P85(f341(f341(f241(a1),f2(a1)),f795(x76303,x76302,x76301)))+~P85(f341(x76301,f2(a1)))+P85(f341(f341(f241(a1),f794(x76303,x76302,x76301)),f2(a1))) % 19.23/19.05 [7638]P142(x76383,x76382,x76381)+~P85(f341(x76383,x76382))+E(f341(f341(f89(a1),f341(f341(f90(a1),x76381),f789(x76381,x76382,x76383))),f788(x76381,x76382,x76383)),x76382)+P85(f341(f341(f242(a1),x76381),f2(a1))) % 19.23/19.05 [7643]P142(x76432,x76433,x76431)+E(x76431,f2(a1))+~P85(f341(x76432,f788(x76431,x76433,x76432)))+P85(f341(f341(f241(a1),f792(x76431,x76433,x76432)),f2(a1))) % 19.23/19.05 [7644]P143(x76442,x76443,x76441)+E(x76441,f2(a1))+~P85(f341(x76442,f796(x76441,x76443,x76442)))+P85(f341(f341(f241(a1),f794(x76441,x76443,x76442)),f2(a1))) % 19.23/19.05 [7649]P143(x76493,x76492,x76491)+E(f341(f341(f89(a1),f341(f341(f90(a1),x76491),f796(x76491,x76492,x76493))),f795(x76491,x76492,x76493)),x76492)+~P85(f341(x76493,f2(a1)))+P85(f341(f341(f242(a1),x76491),f2(a1))) % 19.23/19.05 [7702]P142(x77021,x77022,x77023)+~P85(f341(x77021,x77022))+~P85(f341(x77021,f788(x77023,x77022,x77021)))+P85(f341(f341(f241(a1),f792(x77023,x77022,x77021)),f2(a1))) % 19.23/19.05 [7707]P143(x77071,x77072,x77073)+~P85(f341(x77071,f796(x77073,x77072,x77071)))+~P85(f341(x77071,f2(a1)))+P85(f341(f341(f241(a1),f794(x77073,x77072,x77071)),f2(a1))) % 19.23/19.05 [7781]~P61(x77811)+~P85(f341(f341(f242(x77811),f341(f341(f292(x77811),x77813),x77812)),f2(x77811)))+P85(f341(f341(f242(x77811),x77812),f2(x77811)))+P85(f341(f341(f242(x77811),x77813),f2(x77811))) % 19.23/19.05 [7782]~P122(x77821)+~P85(f341(f341(f241(x77821),f341(f341(f90(x77821),x77823),x77822)),f2(x77821)))+P85(f341(f341(f241(x77821),x77822),f2(x77821)))+P85(f341(f341(f241(x77821),x77823),f2(x77821))) % 19.23/19.05 [7783]~P61(x77831)+~P85(f341(f341(f241(x77831),f341(f341(f292(x77831),x77833),x77832)),f2(x77831)))+P85(f341(f341(f241(x77831),x77832),f2(x77831)))+P85(f341(f341(f241(x77831),x77833),f2(x77831))) % 19.23/19.05 [7895]P142(x78953,x78952,x78951)+E(x78951,f2(a1))+E(f341(f341(f89(a1),f341(f341(f90(a1),x78951),f789(x78951,x78952,x78953))),f788(x78951,x78952,x78953)),x78952)+P85(f341(f341(f242(a1),x78951),f792(x78951,x78952,x78953))) % 19.23/19.05 [7896]P143(x78963,x78962,x78961)+E(x78961,f2(a1))+E(f341(f341(f89(a1),f341(f341(f90(a1),x78961),f796(x78961,x78962,x78963))),f795(x78961,x78962,x78963)),x78962)+P85(f341(f341(f242(a1),x78961),f794(x78961,x78962,x78963))) % 19.23/19.05 [7907]P142(x79073,x79072,x79071)+E(x79071,f2(a1))+E(f341(f341(f89(a1),f341(f341(f90(a1),x79071),f790(x79071,x79072,x79073))),f792(x79071,x79072,x79073)),x79072)+P85(f341(f341(f241(a1),f2(a1)),f788(x79071,x79072,x79073))) % 19.23/19.05 [7908]P143(x79083,x79082,x79081)+E(x79081,f2(a1))+E(f341(f341(f89(a1),f341(f341(f90(a1),x79081),f797(x79081,x79082,x79083))),f794(x79081,x79082,x79083)),x79082)+P85(f341(f341(f241(a1),f2(a1)),f795(x79081,x79082,x79083))) % 19.23/19.05 [7955]P142(x79553,x79552,x79551)+~P85(f341(x79553,x79552))+E(f341(f341(f89(a1),f341(f341(f90(a1),x79551),f789(x79551,x79552,x79553))),f788(x79551,x79552,x79553)),x79552)+P85(f341(f341(f242(a1),x79551),f792(x79551,x79552,x79553))) % 19.23/19.05 [7966]P143(x79663,x79662,x79661)+E(f341(f341(f89(a1),f341(f341(f90(a1),x79661),f796(x79661,x79662,x79663))),f795(x79661,x79662,x79663)),x79662)+P85(f341(f341(f242(a1),x79661),f794(x79661,x79662,x79663)))+~P85(f341(x79663,f2(a1))) % 19.23/19.05 [7972]P142(x79723,x79722,x79721)+~P85(f341(x79723,x79722))+E(f341(f341(f89(a1),f341(f341(f90(a1),x79721),f790(x79721,x79722,x79723))),f792(x79721,x79722,x79723)),x79722)+P85(f341(f341(f241(a1),f2(a1)),f788(x79721,x79722,x79723))) % 19.23/19.05 [7979]P143(x79793,x79792,x79791)+E(f341(f341(f89(a1),f341(f341(f90(a1),x79791),f797(x79791,x79792,x79793))),f794(x79791,x79792,x79793)),x79792)+P85(f341(f341(f241(a1),f2(a1)),f795(x79791,x79792,x79793)))+~P85(f341(x79793,f2(a1))) % 19.23/19.05 [7989]P142(x79893,x79892,x79891)+E(x79891,f2(a1))+E(f341(f341(f89(a1),f341(f341(f90(a1),x79891),f789(x79891,x79892,x79893))),f788(x79891,x79892,x79893)),x79892)+~P85(f341(x79893,f792(x79891,x79892,x79893))) % 19.23/19.05 [7990]P143(x79903,x79902,x79901)+E(x79901,f2(a1))+E(f341(f341(f89(a1),f341(f341(f90(a1),x79901),f796(x79901,x79902,x79903))),f795(x79901,x79902,x79903)),x79902)+~P85(f341(x79903,f797(x79901,x79902,x79903))) % 19.23/19.05 [7991]P142(x79913,x79912,x79911)+E(x79911,f2(a1))+E(f341(f341(f89(a1),f341(f341(f90(a1),x79911),f790(x79911,x79912,x79913))),f792(x79911,x79912,x79913)),x79912)+~P85(f341(x79913,f788(x79911,x79912,x79913))) % 19.23/19.05 [7992]P143(x79923,x79922,x79921)+E(x79921,f2(a1))+E(f341(f341(f89(a1),f341(f341(f90(a1),x79921),f797(x79921,x79922,x79923))),f794(x79921,x79922,x79923)),x79922)+~P85(f341(x79923,f796(x79921,x79922,x79923))) % 19.23/19.05 [8044]P142(x80443,x80442,x80441)+~P85(f341(x80443,x80442))+E(f341(f341(f89(a1),f341(f341(f90(a1),x80441),f789(x80441,x80442,x80443))),f788(x80441,x80442,x80443)),x80442)+~P85(f341(x80443,f792(x80441,x80442,x80443))) % 19.23/19.05 [8045]P142(x80453,x80452,x80451)+~P85(f341(x80453,x80452))+E(f341(f341(f89(a1),f341(f341(f90(a1),x80451),f790(x80451,x80452,x80453))),f792(x80451,x80452,x80453)),x80452)+~P85(f341(x80453,f788(x80451,x80452,x80453))) % 19.23/19.05 [8057]P143(x80573,x80572,x80571)+E(f341(f341(f89(a1),f341(f341(f90(a1),x80571),f796(x80571,x80572,x80573))),f795(x80571,x80572,x80573)),x80572)+~P85(f341(x80573,f797(x80571,x80572,x80573)))+~P85(f341(x80573,f2(a1))) % 19.23/19.05 [8058]P143(x80583,x80582,x80581)+E(f341(f341(f89(a1),f341(f341(f90(a1),x80581),f797(x80581,x80582,x80583))),f794(x80581,x80582,x80583)),x80582)+~P85(f341(x80583,f796(x80581,x80582,x80583)))+~P85(f341(x80583,f2(a1))) % 19.23/19.05 [8154]P142(x81543,x81542,x81541)+E(x81541,f2(a1))+E(f341(f341(f89(a1),f341(f341(f90(a1),x81541),f789(x81541,x81542,x81543))),f788(x81541,x81542,x81543)),x81542)+P85(f341(f341(f241(a1),f792(x81541,x81542,x81543)),f2(a1))) % 19.23/19.05 [8155]P143(x81553,x81552,x81551)+E(x81551,f2(a1))+E(f341(f341(f89(a1),f341(f341(f90(a1),x81551),f796(x81551,x81552,x81553))),f795(x81551,x81552,x81553)),x81552)+P85(f341(f341(f241(a1),f794(x81551,x81552,x81553)),f2(a1))) % 19.23/19.05 [8193]P142(x81933,x81932,x81931)+~P85(f341(x81933,x81932))+E(f341(f341(f89(a1),f341(f341(f90(a1),x81931),f789(x81931,x81932,x81933))),f788(x81931,x81932,x81933)),x81932)+P85(f341(f341(f241(a1),f792(x81931,x81932,x81933)),f2(a1))) % 19.23/19.05 [8198]P143(x81983,x81982,x81981)+E(f341(f341(f89(a1),f341(f341(f90(a1),x81981),f796(x81981,x81982,x81983))),f795(x81981,x81982,x81983)),x81982)+~P85(f341(x81983,f2(a1)))+P85(f341(f341(f241(a1),f794(x81981,x81982,x81983)),f2(a1))) % 19.23/19.05 [8330]P142(x83303,x83302,x83301)+E(x83301,f2(a1))+E(f341(f341(f89(a1),f341(f341(f90(a1),x83301),f790(x83301,x83302,x83303))),f792(x83301,x83302,x83303)),x83302)+E(f341(f341(f89(a1),f341(f341(f90(a1),x83301),f789(x83301,x83302,x83303))),f788(x83301,x83302,x83303)),x83302) % 19.23/19.05 [8331]P143(x83313,x83312,x83311)+E(x83311,f2(a1))+E(f341(f341(f89(a1),f341(f341(f90(a1),x83311),f797(x83311,x83312,x83313))),f794(x83311,x83312,x83313)),x83312)+E(f341(f341(f89(a1),f341(f341(f90(a1),x83311),f796(x83311,x83312,x83313))),f795(x83311,x83312,x83313)),x83312) % 19.23/19.05 [8354]P142(x83543,x83542,x83541)+~P85(f341(x83543,x83542))+E(f341(f341(f89(a1),f341(f341(f90(a1),x83541),f790(x83541,x83542,x83543))),f792(x83541,x83542,x83543)),x83542)+E(f341(f341(f89(a1),f341(f341(f90(a1),x83541),f789(x83541,x83542,x83543))),f788(x83541,x83542,x83543)),x83542) % 19.23/19.05 [8366]P143(x83663,x83662,x83661)+E(f341(f341(f89(a1),f341(f341(f90(a1),x83661),f797(x83661,x83662,x83663))),f794(x83661,x83662,x83663)),x83662)+E(f341(f341(f89(a1),f341(f341(f90(a1),x83661),f796(x83661,x83662,x83663))),f795(x83661,x83662,x83663)),x83662)+~P85(f341(x83663,f2(a1))) % 19.23/19.05 [8960]~P122(x89601)+~E(x89603,f2(x89601))+~E(x89602,f2(x89601))+P85(f341(f341(f241(x89601),f341(f341(f89(x89601),f341(f341(f90(x89601),x89602),x89602)),f341(f341(f90(x89601),x89603),x89603))),f2(x89601))) % 19.23/19.05 [9970]~P113(x99701)+~E(x99703,f2(x99701))+~E(x99702,f2(x99701))+P85(f341(f341(f241(x99701),f341(f341(f89(x99701),f341(f341(f251(x99701),x99702),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106))))),f341(f341(f251(x99701),x99703),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))))),f2(x99701))) % 19.23/19.05 [4724]~E(x47243,x47241)+~P116(x47242)+E(x47241,f2(x47242))+E(f341(f341(f292(x47242),x47243),x47241),f87(x47242)) % 19.23/19.05 [4775]~P93(x47751)+~E(x47753,f185(x47751))+~E(x47752,f185(x47751))+E(f341(f341(f110(x47751),x47752),x47753),f185(x47751)) % 19.23/19.05 [4776]~P97(x47761)+~E(x47763,f248(x47761))+~E(x47762,f248(x47761))+E(f341(f341(f111(x47761),x47762),x47763),f248(x47761)) % 19.23/19.05 [4862]~P116(x48623)+E(x48621,x48622)+E(x48622,f2(x48623))+~E(f341(f341(f292(x48623),x48621),x48622),f87(x48623)) % 19.23/19.05 [4878]~P137(x48782)+E(x48781,f2(x48782))+E(x48783,f2(x48782))+~E(f341(f341(f90(x48782),x48783),x48781),f2(x48782)) % 19.23/19.05 [4880]~P129(x48802)+E(x48801,f2(x48802))+E(x48803,f2(x48802))+~E(f341(f341(f90(x48802),x48803),x48801),f2(x48802)) % 19.23/19.05 [5246]~P114(x52463)+E(x52461,x52462)+E(x52461,f341(f88(x52463),x52462))+~E(f341(f341(f90(x52463),x52461),x52461),f341(f341(f90(x52463),x52462),x52462)) % 19.23/19.05 [5282]~P91(x52821)+E(f341(f88(x52821),x52822),x52823)+~E(f341(f341(f110(x52821),x52822),x52823),f248(x52821))+~E(f341(f341(f111(x52821),x52822),x52823),f185(x52821)) % 19.23/19.05 [5358]~P113(x53583)+E(x53581,x53582)+P85(f341(f341(f242(x53583),x53582),x53581))+P85(f341(f341(f242(x53583),x53581),x53582)) % 19.23/19.05 [5364]~P101(x53643)+E(x53641,x53642)+P85(f341(f341(f242(x53643),x53642),x53641))+P85(f341(f341(f242(x53643),x53641),x53642)) % 19.23/19.05 [5365]~E(x53652,x53653)+~P101(x53651)+P85(f341(f341(f241(x53651),x53652),x53653))+P85(f341(f341(f242(x53651),x53652),x53653)) % 19.23/19.05 [5611]~P100(x56113)+E(x56111,x56112)+~P85(f341(f341(f241(x56113),x56112),x56111))+P85(f341(f341(f242(x56113),x56112),x56111)) % 19.23/19.05 [5617]~P100(x56173)+E(x56171,x56172)+~P85(f341(f341(f241(x56173),x56171),x56172))+P85(f341(f341(f242(x56173),x56171),x56172)) % 19.23/19.05 [5619]~P101(x56193)+E(x56191,x56192)+~P85(f341(f341(f241(x56193),x56191),x56192))+P85(f341(f341(f242(x56193),x56191),x56192)) % 19.23/19.05 [5731]P142(x57311,x57312,x57313)+~P85(f341(x57311,x57312))+P85(f341(f341(f242(a1),x57313),f2(a1)))+P85(f341(f341(f242(a1),f2(a1)),x57313)) % 19.23/19.05 [5782]P143(x57821,x57822,x57823)+~P85(f341(x57821,f2(a1)))+P85(f341(f341(f242(a1),x57823),f2(a1)))+P85(f341(f341(f242(a1),f2(a1)),x57823)) % 19.23/19.05 [5786]~P95(x57861)+E(f341(f341(f110(x57861),x57862),f12(x57861,x57863)),x57862)+~P85(f341(f71(x57861),x57863))+~P85(f341(f341(f343(x57861),x57862),x57863)) % 19.23/19.05 [5787]~P95(x57871)+E(f341(f341(f111(x57871),x57872),f15(x57871,x57873)),x57872)+~P85(f341(f71(x57871),x57873))+~P85(f341(f341(f343(x57871),x57872),x57873)) % 19.23/19.05 [5820]~P101(x58201)+E(f341(f341(f245(x58201),x58202),f17(x58201,x58203)),f17(x58201,x58203))+~P85(f341(f71(x58201),x58203))+~P85(f341(f341(f343(x58201),x58202),x58203)) % 19.23/19.05 [5821]~P101(x58211)+E(f341(f341(f240(x58211),x58212),f16(x58211,x58213)),f16(x58211,x58213))+~P85(f341(f71(x58211),x58213))+~P85(f341(f341(f343(x58211),x58212),x58213)) % 19.23/19.05 [5822]~P95(x58221)+E(f341(f341(f110(x58221),x58222),f15(x58221,x58223)),f15(x58221,x58223))+~P85(f341(f71(x58221),x58223))+~P85(f341(f341(f343(x58221),x58222),x58223)) % 19.23/19.05 [5823]~P95(x58231)+E(f341(f341(f111(x58231),x58232),f12(x58231,x58233)),f12(x58231,x58233))+~P85(f341(f71(x58231),x58233))+~P85(f341(f341(f343(x58231),x58232),x58233)) % 19.23/19.05 [5864]E(x58641,x58642)+~P100(x58643)+~P85(f341(f341(f241(x58643),x58642),x58641))+~P85(f341(f341(f241(x58643),x58641),x58642)) % 19.23/19.05 [6004]~P104(x60041)+P85(f341(f341(f241(x60041),x60043),x60042))+~P85(f341(f341(f241(x60041),x60042),x60043))+P85(f341(f341(f242(x60041),x60042),x60043)) % 19.23/19.05 [6028]~P101(x60281)+~P85(f341(f71(x60281),x60283))+P85(f341(f341(f241(x60281),x60282),f16(x60281,x60283)))+~P85(f341(f341(f343(x60281),x60282),x60283)) % 19.23/19.05 [6082]~P101(x60821)+E(f341(f341(f245(x60821),x60822),f13(x60821,f240(x60821),x60823)),x60822)+~P85(f341(f71(x60821),x60823))+~P85(f341(f341(f343(x60821),x60822),x60823)) % 19.23/19.05 [6083]~P101(x60831)+E(f341(f341(f240(x60831),x60832),f14(x60831,f245(x60831),x60833)),x60832)+~P85(f341(f71(x60831),x60833))+~P85(f341(f341(f343(x60831),x60832),x60833)) % 19.23/19.05 [6224]E(x62241,x62242)+~E(f341(f341(f3(a857),x62241),x62243),f341(f341(f3(a857),x62242),x62243))+~P85(f341(f341(f241(a857),x62243),x62241))+~P85(f341(f341(f241(a857),x62243),x62242)) % 19.23/19.05 [6251]~P101(x62511)+~P85(f341(f71(x62511),x62512))+~P85(f341(f341(f343(x62511),x62513),x62512))+P85(f341(f341(f241(x62511),f17(x62511,x62512)),x62513)) % 19.23/19.05 [6318]P142(x63182,x63183,x63181)+E(x63181,f2(a1))+P85(f341(f341(f242(a1),x63181),f792(x63181,x63183,x63182)))+P85(f341(f341(f242(a1),f2(a1)),x63181)) % 19.23/19.05 [6319]P143(x63192,x63193,x63191)+E(x63191,f2(a1))+P85(f341(f341(f242(a1),x63191),f794(x63191,x63193,x63192)))+P85(f341(f341(f242(a1),f2(a1)),x63191)) % 19.23/19.05 [6320]~P101(x63201)+E(f341(f341(f245(x63201),x63202),f14(x63201,f245(x63201),x63203)),f14(x63201,f245(x63201),x63203))+~P85(f341(f71(x63201),x63203))+~P85(f341(f341(f343(x63201),x63202),x63203)) % 19.23/19.05 [6321]~P101(x63211)+E(f341(f341(f240(x63211),x63212),f13(x63211,f240(x63211),x63213)),f13(x63211,f240(x63211),x63213))+~P85(f341(f71(x63211),x63213))+~P85(f341(f341(f343(x63211),x63212),x63213)) % 19.23/19.05 [6328]~P85(f341(x63281,x63282))+P85(f341(x63281,f821(x63282,x63281,x63283)))+P85(f341(x63281,f2(a857)))+~P85(f341(f341(f242(a857),x63282),x63283)) % 19.23/19.05 [6387]~P85(f341(x63871,x63872))+~P85(f341(f71(x63873),x63872))+P85(f341(x63871,f406(x63871,x63872,x63873)))+P85(f341(x63871,f185(f864(x63873,a850)))) % 19.23/19.05 [6402]~P113(x64021)+~P89(x64021)+P85(f341(f341(f242(x64021),f341(f113(x64021),x64022)),f341(f113(x64021),x64023)))+~P85(f341(f341(f242(a1),x64022),x64023)) % 19.23/19.05 [6403]~P113(x64031)+~P89(x64031)+P85(f341(f341(f241(x64031),f341(f113(x64031),x64032)),f341(f113(x64031),x64033)))+~P85(f341(f341(f241(a1),x64032),x64033)) % 19.23/19.05 [6406]~P85(f341(x64061,x64063))+~P85(f341(f71(x64062),x64063))+P85(f341(f71(x64062),f406(x64061,x64063,x64062)))+P85(f341(x64061,f185(f864(x64062,a850)))) % 19.23/19.05 [6440]P142(x64401,x64402,x64403)+~P85(f341(x64401,x64402))+P85(f341(f341(f242(a1),x64403),f792(x64403,x64402,x64401)))+P85(f341(f341(f242(a1),f2(a1)),x64403)) % 19.23/19.05 [6480]P143(x64801,x64802,x64803)+P85(f341(f341(f242(a1),x64803),f794(x64803,x64802,x64801)))+~P85(f341(x64801,f2(a1)))+P85(f341(f341(f242(a1),f2(a1)),x64803)) % 19.23/19.05 [6507]~P103(x65071)+~P90(x65071)+E(f341(f341(f245(x65071),f341(f113(x65071),x65072)),f341(f113(x65071),x65073)),f341(f113(x65071),x65073))+P85(f341(f341(f241(x65071),f341(f113(x65071),x65072)),f341(f113(x65071),x65073))) % 19.23/19.05 [6508]~P103(x65081)+~P90(x65081)+E(f341(f341(f240(x65081),f341(f113(x65081),x65082)),f341(f113(x65081),x65083)),f341(f113(x65081),x65082))+P85(f341(f341(f241(x65081),f341(f113(x65081),x65082)),f341(f113(x65081),x65083))) % 19.23/19.05 [6570]P142(x65702,x65703,x65701)+E(x65701,f2(a1))+~P85(f341(x65702,f792(x65701,x65703,x65702)))+P85(f341(f341(f242(a1),f2(a1)),x65701)) % 19.23/19.05 [6571]P143(x65712,x65713,x65711)+E(x65711,f2(a1))+~P85(f341(x65712,f797(x65711,x65713,x65712)))+P85(f341(f341(f242(a1),f2(a1)),x65711)) % 19.23/19.05 [6664]P142(x66641,x66642,x66643)+~P85(f341(x66641,x66642))+~P85(f341(x66641,f792(x66643,x66642,x66641)))+P85(f341(f341(f242(a1),f2(a1)),x66643)) % 19.23/19.05 [6694]P143(x66941,x66942,x66943)+~P85(f341(x66941,f797(x66943,x66942,x66941)))+~P85(f341(x66941,f2(a1)))+P85(f341(f341(f242(a1),f2(a1)),x66943)) % 19.23/19.05 [6810]~P89(x68103)+~P113(x68103)+~P85(f341(f341(f242(x68103),f341(f113(x68103),x68101)),f341(f113(x68103),x68102)))+P85(f341(f341(f242(a1),x68101),x68102)) % 19.23/19.05 [6811]~P89(x68113)+~P113(x68113)+~P85(f341(f341(f241(x68113),f341(f113(x68113),x68111)),f341(f113(x68113),x68112)))+P85(f341(f341(f241(a1),x68111),x68112)) % 19.23/19.05 [6840]~P101(x68401)+~P15(x68401,x68403)+P15(x68401,f341(f341(f146(x68401),x68402),x68403))+~P85(f341(f341(f241(x68401),x68402),f777(x68403,x68402,x68401))) % 19.23/19.05 [6841]~P101(x68411)+~P15(x68411,x68413)+P15(x68411,f341(f341(f146(x68411),x68412),x68413))+~P85(f341(f341(f241(x68411),x68412),f780(x68413,x68412,x68411))) % 19.23/19.05 [6928]P142(x69282,x69283,x69281)+E(x69281,f2(a1))+P85(f341(f341(f242(a1),x69281),f2(a1)))+P85(f341(f341(f242(a1),f788(x69281,x69283,x69282)),x69281)) % 19.23/19.05 [6929]P143(x69292,x69293,x69291)+E(x69291,f2(a1))+P85(f341(f341(f242(a1),x69291),f2(a1)))+P85(f341(f341(f242(a1),f795(x69291,x69293,x69292)),x69291)) % 19.23/19.05 [6967]P142(x69672,x69673,x69671)+E(x69671,f2(a1))+P85(f341(f341(f241(a1),f792(x69671,x69673,x69672)),f2(a1)))+P85(f341(f341(f242(a1),f2(a1)),x69671)) % 19.23/19.05 [6968]P143(x69682,x69683,x69681)+E(x69681,f2(a1))+P85(f341(f341(f241(a1),f794(x69681,x69683,x69682)),f2(a1)))+P85(f341(f341(f242(a1),f2(a1)),x69681)) % 19.23/19.05 [6986]~P101(x69861)+~P15(x69861,x69863)+E(f341(f341(f144(x69861,x69861,f7(x69861)),x69862),f157(x69861,x69862,x69863)),x69863)+~P85(f341(f341(f343(x69861),x69862),f341(f163(x69861),x69863))) % 19.23/19.05 [7036]P142(x70361,x70362,x70363)+~P85(f341(x70361,x70362))+P85(f341(f341(f242(a1),x70363),f2(a1)))+P85(f341(f341(f242(a1),f788(x70363,x70362,x70361)),x70363)) % 19.23/19.05 [7042]~P103(x70421)+~P90(x70421)+E(f341(f341(f245(x70421),f341(f113(x70421),x70422)),f341(f113(x70421),x70423)),f341(f113(x70421),x70422))+~P85(f341(f341(f241(x70421),f341(f113(x70421),x70422)),f341(f113(x70421),x70423))) % 19.23/19.05 [7043]~P103(x70431)+~P90(x70431)+E(f341(f341(f240(x70431),f341(f113(x70431),x70432)),f341(f113(x70431),x70433)),f341(f113(x70431),x70433))+~P85(f341(f341(f241(x70431),f341(f113(x70431),x70432)),f341(f113(x70431),x70433))) % 19.23/19.05 [7056]P143(x70561,x70562,x70563)+~P85(f341(x70561,f2(a1)))+P85(f341(f341(f242(a1),x70563),f2(a1)))+P85(f341(f341(f242(a1),f795(x70563,x70562,x70561)),x70563)) % 19.23/19.05 [7066]P142(x70661,x70662,x70663)+~P85(f341(x70661,x70662))+P85(f341(f341(f241(a1),f792(x70663,x70662,x70661)),f2(a1)))+P85(f341(f341(f242(a1),f2(a1)),x70663)) % 19.23/19.05 [7090]P143(x70901,x70902,x70903)+~P85(f341(x70901,f2(a1)))+P85(f341(f341(f241(a1),f794(x70903,x70902,x70901)),f2(a1)))+P85(f341(f341(f242(a1),f2(a1)),x70903)) % 19.23/19.05 [7116]~P85(f341(x71161,x71162))+P85(f341(x71161,f2(a857)))+~P85(f341(f341(f242(a857),x71162),x71163))+P85(f341(f341(f242(a857),f821(x71162,x71161,x71163)),x71163)) % 19.23/19.05 [7133]~P101(x71331)+~P15(x71331,x71333)+P15(x71331,f341(f341(f146(x71331),x71332),x71333))+P85(f341(f341(f343(x71331),f777(x71333,x71332,x71331)),f341(f163(x71331),x71333))) % 19.23/19.05 [7134]~P101(x71341)+~P15(x71341,x71343)+P15(x71341,f341(f341(f146(x71341),x71342),x71343))+P85(f341(f341(f343(x71341),f780(x71343,x71342,x71341)),f341(f163(x71341),x71343))) % 19.23/19.05 [7256]~P101(x72561)+~P6(x72561)+~P85(f341(f341(f242(x72561),x72563),f52(x72561,x72562)))+P85(f341(f341(f343(x72561),f681(x72562,x72563,x72561)),x72562)) % 19.23/19.05 [7425]~P101(x74251)+~P6(x74251)+~P85(f341(f341(f242(x74251),f53(x74251,x74253)),x74252))+P85(f341(f341(f242(x74251),f685(x74252,x74253,x74251)),x74252)) % 19.23/19.05 [7426]~P101(x74261)+~P6(x74261)+~P85(f341(f341(f242(x74261),f53(x74261,x74263)),x74262))+P85(f341(f341(f343(x74261),f685(x74262,x74263,x74261)),x74263)) % 19.23/19.05 [7439]P142(x74392,x74393,x74391)+E(x74391,f2(a1))+P85(f341(f341(f242(a1),x74391),f792(x74391,x74393,x74392)))+P85(f341(f341(f242(a1),f788(x74391,x74393,x74392)),x74391)) % 19.23/19.05 [7440]P143(x74402,x74403,x74401)+E(x74401,f2(a1))+P85(f341(f341(f242(a1),x74401),f794(x74401,x74403,x74402)))+P85(f341(f341(f242(a1),f795(x74401,x74403,x74402)),x74401)) % 19.23/19.05 [7536]P142(x75363,x75362,x75361)+E(x75361,f2(a1))+E(f341(f341(f89(a1),f341(f341(f90(a1),x75361),f790(x75361,x75362,x75363))),f792(x75361,x75362,x75363)),x75362)+P85(f341(f341(f242(a1),f2(a1)),x75361)) % 19.23/19.05 [7537]P143(x75373,x75372,x75371)+E(x75371,f2(a1))+E(f341(f341(f89(a1),f341(f341(f90(a1),x75371),f797(x75371,x75372,x75373))),f794(x75371,x75372,x75373)),x75372)+P85(f341(f341(f242(a1),f2(a1)),x75371)) % 19.23/19.05 [7539]~P125(x75391)+~P85(f341(f341(f242(x75391),x75393),f2(x75391)))+P85(f341(f341(f242(x75391),f341(f341(f90(x75391),x75392),x75393)),f2(x75391)))+~P85(f341(f341(f242(x75391),f2(x75391)),x75392)) % 19.23/19.05 [7540]~P125(x75401)+~P85(f341(f341(f242(x75401),x75402),f2(x75401)))+P85(f341(f341(f242(x75401),f341(f341(f90(x75401),x75402),x75403)),f2(x75401)))+~P85(f341(f341(f242(x75401),f2(x75401)),x75403)) % 19.23/19.05 [7541]~P61(x75411)+~P85(f341(f341(f242(x75411),x75413),f2(x75411)))+P85(f341(f341(f242(x75411),f341(f341(f292(x75411),x75412),x75413)),f2(x75411)))+~P85(f341(f341(f242(x75411),f2(x75411)),x75412)) % 19.23/19.05 [7542]~P61(x75421)+~P85(f341(f341(f242(x75421),x75422),f2(x75421)))+P85(f341(f341(f242(x75421),f341(f341(f292(x75421),x75422),x75423)),f2(x75421)))+~P85(f341(f341(f242(x75421),f2(x75421)),x75423)) % 19.23/19.05 [7543]~P62(x75431)+~P85(f341(f341(f242(x75431),x75433),f2(x75431)))+P85(f341(f341(f242(x75431),f341(f341(f292(x75431),x75432),x75433)),f2(x75431)))+~P85(f341(f341(f242(x75431),f2(x75431)),x75432)) % 19.23/19.05 [7544]~P62(x75441)+~P85(f341(f341(f242(x75441),x75442),f2(x75441)))+P85(f341(f341(f242(x75441),f341(f341(f292(x75441),x75442),x75443)),f2(x75441)))+~P85(f341(f341(f242(x75441),f2(x75441)),x75443)) % 19.23/19.05 [7546]~P122(x75461)+~P85(f341(f341(f241(x75461),x75463),f2(x75461)))+P85(f341(f341(f241(x75461),f341(f341(f90(x75461),x75462),x75463)),f2(x75461)))+~P85(f341(f341(f241(x75461),f2(x75461)),x75462)) % 19.23/19.05 [7547]~P122(x75471)+~P85(f341(f341(f241(x75471),x75472),f2(x75471)))+P85(f341(f341(f241(x75471),f341(f341(f90(x75471),x75472),x75473)),f2(x75471)))+~P85(f341(f341(f241(x75471),f2(x75471)),x75473)) % 19.23/19.05 [7549]~P130(x75491)+~P85(f341(f341(f241(x75491),x75493),f2(x75491)))+P85(f341(f341(f241(x75491),f341(f341(f90(x75491),x75492),x75493)),f2(x75491)))+~P85(f341(f341(f241(x75491),f2(x75491)),x75492)) % 19.23/19.05 [7551]~P130(x75511)+~P85(f341(f341(f241(x75511),x75512),f2(x75511)))+P85(f341(f341(f241(x75511),f341(f341(f90(x75511),x75512),x75513)),f2(x75511)))+~P85(f341(f341(f241(x75511),f2(x75511)),x75513)) % 19.23/19.05 [7552]~P61(x75521)+~P85(f341(f341(f241(x75521),x75523),f2(x75521)))+P85(f341(f341(f241(x75521),f341(f341(f292(x75521),x75522),x75523)),f2(x75521)))+~P85(f341(f341(f241(x75521),f2(x75521)),x75522)) % 19.23/19.05 [7553]~P61(x75531)+~P85(f341(f341(f241(x75531),x75532),f2(x75531)))+P85(f341(f341(f241(x75531),f341(f341(f292(x75531),x75532),x75533)),f2(x75531)))+~P85(f341(f341(f241(x75531),f2(x75531)),x75533)) % 19.23/19.05 [7554]~P62(x75541)+~P85(f341(f341(f242(x75541),x75543),f2(x75541)))+P85(f341(f341(f241(x75541),f341(f341(f292(x75541),x75542),x75543)),f2(x75541)))+~P85(f341(f341(f241(x75541),f2(x75541)),x75542)) % 19.23/19.05 [7555]~P62(x75551)+~P85(f341(f341(f241(x75551),x75552),f2(x75551)))+P85(f341(f341(f241(x75551),f341(f341(f292(x75551),x75552),x75553)),f2(x75551)))+~P85(f341(f341(f242(x75551),f2(x75551)),x75553)) % 19.23/19.05 [7571]P142(x75711,x75712,x75713)+~P85(f341(x75711,x75712))+P85(f341(f341(f242(a1),x75713),f792(x75713,x75712,x75711)))+P85(f341(f341(f242(a1),f788(x75713,x75712,x75711)),x75713)) % 19.23/19.05 [7584]P143(x75841,x75842,x75843)+P85(f341(f341(f242(a1),x75843),f794(x75843,x75842,x75841)))+~P85(f341(x75841,f2(a1)))+P85(f341(f341(f242(a1),f795(x75843,x75842,x75841)),x75843)) % 19.23/19.05 [7636]P142(x76362,x76363,x76361)+E(x76361,f2(a1))+~P85(f341(x76362,f792(x76361,x76363,x76362)))+P85(f341(f341(f242(a1),f788(x76361,x76363,x76362)),x76361)) % 19.23/19.05 [7637]P143(x76372,x76373,x76371)+E(x76371,f2(a1))+~P85(f341(x76372,f797(x76371,x76373,x76372)))+P85(f341(f341(f242(a1),f795(x76371,x76373,x76372)),x76371)) % 19.23/19.05 [7646]P142(x76463,x76462,x76461)+~P85(f341(x76463,x76462))+E(f341(f341(f89(a1),f341(f341(f90(a1),x76461),f790(x76461,x76462,x76463))),f792(x76461,x76462,x76463)),x76462)+P85(f341(f341(f242(a1),f2(a1)),x76461)) % 19.23/19.05 [7664]P143(x76643,x76642,x76641)+E(f341(f341(f89(a1),f341(f341(f90(a1),x76641),f797(x76641,x76642,x76643))),f794(x76641,x76642,x76643)),x76642)+~P85(f341(x76643,f2(a1)))+P85(f341(f341(f242(a1),f2(a1)),x76641)) % 19.23/19.05 [7688]~P85(f341(x76881,x76883))+~P85(f341(f71(x76882),x76883))+P85(f341(f341(f343(x76882),f435(x76881,x76883,x76882)),f406(x76881,x76883,x76882)))+P85(f341(x76881,f185(f864(x76882,a850)))) % 19.23/19.05 [7698]P142(x76981,x76982,x76983)+~P85(f341(x76981,x76982))+~P85(f341(x76981,f792(x76983,x76982,x76981)))+P85(f341(f341(f242(a1),f788(x76983,x76982,x76981)),x76983)) % 19.23/19.05 [7704]P143(x77041,x77042,x77043)+~P85(f341(x77041,f797(x77043,x77042,x77041)))+~P85(f341(x77041,f2(a1)))+P85(f341(f341(f242(a1),f795(x77043,x77042,x77041)),x77043)) % 19.23/19.05 [7812]~P61(x78121)+~P85(f341(f341(f242(x78121),f341(f341(f292(x78121),x78123),x78122)),f2(x78121)))+P85(f341(f341(f242(x78121),x78122),f2(x78121)))+P85(f341(f341(f242(x78121),f2(x78121)),x78122)) % 19.23/19.05 [7813]~P61(x78131)+~P85(f341(f341(f242(x78131),f341(f341(f292(x78131),x78132),x78133)),f2(x78131)))+P85(f341(f341(f242(x78131),x78132),f2(x78131)))+P85(f341(f341(f242(x78131),f2(x78131)),x78132)) % 19.23/19.05 [7814]~P122(x78141)+~P85(f341(f341(f241(x78141),f341(f341(f90(x78141),x78143),x78142)),f2(x78141)))+P85(f341(f341(f241(x78141),x78142),f2(x78141)))+P85(f341(f341(f241(x78141),f2(x78141)),x78142)) % 19.23/19.05 [7815]~P122(x78151)+~P85(f341(f341(f241(x78151),f341(f341(f90(x78151),x78152),x78153)),f2(x78151)))+P85(f341(f341(f241(x78151),x78152),f2(x78151)))+P85(f341(f341(f241(x78151),f2(x78151)),x78152)) % 19.23/19.05 [7816]~P61(x78161)+~P85(f341(f341(f241(x78161),f341(f341(f292(x78161),x78163),x78162)),f2(x78161)))+P85(f341(f341(f241(x78161),x78162),f2(x78161)))+P85(f341(f341(f241(x78161),f2(x78161)),x78162)) % 19.23/19.05 [7817]~P61(x78171)+~P85(f341(f341(f241(x78171),f341(f341(f292(x78171),x78172),x78173)),f2(x78171)))+P85(f341(f341(f241(x78171),x78172),f2(x78171)))+P85(f341(f341(f241(x78171),f2(x78171)),x78172)) % 19.23/19.05 [7843]~P61(x78431)+~P85(f341(f341(f242(x78431),f341(f341(f292(x78431),x78432),x78433)),f2(x78431)))+P85(f341(f341(f242(x78431),f2(x78431)),x78432))+P85(f341(f341(f242(x78431),f2(x78431)),x78433)) % 19.23/19.05 [7844]~P122(x78441)+~P85(f341(f341(f241(x78441),f341(f341(f90(x78441),x78442),x78443)),f2(x78441)))+P85(f341(f341(f241(x78441),f2(x78441)),x78442))+P85(f341(f341(f241(x78441),f2(x78441)),x78443)) % 19.23/19.05 [7845]~P61(x78451)+~P85(f341(f341(f241(x78451),f341(f341(f292(x78451),x78452),x78453)),f2(x78451)))+P85(f341(f341(f241(x78451),f2(x78451)),x78452))+P85(f341(f341(f241(x78451),f2(x78451)),x78453)) % 19.23/19.05 [7864]P142(x78642,x78643,x78641)+E(x78641,f2(a1))+P85(f341(f341(f241(a1),f792(x78641,x78643,x78642)),f2(a1)))+P85(f341(f341(f242(a1),f788(x78641,x78643,x78642)),x78641)) % 19.23/19.05 [7865]P143(x78652,x78653,x78651)+E(x78651,f2(a1))+P85(f341(f341(f241(a1),f794(x78651,x78653,x78652)),f2(a1)))+P85(f341(f341(f242(a1),f795(x78651,x78653,x78652)),x78651)) % 19.23/19.05 [7871]~P120(x78711)+~P85(f341(f341(f242(x78711),x78712),f87(x78711)))+P85(f341(f341(f242(x78711),f341(f341(f251(x78711),x78712),f341(a121,x78713))),f87(x78711)))+~P85(f341(f341(f242(x78711),f2(x78711)),x78712)) % 19.23/19.05 [7925]~P101(x79251)+~E(x79253,f122(x79251))+~P15(x79251,f341(f148(x79251),x79253))+E(f341(f138(x79251,x79251,f341(f9(x79251,x79251,x79251),f240(x79251)),x79252),f341(f148(x79251),x79253)),x79252) % 19.23/19.05 [7927]P142(x79271,x79272,x79273)+~P85(f341(x79271,x79272))+P85(f341(f341(f241(a1),f792(x79273,x79272,x79271)),f2(a1)))+P85(f341(f341(f242(a1),f788(x79273,x79272,x79271)),x79273)) % 19.23/19.05 [7939]P143(x79391,x79392,x79393)+~P85(f341(x79391,f2(a1)))+P85(f341(f341(f241(a1),f794(x79393,x79392,x79391)),f2(a1)))+P85(f341(f341(f242(a1),f795(x79393,x79392,x79391)),x79393)) % 19.23/19.05 [8149]P142(x81493,x81492,x81491)+E(x81491,f2(a1))+E(f341(f341(f89(a1),f341(f341(f90(a1),x81491),f790(x81491,x81492,x81493))),f792(x81491,x81492,x81493)),x81492)+P85(f341(f341(f242(a1),f788(x81491,x81492,x81493)),x81491)) % 19.23/19.05 [8150]P143(x81503,x81502,x81501)+E(x81501,f2(a1))+E(f341(f341(f89(a1),f341(f341(f90(a1),x81501),f797(x81501,x81502,x81503))),f794(x81501,x81502,x81503)),x81502)+P85(f341(f341(f242(a1),f795(x81501,x81502,x81503)),x81501)) % 19.23/19.05 [8185]P142(x81853,x81852,x81851)+~P85(f341(x81853,x81852))+E(f341(f341(f89(a1),f341(f341(f90(a1),x81851),f790(x81851,x81852,x81853))),f792(x81851,x81852,x81853)),x81852)+P85(f341(f341(f242(a1),f788(x81851,x81852,x81853)),x81851)) % 19.23/19.05 [8186]~P68(x81861)+~P71(x81861)+~P37(x81863)+E(f341(f341(f11(a857,x81861),f341(f341(f10(a1,x81861,a857),x81862),f109(a1))),f341(f312(a1,a857,a114),x81863)),f341(f341(f11(a1,x81861),x81862),x81863)) % 19.23/19.05 [8187]~P68(x81871)+~P71(x81871)+~P37(x81873)+E(f341(f341(f8(a857,x81871),f341(f341(f10(a1,x81871,a857),x81872),f109(a1))),f341(f312(a1,a857,a114),x81873)),f341(f341(f8(a1,x81871),x81872),x81873)) % 19.23/19.05 [8195]P143(x81953,x81952,x81951)+E(f341(f341(f89(a1),f341(f341(f90(a1),x81951),f797(x81951,x81952,x81953))),f794(x81951,x81952,x81953)),x81952)+~P85(f341(x81953,f2(a1)))+P85(f341(f341(f242(a1),f795(x81951,x81952,x81953)),x81951)) % 19.23/19.05 [8213]~E(x82132,f2(a857))+~E(f341(f249(a857,a857),x82133),f2(a857))+~E(x82131,f341(f341(f89(a857),f341(f341(f90(a857),f341(f249(a857,a857),x82133)),x82132)),f341(f259(a857,a857),x82133)))+P85(f341(f63(x82131,x82132),x82133)) % 19.23/19.05 [9064]P85(f341(f341(f241(a1),x90641),f2(a1)))+~P85(f341(f341(f242(a1),f341(f341(f89(a1),f341(f341(f90(a1),x90642),x90641)),x90643)),f2(a1)))+~P85(f341(f341(f242(a1),f2(a1)),x90642))+~P85(f341(f341(f241(a1),f2(a1)),x90643)) % 19.23/19.05 [5680]~P95(x56802)+E(x56801,f185(f864(x56802,a850)))+~P85(f341(f71(x56802),x56801))+E(f15(x56802,f341(f341(f311(x56802),x56803),x56801)),f341(f341(f110(x56802),x56803),f15(x56802,x56801))) % 19.23/19.05 [5681]~P95(x56812)+E(x56811,f185(f864(x56812,a850)))+~P85(f341(f71(x56812),x56811))+E(f12(x56812,f341(f341(f311(x56812),x56813),x56811)),f341(f341(f111(x56812),x56813),f12(x56812,x56811))) % 19.23/19.05 [5682]~P101(x56822)+E(x56821,f185(f864(x56822,a850)))+~P85(f341(f71(x56822),x56821))+E(f16(x56822,f341(f341(f311(x56822),x56823),x56821)),f341(f341(f240(x56822),x56823),f16(x56822,x56821))) % 19.23/19.05 [5683]~P101(x56832)+E(x56831,f185(f864(x56832,a850)))+~P85(f341(f71(x56832),x56831))+E(f17(x56832,f341(f341(f311(x56832),x56833),x56831)),f341(f341(f245(x56832),x56833),f17(x56832,x56831))) % 19.23/19.05 [6001]~P122(x60011)+~E(x60013,f2(x60011))+~E(x60012,f2(x60011))+E(f341(f341(f89(x60011),f341(f341(f90(x60011),x60012),x60012)),f341(f341(f90(x60011),x60013),x60013)),f2(x60011)) % 19.23/19.05 [6076]~P92(x60762)+E(x60761,f185(f864(x60762,a850)))+~P85(f341(f71(x60762),x60761))+E(f341(f73(x60762,f90(x60762)),f341(f341(f311(x60762),x60763),x60761)),f341(f341(f90(x60762),x60763),f341(f73(x60762,f90(x60762)),x60761))) % 19.23/19.05 [6202]~P101(x62022)+E(x62021,f185(f864(x62022,a850)))+~P85(f341(f71(x62022),x62021))+E(f13(x62022,f240(x62022),f341(f341(f311(x62022),x62023),x62021)),f341(f341(f240(x62022),x62023),f13(x62022,f240(x62022),x62021))) % 19.23/19.05 [6203]~P101(x62032)+E(x62031,f185(f864(x62032,a850)))+~P85(f341(f71(x62032),x62031))+E(f14(x62032,f245(x62032),f341(f341(f311(x62032),x62033),x62031)),f341(f341(f245(x62032),x62033),f14(x62032,f245(x62032),x62031))) % 19.23/19.05 [6729]~P65(x67291)+~P85(f341(f71(x67291),x67293))+E(f341(f73(x67291,f90(x67291)),f341(f341(f311(x67291),x67292),x67293)),f341(f341(f74(x67291,x67291,f90(x67291)),x67292),x67293))+P85(f341(f341(f343(x67291),x67292),x67293)) % 19.23/19.05 [6815]~E(f341(f341(f89(a1),x68152),f341(f341(f90(a1),x68153),x68151)),x68153)+~P85(f341(f341(f242(a1),f2(a1)),x68153))+P85(f341(f341(f241(a1),f87(a1)),x68151))+~P85(f341(f341(f242(a1),x68152),x68153)) % 19.23/19.05 [6846]~E(f341(f341(f89(a1),x68462),f341(f341(f90(a1),x68463),x68461)),x68463)+P85(f341(f341(f241(a1),x68461),f87(a1)))+~P85(f341(f341(f242(a1),f2(a1)),x68463))+~P85(f341(f341(f241(a1),f2(a1)),x68462)) % 19.23/19.05 [6864]E(x68641,f2(a857))+~P85(f341(f63(x68643,x68641),x68642))+~P85(f341(f341(f242(a857),f2(a857)),x68641))+P85(f341(f341(f242(a857),f341(f259(a857,a857),x68642)),x68641)) % 19.23/19.05 [6893]~P134(x68931)+~P85(f341(f341(f241(x68931),x68932),f2(x68931)))+~P85(f341(f341(f241(x68931),x68933),f2(x68931)))+E(f341(f341(f90(x68931),f341(f84(x68931),x68932)),f341(f84(x68931),x68933)),f341(f84(x68931),f341(f341(f90(x68931),x68932),x68933))) % 19.23/19.05 [6944]~P134(x69441)+~P85(f341(f341(f241(x69441),x69442),f2(x69441)))+E(f341(f341(f90(x69441),f341(f84(x69441),x69442)),f341(f84(x69441),x69443)),f341(f84(x69441),f341(f341(f90(x69441),x69442),x69443)))+~P85(f341(f341(f241(x69441),f2(x69441)),x69443)) % 19.23/19.05 [6945]~P134(x69451)+~P85(f341(f341(f241(x69451),x69453),f2(x69451)))+E(f341(f341(f90(x69451),f341(f84(x69451),x69452)),f341(f84(x69451),x69453)),f341(f84(x69451),f341(f341(f90(x69451),x69452),x69453)))+~P85(f341(f341(f241(x69451),f2(x69451)),x69452)) % 19.23/19.05 [6995]~P134(x69951)+E(f341(f341(f90(x69951),f341(f84(x69951),x69952)),f341(f84(x69951),x69953)),f341(f84(x69951),f341(f341(f90(x69951),x69952),x69953)))+~P85(f341(f341(f241(x69951),f2(x69951)),x69952))+~P85(f341(f341(f241(x69951),f2(x69951)),x69953)) % 19.23/19.05 [7013]~P122(x70131)+~P85(f341(f341(f242(x70131),x70133),f2(x70131)))+~P85(f341(f341(f242(x70131),x70132),f2(x70131)))+P85(f341(f341(f242(x70131),f2(x70131)),f341(f341(f90(x70131),x70132),x70133))) % 19.23/19.05 [7014]~P61(x70141)+~P85(f341(f341(f242(x70141),x70143),f2(x70141)))+~P85(f341(f341(f242(x70141),x70142),f2(x70141)))+P85(f341(f341(f242(x70141),f2(x70141)),f341(f341(f292(x70141),x70142),x70143))) % 19.23/19.05 [7015]~P62(x70151)+~P85(f341(f341(f242(x70151),x70153),f2(x70151)))+~P85(f341(f341(f242(x70151),x70152),f2(x70151)))+P85(f341(f341(f242(x70151),f2(x70151)),f341(f341(f292(x70151),x70152),x70153))) % 19.23/19.05 [7016]~P122(x70161)+~P85(f341(f341(f241(x70161),x70163),f2(x70161)))+~P85(f341(f341(f241(x70161),x70162),f2(x70161)))+P85(f341(f341(f241(x70161),f2(x70161)),f341(f341(f90(x70161),x70162),x70163))) % 19.23/19.05 [7018]~P131(x70181)+~P85(f341(f341(f241(x70181),x70183),f2(x70181)))+~P85(f341(f341(f241(x70181),x70182),f2(x70181)))+P85(f341(f341(f241(x70181),f2(x70181)),f341(f341(f90(x70181),x70182),x70183))) % 19.23/19.05 [7019]~P61(x70191)+~P85(f341(f341(f241(x70191),x70193),f2(x70191)))+~P85(f341(f341(f241(x70191),x70192),f2(x70191)))+P85(f341(f341(f241(x70191),f2(x70191)),f341(f341(f292(x70191),x70192),x70193))) % 19.23/19.05 [7020]~P62(x70201)+~P85(f341(f341(f242(x70201),x70203),f2(x70201)))+~P85(f341(f341(f241(x70201),x70202),f2(x70201)))+P85(f341(f341(f241(x70201),f2(x70201)),f341(f341(f292(x70201),x70202),x70203))) % 19.23/19.05 [7021]~P120(x70211)+~P85(f341(f341(f242(a857),f2(a857)),x70213))+~P85(f341(f341(f242(x70211),f87(x70211)),x70212))+P85(f341(f341(f242(x70211),f87(x70211)),f341(f341(f251(x70211),x70212),x70213))) % 19.23/19.05 [7117]~P81(x71171)+~P85(f341(f341(f242(x71171),f2(x71171)),x71173))+~P85(f341(f341(f242(x71171),f2(x71171)),x71172))+P85(f341(f341(f242(x71171),f2(x71171)),f341(f341(f89(x71171),x71172),x71173))) % 19.23/19.05 [7120]~P125(x71201)+~P85(f341(f341(f242(x71201),f2(x71201)),x71203))+~P85(f341(f341(f242(x71201),f2(x71201)),x71202))+P85(f341(f341(f242(x71201),f2(x71201)),f341(f341(f90(x71201),x71202),x71203))) % 19.23/19.05 [7121]~P61(x71211)+~P85(f341(f341(f242(x71211),f2(x71211)),x71213))+~P85(f341(f341(f242(x71211),f2(x71211)),x71212))+P85(f341(f341(f242(x71211),f2(x71211)),f341(f341(f292(x71211),x71212),x71213))) % 19.23/19.05 [7122]~P62(x71221)+~P85(f341(f341(f242(x71221),f2(x71221)),x71223))+~P85(f341(f341(f242(x71221),f2(x71221)),x71222))+P85(f341(f341(f242(x71221),f2(x71221)),f341(f341(f292(x71221),x71222),x71223))) % 19.23/19.05 [7123]~P120(x71231)+~P85(f341(f341(f242(x71231),f87(x71231)),x71233))+~P85(f341(f341(f242(x71231),f87(x71231)),x71232))+P85(f341(f341(f242(x71231),f87(x71231)),f341(f341(f90(x71231),x71232),x71233))) % 19.23/19.05 [7125]~P122(x71251)+~P85(f341(f341(f241(x71251),f2(x71251)),x71253))+~P85(f341(f341(f241(x71251),f2(x71251)),x71252))+P85(f341(f341(f241(x71251),f2(x71251)),f341(f341(f90(x71251),x71252),x71253))) % 19.23/19.05 [7126]~P130(x71261)+~P85(f341(f341(f241(x71261),f2(x71261)),x71263))+~P85(f341(f341(f241(x71261),f2(x71261)),x71262))+P85(f341(f341(f241(x71261),f2(x71261)),f341(f341(f90(x71261),x71262),x71263))) % 19.23/19.05 [7127]~P131(x71271)+~P85(f341(f341(f241(x71271),f2(x71271)),x71273))+~P85(f341(f341(f241(x71271),f2(x71271)),x71272))+P85(f341(f341(f241(x71271),f2(x71271)),f341(f341(f90(x71271),x71272),x71273))) % 19.23/19.05 [7128]~P61(x71281)+~P85(f341(f341(f241(x71281),f2(x71281)),x71283))+~P85(f341(f341(f241(x71281),f2(x71281)),x71282))+P85(f341(f341(f241(x71281),f2(x71281)),f341(f341(f292(x71281),x71282),x71283))) % 19.23/19.05 [7129]~P62(x71291)+~P85(f341(f341(f242(x71291),f2(x71291)),x71293))+~P85(f341(f341(f241(x71291),f2(x71291)),x71292))+P85(f341(f341(f241(x71291),f2(x71291)),f341(f341(f292(x71291),x71292),x71293))) % 19.23/19.05 [7207]~P95(x72071)+~P85(f341(f71(x72071),x72073))+E(f15(x72071,f341(f341(f311(x72071),x72072),x72073)),x72072)+~E(f341(f341(f3(f864(x72071,a850)),x72073),f341(f341(f311(x72071),x72072),f185(f864(x72071,a850)))),f185(f864(x72071,a850))) % 19.23/19.05 [7208]~P95(x72081)+~P85(f341(f71(x72081),x72083))+E(f12(x72081,f341(f341(f311(x72081),x72082),x72083)),x72082)+~E(f341(f341(f3(f864(x72081,a850)),x72083),f341(f341(f311(x72081),x72082),f185(f864(x72081,a850)))),f185(f864(x72081,a850))) % 19.23/19.05 [7209]~P101(x72091)+~P85(f341(f71(x72091),x72093))+E(f16(x72091,f341(f341(f311(x72091),x72092),x72093)),x72092)+~E(f341(f341(f3(f864(x72091,a850)),x72093),f341(f341(f311(x72091),x72092),f185(f864(x72091,a850)))),f185(f864(x72091,a850))) % 19.23/19.05 [7210]~P101(x72101)+~P85(f341(f71(x72101),x72103))+E(f17(x72101,f341(f341(f311(x72101),x72102),x72103)),x72102)+~E(f341(f341(f3(f864(x72101,a850)),x72103),f341(f341(f311(x72101),x72102),f185(f864(x72101,a850)))),f185(f864(x72101,a850))) % 19.23/19.05 [7211]~P61(x72111)+P85(f341(f341(f242(x72111),x72112),f2(x72111)))+P85(f341(f341(f242(x72111),f2(x72111)),x72113))+~P85(f341(f341(f242(x72111),f2(x72111)),f341(f341(f292(x72111),x72113),x72112))) % 19.23/19.05 [7212]~P61(x72121)+P85(f341(f341(f242(x72121),x72122),f2(x72121)))+P85(f341(f341(f242(x72121),f2(x72121)),x72123))+~P85(f341(f341(f242(x72121),f2(x72121)),f341(f341(f292(x72121),x72122),x72123))) % 19.23/19.05 [7213]~P61(x72131)+P85(f341(f341(f242(x72131),x72132),f2(x72131)))+P85(f341(f341(f242(x72131),f2(x72131)),x72132))+~P85(f341(f341(f242(x72131),f2(x72131)),f341(f341(f292(x72131),x72133),x72132))) % 19.23/19.05 [7214]~P61(x72141)+P85(f341(f341(f242(x72141),x72142),f2(x72141)))+P85(f341(f341(f242(x72141),f2(x72141)),x72142))+~P85(f341(f341(f242(x72141),f2(x72141)),f341(f341(f292(x72141),x72142),x72143))) % 19.23/19.05 [7215]~P122(x72151)+P85(f341(f341(f241(x72151),x72152),f2(x72151)))+P85(f341(f341(f241(x72151),f2(x72151)),x72153))+~P85(f341(f341(f241(x72151),f2(x72151)),f341(f341(f90(x72151),x72153),x72152))) % 19.23/19.05 [7216]~P122(x72161)+P85(f341(f341(f241(x72161),x72162),f2(x72161)))+P85(f341(f341(f241(x72161),f2(x72161)),x72163))+~P85(f341(f341(f241(x72161),f2(x72161)),f341(f341(f90(x72161),x72162),x72163))) % 19.23/19.05 [7217]~P61(x72171)+P85(f341(f341(f241(x72171),x72172),f2(x72171)))+P85(f341(f341(f241(x72171),f2(x72171)),x72173))+~P85(f341(f341(f241(x72171),f2(x72171)),f341(f341(f292(x72171),x72173),x72172))) % 19.23/19.05 [7218]~P61(x72181)+P85(f341(f341(f241(x72181),x72182),f2(x72181)))+P85(f341(f341(f241(x72181),f2(x72181)),x72183))+~P85(f341(f341(f241(x72181),f2(x72181)),f341(f341(f292(x72181),x72182),x72183))) % 19.23/19.05 [7219]~P122(x72191)+P85(f341(f341(f241(x72191),x72192),f2(x72191)))+P85(f341(f341(f241(x72191),f2(x72191)),x72192))+~P85(f341(f341(f241(x72191),f2(x72191)),f341(f341(f90(x72191),x72193),x72192))) % 19.23/19.05 [7220]~P122(x72201)+P85(f341(f341(f241(x72201),x72202),f2(x72201)))+P85(f341(f341(f241(x72201),f2(x72201)),x72202))+~P85(f341(f341(f241(x72201),f2(x72201)),f341(f341(f90(x72201),x72202),x72203))) % 19.23/19.05 [7221]~P61(x72211)+P85(f341(f341(f241(x72211),x72212),f2(x72211)))+P85(f341(f341(f241(x72211),f2(x72211)),x72212))+~P85(f341(f341(f241(x72211),f2(x72211)),f341(f341(f292(x72211),x72213),x72212))) % 19.23/19.05 [7222]~P61(x72221)+P85(f341(f341(f241(x72221),x72222),f2(x72221)))+P85(f341(f341(f241(x72221),f2(x72221)),x72222))+~P85(f341(f341(f241(x72221),f2(x72221)),f341(f341(f292(x72221),x72222),x72223))) % 19.23/19.05 [7307]~P85(f341(f341(f288(a857),x73071),x73073))+P85(f341(f341(f288(a857),x73071),x73072))+~P85(f341(f341(f241(a857),x73072),x73073))+~P85(f341(f341(f288(a857),x73071),f341(f341(f3(a857),x73073),x73072))) % 19.23/19.05 [7308]~P85(f341(f341(f288(a857),x73081),x73083))+P85(f341(f341(f288(a857),x73081),x73082))+~P85(f341(f341(f241(a857),x73083),x73082))+~P85(f341(f341(f288(a857),x73081),f341(f341(f3(a857),x73082),x73083))) % 19.23/19.05 [7323]~E(f341(f341(f111(f864(x73231,a850)),f341(f163(x73231),x73232)),f341(f163(x73231),x73233)),f185(f864(x73231,a850)))+~P85(f341(f134(x73231),x73233))+~P85(f341(f134(x73231),x73232))+P85(f341(f134(x73231),f341(f341(f132(x73231),x73232),x73233))) % 19.23/19.05 [7324]~P101(x73241)+~P85(f341(f71(x73241),x73243))+E(f13(x73241,f240(x73241),f341(f341(f311(x73241),x73242),x73243)),x73242)+~E(f341(f341(f3(f864(x73241,a850)),x73243),f341(f341(f311(x73241),x73242),f185(f864(x73241,a850)))),f185(f864(x73241,a850))) % 19.23/19.05 [7325]~P101(x73251)+~P85(f341(f71(x73251),x73253))+E(f14(x73251,f245(x73251),f341(f341(f311(x73251),x73252),x73253)),x73252)+~E(f341(f341(f3(f864(x73251,a850)),x73253),f341(f341(f311(x73251),x73252),f185(f864(x73251,a850)))),f185(f864(x73251,a850))) % 19.23/19.05 [7343]~P113(x73431)+~P85(f341(f341(f242(x73431),x73432),x73433))+~P85(f341(f341(f242(x73431),f341(f88(x73431),x73432)),x73433))+P85(f341(f341(f242(x73431),f341(f84(x73431),x73432)),x73433)) % 19.23/19.05 [7345]~P79(x73451)+~P85(f341(f341(f241(x73451),x73452),x73453))+~P85(f341(f341(f241(x73451),f341(f88(x73451),x73452)),x73453))+P85(f341(f341(f241(x73451),f341(f84(x73451),x73452)),x73453)) % 19.23/19.05 [7414]~P125(x74141)+P85(f341(f341(f242(x74141),f2(x74141)),x74142))+~P85(f341(f341(f242(x74141),f2(x74141)),x74143))+~P85(f341(f341(f242(x74141),f2(x74141)),f341(f341(f90(x74141),x74143),x74142))) % 19.23/19.05 [7415]~P125(x74151)+P85(f341(f341(f242(x74151),f2(x74151)),x74152))+~P85(f341(f341(f242(x74151),f2(x74151)),x74153))+~P85(f341(f341(f242(x74151),f2(x74151)),f341(f341(f90(x74151),x74152),x74153))) % 19.23/19.05 [7721]E(x77211,x77212)+~P85(f341(f71(x77213),x77211))+~P85(f341(f341(f241(a857),f341(f50(x77213),x77211)),f341(f50(x77213),x77212)))+~P85(f341(f341(f241(f864(x77213,a850)),x77212),x77211)) % 19.23/19.05 [7868]~P85(f341(f341(f242(a1),x78681),f2(a1)))+~P85(f341(f341(f242(a1),f2(a1)),x78682))+~P85(f341(f341(f241(a1),x78682),x78683))+P85(f341(f341(f241(a1),f341(f341(f51(a1),x78681),x78682)),f341(f341(f51(a1),x78681),x78683))) % 19.23/19.05 [7879]~P85(f341(f341(f242(a1),f2(a1)),x78793))+~P85(f341(f341(f241(a1),f2(a1)),x78791))+~P85(f341(f341(f241(a1),x78793),x78792))+P85(f341(f341(f241(a1),f341(f341(f51(a1),x78791),x78792)),f341(f341(f51(a1),x78791),x78793))) % 19.23/19.05 [8014]E(f341(x80141,f824(x80142,x80141,x80143)),x80142)+~P85(f341(f341(f241(a1),x80142),f341(x80141,x80143)))+P85(f341(f341(f242(a857),f825(x80142,x80141,x80143)),x80143))+~P85(f341(f341(f241(a1),f341(x80141,f2(a857))),x80142)) % 19.23/19.05 [8015]E(f341(x80151,f827(x80152,x80151,x80153)),x80152)+~P85(f341(f341(f241(a1),x80152),f341(x80151,x80153)))+P85(f341(f341(f242(a857),f828(x80152,x80151,x80153)),x80153))+~P85(f341(f341(f241(a1),f341(x80151,f2(a857))),x80152)) % 19.23/19.05 [8111]~P85(f341(f71(x81111),x81113))+~P85(f341(f341(f242(a857),f341(f50(x81111),x81112)),f341(f50(x81111),x81113)))+~P85(f341(f341(f241(f864(x81111,a850)),x81112),x81113))+P85(f341(f341(f242(f864(x81111,a850)),x81112),x81113)) % 19.23/19.05 [8139]E(f341(f341(f3(a1),f460(x81393,x81391,x81392)),f461(x81393,x81391,x81392)),x81391)+E(f341(f341(f89(a1),x81391),x81392),x81391)+~P85(f341(f341(f242(a1),f2(a1)),x81392))+~P85(f341(f341(f343(a1),f341(f341(f89(a1),x81391),f87(a1))),x81393)) % 19.23/19.05 [8140]E(f341(f341(f89(a1),f462(x81403,x81401,x81402)),f463(x81403,x81401,x81402)),x81401)+E(f341(f341(f3(a1),x81401),x81402),x81401)+~P85(f341(f341(f242(a1),f2(a1)),x81402))+~P85(f341(f341(f343(a1),f341(f341(f3(a1),x81401),f87(a1))),x81403)) % 19.23/19.05 [8191]~P85(f341(f341(f241(a857),x81913),x81911))+P85(f341(f341(f242(a857),x81911),x81912))+~P85(f341(f341(f241(a857),x81913),x81912))+~P85(f341(f341(f242(a857),f341(f341(f3(a857),x81911),x81913)),f341(f341(f3(a857),x81912),x81913))) % 19.23/19.05 [8192]~P85(f341(f341(f241(a857),x81923),x81921))+P85(f341(f341(f241(a857),x81921),x81922))+~P85(f341(f341(f241(a857),x81923),x81922))+~P85(f341(f341(f241(a857),f341(f341(f3(a857),x81921),x81923)),f341(f341(f3(a857),x81922),x81923))) % 19.23/19.05 [8206]~P101(x82062)+E(x82061,f122(x82062))+~P15(x82062,f341(f148(x82062),x82061))+E(f341(f138(x82062,x82062,f341(f9(x82062,x82062,x82062),f240(x82062)),x82063),f341(f148(x82062),x82061)),f341(f341(f240(x82062),f341(f341(f158(x82062),x82061),f2(a857))),x82063)) % 19.23/19.05 [8272]E(f341(f341(f89(a1),x82721),x82722),x82721)+~P85(f341(f341(f242(a1),f2(a1)),x82722))+P85(f341(f341(f343(a1),f460(x82723,x82721,x82722)),x82723))+~P85(f341(f341(f343(a1),f341(f341(f89(a1),x82721),f87(a1))),x82723)) % 19.23/19.05 [8273]E(f341(f341(f3(a1),x82731),x82732),x82731)+~P85(f341(f341(f242(a1),f2(a1)),x82732))+P85(f341(f341(f343(a1),f462(x82733,x82731,x82732)),x82733))+~P85(f341(f341(f343(a1),f341(f341(f3(a1),x82731),f87(a1))),x82733)) % 19.23/19.05 [8352]~P85(f341(f341(f241(a1),x83521),f341(x83522,x83523)))+P85(f341(f341(f241(a857),f824(x83521,x83522,x83523)),x83523))+P85(f341(f341(f242(a857),f825(x83521,x83522,x83523)),x83523))+~P85(f341(f341(f241(a1),f341(x83522,f2(a857))),x83521)) % 19.23/19.05 [8353]~P85(f341(f341(f241(a1),x83531),f341(x83532,x83533)))+P85(f341(f341(f241(a857),f827(x83531,x83532,x83533)),x83533))+P85(f341(f341(f242(a857),f828(x83531,x83532,x83533)),x83533))+~P85(f341(f341(f241(a1),f341(x83532,f2(a857))),x83531)) % 19.23/19.05 [8427]E(f341(f341(f89(a1),x84271),x84272),x84271)+~P85(f341(f341(f242(a1),f2(a1)),x84272))+P85(f341(f341(f343(a1),f461(x84273,x84271,x84272)),f304(a1,f87(a1),x84272)))+~P85(f341(f341(f343(a1),f341(f341(f89(a1),x84271),f87(a1))),x84273)) % 19.23/19.05 [8428]E(f341(f341(f3(a1),x84281),x84282),x84281)+~P85(f341(f341(f242(a1),f2(a1)),x84282))+P85(f341(f341(f343(a1),f463(x84283,x84281,x84282)),f304(a1,f87(a1),x84282)))+~P85(f341(f341(f343(a1),f341(f341(f3(a1),x84281),f87(a1))),x84283)) % 19.23/19.05 [8552]~P120(x85521)+~P85(f341(f341(f242(x85521),x85522),f87(x85521)))+~P85(f341(f341(f242(x85521),f2(x85521)),x85522))+P85(f341(f341(f242(x85521),f341(f341(f90(x85521),x85522),f341(f341(f251(x85521),x85522),x85523))),f341(f341(f251(x85521),x85522),x85523))) % 19.23/19.05 [8628]~P85(f341(x86281,x86282))+P85(f341(x86281,f2(a857)))+~P85(f341(f341(f242(a857),x86282),x86283))+~P85(f341(x86281,f60(a857,f341(a121,f821(x86282,x86281,x86283)),x86283))) % 19.23/19.05 [8758]E(f844(x87581,x87582,x87583),f2(a857))+P85(f341(f341(x87581,x87583),x87582))+P85(f341(f341(x87581,f844(x87581,x87582,x87583)),f60(a857,f843(x87581,x87582,x87583),f844(x87581,x87582,x87583))))+~P85(f341(f330(f863(a857,a857),a222),f341(f341(f250(a857,a857),x87583),x87582))) % 19.23/19.05 [8790]~P26(x87901,x87901,x87902,x87903)+E(f341(f312(x87901,x87901,x87902),x87903),x87903)+~P85(f341(f71(x87901),x87903))+~P85(f341(f341(f241(f864(x87901,a850)),f341(f312(x87901,x87901,x87902),x87903)),x87903)) % 19.23/19.05 [9011]P85(f341(f341(x90111,x90112),x90113))+~P85(f341(f341(f242(a1),f842(x90111,x90113,x90112)),f2(a1)))+P85(f341(f341(x90111,f341(f88(a1),f841(x90111,x90113,x90112))),f341(f88(a1),f842(x90111,x90113,x90112))))+~P85(f341(f330(f863(a1,a1),a224),f341(f341(f250(a1,a1),x90112),x90113))) % 19.23/19.05 [9171]P85(f341(f341(x91711,x91712),x91713))+P85(f341(f341(x91711,f341(f341(f89(a1),f741(x91711,x91713,x91712)),f87(a1))),f744(x91711,x91713,x91712)))+~P85(f341(f341(f241(a1),f741(x91711,x91713,x91712)),f744(x91711,x91713,x91712)))+~P85(f341(f330(f863(a1,a1),a173),f341(f341(f250(a1,a1),x91712),x91713))) % 19.23/19.05 [9855]E(f341(x98551,f824(x98552,x98551,x98553)),x98552)+~P85(f341(f341(f241(a1),x98552),f341(x98551,x98553)))+~P85(f341(f341(f241(a1),f341(f84(a1),f341(f341(f3(a1),f341(x98551,f341(f341(f89(a857),f825(x98552,x98551,x98553)),f87(a857)))),f341(x98551,f825(x98552,x98551,x98553))))),f87(a1)))+~P85(f341(f341(f241(a1),f341(x98551,f2(a857))),x98552)) % 19.23/19.05 [9856]E(f341(x98561,f827(x98562,x98561,x98563)),x98562)+~P85(f341(f341(f241(a1),x98562),f341(x98561,x98563)))+~P85(f341(f341(f241(a1),f341(f84(a1),f341(f341(f3(a1),f341(x98561,f341(f341(f89(a857),f828(x98562,x98561,x98563)),f87(a857)))),f341(x98561,f828(x98562,x98561,x98563))))),f87(a1)))+~P85(f341(f341(f241(a1),f341(x98561,f2(a857))),x98562)) % 19.23/19.05 [9860]~P85(f341(f341(f241(a1),x98601),f341(x98602,x98603)))+~P85(f341(f341(f241(a1),f341(f84(a1),f341(f341(f3(a1),f341(x98602,f341(f341(f89(a857),f825(x98601,x98602,x98603)),f87(a857)))),f341(x98602,f825(x98601,x98602,x98603))))),f87(a1)))+P85(f341(f341(f241(a857),f824(x98601,x98602,x98603)),x98603))+~P85(f341(f341(f241(a1),f341(x98602,f2(a857))),x98601)) % 19.23/19.05 [9861]~P85(f341(f341(f241(a1),x98611),f341(x98612,x98613)))+~P85(f341(f341(f241(a1),f341(f84(a1),f341(f341(f3(a1),f341(x98612,f341(f341(f89(a857),f828(x98611,x98612,x98613)),f87(a857)))),f341(x98612,f828(x98611,x98612,x98613))))),f87(a1)))+P85(f341(f341(f241(a857),f827(x98611,x98612,x98613)),x98613))+~P85(f341(f341(f241(a1),f341(x98612,f2(a857))),x98611)) % 19.23/19.05 [9913]E(x99131,x99132)+~E(f341(f138(f858(x99133),f858(x99133),f132(x99133),f122(x99133)),x99131),f341(f138(f858(x99133),f858(x99133),f132(x99133),f122(x99133)),x99132))+~E(f341(f186(f858(f858(x99133))),x99131),f341(f186(f858(f858(x99133))),x99132))+~P85(f341(f341(f260(f858(x99133),f858(x99133),a850),f341(f341(f9(f858(x99133),f864(f858(x99133),a857),f864(f858(x99133),a850)),f341(f341(f10(f864(a857,a850),f864(f864(f858(x99133),a857),f864(f858(x99133),a850)),f858(x99133)),f10(a857,a850,f858(x99133))),f341(f341(f10(a857,f864(a857,a850),f858(x99133)),a338),f186(f858(x99133))))),f186(f858(x99133)))),f786(x99131,x99132,x99133))) % 19.23/19.05 [9914]E(x99141,x99142)+~E(f341(f138(f858(x99143),f858(x99143),f132(x99143),f122(x99143)),x99141),f341(f138(f858(x99143),f858(x99143),f132(x99143),f122(x99143)),x99142))+~E(f341(f186(f858(f858(x99143))),x99141),f341(f186(f858(f858(x99143))),x99142))+~P85(f341(f341(f260(f858(x99143),f858(x99143),a850),f341(f341(f9(f858(x99143),f864(f858(x99143),a857),f864(f858(x99143),a850)),f341(f341(f10(f864(a857,a850),f864(f864(f858(x99143),a857),f864(f858(x99143),a850)),f858(x99143)),f10(a857,a850,f858(x99143))),f341(f341(f10(a857,f864(a857,a850),f858(x99143)),a338),f186(f858(x99143))))),f186(f858(x99143)))),f787(x99142,x99141,x99143))) % 19.23/19.05 [6718]~E(f87(a857),f2(a857))+~P85(f341(f71(x67181),x67183))+~P85(f341(f71(x67181),x67182))+E(f341(f341(f89(a857),f341(f50(x67181),x67182)),f341(f50(x67181),x67183)),f341(f50(x67181),f341(f341(f110(f864(x67181,a850)),x67182),x67183))) % 19.23/19.05 [7135]~P101(x71351)+~P85(f341(f71(x71351),x71352))+~P85(f341(f341(f343(x71351),x71353),x71352))+P85(f341(f341(f241(x71351),f341(f73(x71351,f245(x71351)),x71352)),x71353)) % 19.23/19.05 [7136]~P99(x71361)+~P85(f341(f71(x71361),x71362))+~P85(f341(f341(f343(x71361),x71363),x71362))+P85(f341(f341(f241(x71361),f341(f73(x71361,f111(x71361)),x71362)),x71363)) % 19.23/19.05 [7411]~P85(f341(f71(x74111),x74113))+~P85(f341(f71(x74111),x74112))+~E(f341(f341(f111(f864(x74111,a850)),x74112),x74113),f185(f864(x74111,a850)))+E(f341(f341(f89(a857),f341(f50(x74111),x74112)),f341(f50(x74111),x74113)),f341(f50(x74111),f341(f341(f110(f864(x74111,a850)),x74112),x74113))) % 19.23/19.05 [8196]~P35(x81961,x81963)+~P35(x81961,x81962)+~E(f341(f341(f111(f864(x81961,a850)),f341(f270(x81961,x81961),x81962)),f341(f268(x81961,x81961),x81963)),f185(f864(x81961,a850)))+P35(x81961,f341(f341(f110(f864(f863(x81961,x81961),a850)),x81962),x81963)) % 19.23/19.05 [8285]E(x82851,f341(f341(f51(a857),x82852),x82853))+~P85(f341(f341(f242(a857),f2(a857)),x82853))+~P85(f341(f341(f242(a857),x82852),f341(f341(f90(a857),x82853),f341(a121,x82851))))+~P85(f341(f341(f241(a857),f341(f341(f90(a857),x82853),x82851)),x82852)) % 19.23/19.05 [8425]~P85(f341(f71(x84251),x84252))+~P85(f341(f71(x84251),x84253))+E(f341(f341(f89(a857),f341(f50(x84251),x84252)),f341(f50(x84251),x84253)),f341(f50(x84251),f341(f341(f110(f864(x84251,a850)),x84252),x84253)))+P85(f341(f341(f343(x84251),f393(x84253,x84252,x84251)),f341(f341(f111(f864(x84251,a850)),x84252),x84253))) % 19.23/19.05 [8769]~P122(x87692)+~E(x87691,f2(x87692))+~E(x87693,f2(x87692))+~P85(f341(f341(f242(x87692),f2(x87692)),f341(f341(f89(x87692),f341(f341(f90(x87692),x87693),x87693)),f341(f341(f90(x87692),x87691),x87691)))) % 19.23/19.05 [9242]~P35(x92421,x92423)+~P35(x92421,x92422)+P35(x92421,f341(f341(f110(f864(f863(x92421,x92421),a850)),x92422),x92423))+~P85(f341(f341(f241(f864(f863(x92421,x92421),a850)),f341(f341(f290(x92421,x92421,x92421),x92422),x92423)),x92422)) % 19.23/19.05 [9367]~P85(f341(x93671,x93673))+~P85(f341(f71(x93672),x93673))+P85(f341(x93671,f185(f864(x93672,a850))))+~P85(f341(x93671,f341(f341(f3(f864(x93672,a850)),f406(x93671,x93673,x93672)),f341(f341(f311(x93672),f435(x93671,x93673,x93672)),f185(f864(x93672,a850)))))) % 19.23/19.05 [8582]~P85(f341(f341(f242(a1),f2(a1)),x85823))+P85(f341(f341(f241(a1),f2(a1)),x85821))+~P85(f341(f341(f242(a1),x85822),x85823))+~P85(f341(f341(f241(a1),f2(a1)),f341(f341(f89(a1),f341(f341(f90(a1),x85823),x85821)),x85822))) % 19.23/19.05 [8602]~P95(x86021)+~P85(f341(f71(x86021),x86022))+E(f341(f341(f3(f864(x86021,a850)),x86022),f341(f341(f311(x86021),x86023),f185(f864(x86021,a850)))),f185(f864(x86021,a850)))+E(f341(f341(f110(x86021),x86023),f15(x86021,f341(f341(f3(f864(x86021,a850)),x86022),f341(f341(f311(x86021),x86023),f185(f864(x86021,a850)))))),f15(x86021,f341(f341(f311(x86021),x86023),x86022))) % 19.23/19.05 [8603]~P95(x86031)+~P85(f341(f71(x86031),x86032))+E(f341(f341(f3(f864(x86031,a850)),x86032),f341(f341(f311(x86031),x86033),f185(f864(x86031,a850)))),f185(f864(x86031,a850)))+E(f341(f341(f111(x86031),x86033),f12(x86031,f341(f341(f3(f864(x86031,a850)),x86032),f341(f341(f311(x86031),x86033),f185(f864(x86031,a850)))))),f12(x86031,f341(f341(f311(x86031),x86033),x86032))) % 19.23/19.05 [8604]~P101(x86041)+~P85(f341(f71(x86041),x86042))+E(f341(f341(f3(f864(x86041,a850)),x86042),f341(f341(f311(x86041),x86043),f185(f864(x86041,a850)))),f185(f864(x86041,a850)))+E(f341(f341(f240(x86041),x86043),f16(x86041,f341(f341(f3(f864(x86041,a850)),x86042),f341(f341(f311(x86041),x86043),f185(f864(x86041,a850)))))),f16(x86041,f341(f341(f311(x86041),x86043),x86042))) % 19.23/19.05 [8605]~P101(x86051)+~P85(f341(f71(x86051),x86052))+E(f341(f341(f3(f864(x86051,a850)),x86052),f341(f341(f311(x86051),x86053),f185(f864(x86051,a850)))),f185(f864(x86051,a850)))+E(f341(f341(f245(x86051),x86053),f17(x86051,f341(f341(f3(f864(x86051,a850)),x86052),f341(f341(f311(x86051),x86053),f185(f864(x86051,a850)))))),f17(x86051,f341(f341(f311(x86051),x86053),x86052))) % 19.23/19.05 [8667]~P101(x86671)+~P85(f341(f71(x86671),x86672))+E(f341(f341(f3(f864(x86671,a850)),x86672),f341(f341(f311(x86671),x86673),f185(f864(x86671,a850)))),f185(f864(x86671,a850)))+E(f341(f341(f240(x86671),x86673),f13(x86671,f240(x86671),f341(f341(f3(f864(x86671,a850)),x86672),f341(f341(f311(x86671),x86673),f185(f864(x86671,a850)))))),f13(x86671,f240(x86671),f341(f341(f311(x86671),x86673),x86672))) % 19.23/19.05 [8668]~P101(x86681)+~P85(f341(f71(x86681),x86682))+E(f341(f341(f3(f864(x86681,a850)),x86682),f341(f341(f311(x86681),x86683),f185(f864(x86681,a850)))),f185(f864(x86681,a850)))+E(f341(f341(f245(x86681),x86683),f14(x86681,f245(x86681),f341(f341(f3(f864(x86681,a850)),x86682),f341(f341(f311(x86681),x86683),f185(f864(x86681,a850)))))),f14(x86681,f245(x86681),f341(f341(f311(x86681),x86683),x86682))) % 19.23/19.05 [9185]E(x91851,x91852)+~E(f341(f138(f858(x91853),f858(x91853),f132(x91853),f122(x91853)),x91851),f341(f138(f858(x91853),f858(x91853),f132(x91853),f122(x91853)),x91852))+~E(f341(f186(f858(f858(x91853))),x91851),f341(f186(f858(f858(x91853))),x91852))+P85(f341(f341(f343(f863(f858(x91853),f858(x91853))),f786(x91851,x91852,x91853)),f341(f163(f863(f858(x91853),f858(x91853))),f341(f341(f172(f858(x91853),f858(x91853)),x91852),x91851)))) % 19.23/19.05 [9186]E(x91861,x91862)+~E(f341(f138(f858(x91863),f858(x91863),f132(x91863),f122(x91863)),x91861),f341(f138(f858(x91863),f858(x91863),f132(x91863),f122(x91863)),x91862))+~E(f341(f186(f858(f858(x91863))),x91861),f341(f186(f858(f858(x91863))),x91862))+P85(f341(f341(f343(f863(f858(x91863),f858(x91863))),f787(x91862,x91861,x91863)),f341(f163(f863(f858(x91863),f858(x91863))),f341(f341(f172(f858(x91863),f858(x91863)),x91861),x91862)))) % 19.23/19.05 [10003]~P73(x100032)+E(x100031,f185(f864(x100032,a850)))+~P85(f341(f71(x100032),x100031))+E(f16(x100032,f341(f265(x100032),f341(f341(f10(f864(x100032,a850),a850,x100032),f96(x100032)),f341(f341(f9(x100032,f864(x100032,a850),f864(x100032,a850)),f341(f341(f10(f864(x100032,f864(a850,a850)),f864(f864(x100032,a850),f864(x100032,a850)),x100032),f20(x100032,a850,a850)),f341(f341(f10(f864(x100032,a850),f864(x100032,f864(a850,a850)),x100032),f341(f10(a850,f864(a850,a850),x100032),a339)),f341(f341(f9(x100032,f864(x100032,x100032),f864(x100032,a850)),f341(f341(f10(f864(x100032,a850),f864(f864(x100032,x100032),f864(x100032,a850)),x100032),f10(x100032,a850,x100032)),a338)),f341(f89(x100032),x100033))))),f341(f341(f9(x100032,f864(x100032,a850),a850),f343(x100032)),x100031))))),f341(f341(f89(x100032),x100033),f16(x100032,x100031))) % 19.23/19.05 [10004]~P73(x100042)+E(x100041,f185(f864(x100042,a850)))+~P85(f341(f71(x100042),x100041))+E(f17(x100042,f341(f265(x100042),f341(f341(f10(f864(x100042,a850),a850,x100042),f96(x100042)),f341(f341(f9(x100042,f864(x100042,a850),f864(x100042,a850)),f341(f341(f10(f864(x100042,f864(a850,a850)),f864(f864(x100042,a850),f864(x100042,a850)),x100042),f20(x100042,a850,a850)),f341(f341(f10(f864(x100042,a850),f864(x100042,f864(a850,a850)),x100042),f341(f10(a850,f864(a850,a850),x100042),a339)),f341(f341(f9(x100042,f864(x100042,x100042),f864(x100042,a850)),f341(f341(f10(f864(x100042,a850),f864(f864(x100042,x100042),f864(x100042,a850)),x100042),f10(x100042,a850,x100042)),a338)),f341(f89(x100042),x100043))))),f341(f341(f9(x100042,f864(x100042,a850),a850),f343(x100042)),x100041))))),f341(f341(f89(x100042),x100043),f17(x100042,x100041))) % 19.23/19.05 [10005]~P96(x100052)+E(x100051,f185(f864(x100052,a850)))+~P85(f341(f71(x100052),x100051))+E(f12(x100052,f341(f265(x100052),f341(f341(f10(f864(x100052,a850),a850,x100052),f96(x100052)),f341(f341(f9(x100052,f864(x100052,a850),f864(x100052,a850)),f341(f341(f10(f864(x100052,f864(a850,a850)),f864(f864(x100052,a850),f864(x100052,a850)),x100052),f20(x100052,a850,a850)),f341(f341(f10(f864(x100052,a850),f864(x100052,f864(a850,a850)),x100052),f341(f10(a850,f864(a850,a850),x100052),a339)),f341(f341(f9(x100052,f864(x100052,x100052),f864(x100052,a850)),f341(f341(f10(f864(x100052,a850),f864(f864(x100052,x100052),f864(x100052,a850)),x100052),f10(x100052,a850,x100052)),a338)),f341(f110(x100052),x100053))))),f341(f341(f9(x100052,f864(x100052,a850),a850),f343(x100052)),x100051))))),f341(f341(f110(x100052),x100053),f12(x100052,x100051))) % 19.23/19.05 [10006]~P96(x100062)+E(x100061,f185(f864(x100062,a850)))+~P85(f341(f71(x100062),x100061))+E(f15(x100062,f341(f265(x100062),f341(f341(f10(f864(x100062,a850),a850,x100062),f96(x100062)),f341(f341(f9(x100062,f864(x100062,a850),f864(x100062,a850)),f341(f341(f10(f864(x100062,f864(a850,a850)),f864(f864(x100062,a850),f864(x100062,a850)),x100062),f20(x100062,a850,a850)),f341(f341(f10(f864(x100062,a850),f864(x100062,f864(a850,a850)),x100062),f341(f10(a850,f864(a850,a850),x100062),a339)),f341(f341(f9(x100062,f864(x100062,x100062),f864(x100062,a850)),f341(f341(f10(f864(x100062,a850),f864(f864(x100062,x100062),f864(x100062,a850)),x100062),f10(x100062,a850,x100062)),a338)),f341(f111(x100062),x100063))))),f341(f341(f9(x100062,f864(x100062,a850),a850),f343(x100062)),x100061))))),f341(f341(f111(x100062),x100063),f15(x100062,x100061))) % 19.23/19.05 [10007]~P101(x100072)+E(x100071,f185(f864(x100072,a850)))+~P85(f341(f71(x100072),x100071))+E(f13(x100072,f240(x100072),f341(f265(x100072),f341(f341(f10(f864(x100072,a850),a850,x100072),f96(x100072)),f341(f341(f9(x100072,f864(x100072,a850),f864(x100072,a850)),f341(f341(f10(f864(x100072,f864(a850,a850)),f864(f864(x100072,a850),f864(x100072,a850)),x100072),f20(x100072,a850,a850)),f341(f341(f10(f864(x100072,a850),f864(x100072,f864(a850,a850)),x100072),f341(f10(a850,f864(a850,a850),x100072),a339)),f341(f341(f9(x100072,f864(x100072,x100072),f864(x100072,a850)),f341(f341(f10(f864(x100072,a850),f864(f864(x100072,x100072),f864(x100072,a850)),x100072),f10(x100072,a850,x100072)),a338)),f341(f245(x100072),x100073))))),f341(f341(f9(x100072,f864(x100072,a850),a850),f343(x100072)),x100071))))),f341(f341(f245(x100072),x100073),f13(x100072,f240(x100072),x100071))) % 19.23/19.05 [10008]~P101(x100082)+E(x100081,f185(f864(x100082,a850)))+~P85(f341(f71(x100082),x100081))+E(f14(x100082,f245(x100082),f341(f265(x100082),f341(f341(f10(f864(x100082,a850),a850,x100082),f96(x100082)),f341(f341(f9(x100082,f864(x100082,a850),f864(x100082,a850)),f341(f341(f10(f864(x100082,f864(a850,a850)),f864(f864(x100082,a850),f864(x100082,a850)),x100082),f20(x100082,a850,a850)),f341(f341(f10(f864(x100082,a850),f864(x100082,f864(a850,a850)),x100082),f341(f10(a850,f864(a850,a850),x100082),a339)),f341(f341(f9(x100082,f864(x100082,x100082),f864(x100082,a850)),f341(f341(f10(f864(x100082,a850),f864(f864(x100082,x100082),f864(x100082,a850)),x100082),f10(x100082,a850,x100082)),a338)),f341(f240(x100082),x100083))))),f341(f341(f9(x100082,f864(x100082,a850),a850),f343(x100082)),x100081))))),f341(f341(f240(x100082),x100083),f14(x100082,f245(x100082),x100081))) % 19.23/19.05 [9736]~P113(x97361)+~E(x97363,f2(x97361))+~E(x97362,f2(x97361))+E(f341(f341(f89(x97361),f341(f341(f251(x97361),x97362),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106))))),f341(f341(f251(x97361),x97363),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106))))),f2(x97361)) % 19.23/19.05 [9898]~P120(x98981)+~P85(f341(f341(f241(x98981),f2(x98981)),x98983))+P85(f341(f341(f241(x98981),x98982),x98983))+~P85(f341(f341(f241(x98981),f341(f341(f251(x98981),x98982),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106))))),f341(f341(f251(x98981),x98983),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))))) % 19.23/19.05 [9942]~P113(x99422)+~E(x99421,f2(x99422))+~E(x99423,f2(x99422))+~P85(f341(f341(f242(x99422),f2(x99422)),f341(f341(f89(x99422),f341(f341(f251(x99422),x99423),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106))))),f341(f341(f251(x99422),x99421),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106))))))) % 19.23/19.05 [9160]E(x91601,x91602)+~E(f762(x91601,x91602,x91604,x91603),f764(x91601,x91602,x91604,x91603))+P85(f341(f341(f343(f863(f858(x91603),f858(x91603))),f341(f341(f250(f858(x91603),f858(x91603)),x91602),x91601)),f143(x91603,x91604)))+P85(f341(f341(f343(f863(f858(x91603),f858(x91603))),f341(f341(f250(f858(x91603),f858(x91603)),x91601),x91602)),f143(x91603,x91604))) % 19.23/19.05 [4761]~P59(x47612)+~E(x47614,f2(x47612))+~E(x47611,f2(x47612))+E(x47611,f341(f341(f292(x47612),x47613),x47614)) % 19.23/19.05 [4762]~P59(x47621)+~E(x47623,f2(x47621))+~E(x47624,f2(x47621))+E(f341(f341(f292(x47621),x47622),x47623),x47624) % 19.23/19.05 [4869]~P59(x48692)+E(x48691,f2(x48692))+~E(x48693,f2(x48692))+~E(x48691,f341(f341(f292(x48692),x48694),x48693)) % 19.23/19.05 [4870]~P59(x48702)+E(x48701,f2(x48702))+~E(x48703,f2(x48702))+~E(f341(f341(f292(x48702),x48704),x48703),x48701) % 19.23/19.05 [5050]~P116(x50502)+E(x50501,f2(x50502))+~E(f341(f341(f292(x50502),x50503),x50501),x50504)+E(x50503,f341(f341(f90(x50502),x50504),x50501)) % 19.23/19.05 [5052]~P116(x50522)+E(x50521,f2(x50522))+~E(f341(f341(f90(x50522),x50523),x50521),x50524)+E(x50523,f341(f341(f292(x50522),x50524),x50521)) % 19.23/19.05 [5053]~P59(x50532)+E(x50531,f2(x50532))+~E(f341(f341(f292(x50532),x50533),x50531),x50534)+E(x50533,f341(f341(f90(x50532),x50534),x50531)) % 19.23/19.05 [5054]~P59(x50542)+E(x50541,f2(x50542))+~E(f341(f341(f90(x50542),x50543),x50541),x50544)+E(x50543,f341(f341(f292(x50542),x50544),x50541)) % 19.23/19.05 [5055]~P116(x50552)+E(x50551,f2(x50552))+~E(x50553,f341(f341(f292(x50552),x50554),x50551))+E(f341(f341(f90(x50552),x50553),x50551),x50554) % 19.23/19.05 [5057]~P116(x50572)+E(x50571,f2(x50572))+~E(x50573,f341(f341(f90(x50572),x50574),x50571))+E(f341(f341(f292(x50572),x50573),x50571),x50574) % 19.23/19.05 [5058]~P59(x50582)+E(x50581,f2(x50582))+~E(x50583,f341(f341(f292(x50582),x50584),x50581))+E(f341(f341(f90(x50582),x50583),x50581),x50584) % 19.23/19.05 [5059]~P59(x50592)+E(x50591,f2(x50592))+~E(x50593,f341(f341(f90(x50592),x50594),x50591))+E(f341(f341(f292(x50592),x50593),x50591),x50594) % 19.23/19.05 [5091]~P59(x50912)+~E(x50911,f2(x50912))+~E(f341(f341(f90(x50912),x50911),x50914),x50913)+E(x50911,f341(f341(f292(x50912),x50913),x50914)) % 19.23/19.05 [5092]~P59(x50921)+~E(x50924,f2(x50921))+~E(x50922,f341(f341(f90(x50921),x50924),x50923))+E(f341(f341(f292(x50921),x50922),x50923),x50924) % 19.23/19.05 [5158]~E(x51583,x51584)+~E(x51582,x51583)+~P100(x51581)+E(f304(x51581,x51582,x51583),f341(f341(f311(x51581),x51584),f185(f864(x51581,a850)))) % 19.23/19.05 [5352]~E(f140(x53522,x53521),x53524)+~E(f123(x53522,x53521),x53523)+E(x53521,f122(x53522))+E(f341(f341(f132(x53522),x53523),f341(f341(f146(x53522),x53524),f122(x53522))),x53521) % 19.23/19.05 [5969]~P120(x59693)+E(x59691,x59692)+~E(f341(f341(f251(x59693),x59694),x59691),f341(f341(f251(x59693),x59694),x59692))+~P85(f341(f341(f242(x59693),f87(x59693)),x59694)) % 19.23/19.05 [5970]E(x59701,x59702)+~E(f341(f341(f311(x59703),x59704),x59701),f341(f341(f311(x59703),x59704),x59702))+P85(f341(f341(f343(x59703),x59704),x59702))+P85(f341(f341(f343(x59703),x59704),x59701)) % 19.23/19.05 [6008]E(f341(x60081,x60082),f2(a857))+~E(f341(f341(f8(x60083,a857),x60081),x60084),f2(a857))+~P85(f341(f71(x60083),x60084))+~P85(f341(f341(f343(x60083),x60082),x60084)) % 19.23/19.05 [6009]E(f341(x60091,x60092),f87(a857))+~E(f341(f341(f11(x60093,a857),x60091),x60094),f87(a857))+~P85(f341(f71(x60093),x60094))+~P85(f341(f341(f343(x60093),x60092),x60094)) % 19.23/19.05 [6233]~P100(x62331)+~P85(f341(f341(f242(x62331),x62334),x62333))+P85(f341(f341(f242(x62331),x62332),x62333))+~P85(f341(f341(f242(x62331),x62332),x62334)) % 19.23/19.05 [6234]~P100(x62341)+~P85(f341(f341(f241(x62341),x62344),x62343))+P85(f341(f341(f242(x62341),x62342),x62343))+~P85(f341(f341(f242(x62341),x62342),x62344)) % 19.23/19.05 [6235]~P100(x62351)+~P85(f341(f341(f241(x62351),x62352),x62354))+P85(f341(f341(f242(x62351),x62352),x62353))+~P85(f341(f341(f242(x62351),x62354),x62353)) % 19.23/19.05 [6236]~P104(x62361)+~P85(f341(f341(f242(x62361),x62362),x62364))+P85(f341(f341(f242(x62361),x62362),x62363))+~P85(f341(f341(f242(x62361),x62364),x62363)) % 19.23/19.05 [6237]~P104(x62371)+~P85(f341(f341(f241(x62371),x62372),x62374))+P85(f341(f341(f242(x62371),x62372),x62373))+~P85(f341(f341(f242(x62371),x62374),x62373)) % 19.23/19.05 [6238]~P104(x62381)+~P85(f341(f341(f241(x62381),x62384),x62383))+P85(f341(f341(f242(x62381),x62382),x62383))+~P85(f341(f341(f242(x62381),x62382),x62384)) % 19.23/19.05 [6239]~P100(x62391)+~P85(f341(f341(f241(x62391),x62394),x62393))+P85(f341(f341(f241(x62391),x62392),x62393))+~P85(f341(f341(f241(x62391),x62392),x62394)) % 19.23/19.05 [6240]~P104(x62401)+~P85(f341(f341(f241(x62401),x62402),x62404))+P85(f341(f341(f241(x62401),x62402),x62403))+~P85(f341(f341(f241(x62401),x62404),x62403)) % 19.23/19.05 [6241]~P86(x62411)+~P85(f341(f341(f288(x62411),x62412),x62414))+P85(f341(f341(f288(x62411),x62412),x62413))+~P85(f341(f341(f288(x62411),x62414),x62413)) % 19.23/19.05 [6485]~P6(x64851)+~P85(f341(f341(f241(x64851),x64852),f53(x64851,x64854)))+P85(f341(f341(f241(x64851),x64852),x64853))+~P85(f341(f341(f343(x64851),x64853),x64854)) % 19.23/19.05 [6635]~P101(x66351)+~P15(x66351,f341(f341(f146(x66351),x66352),x66354))+~P85(f341(f341(f343(x66351),x66353),f341(f163(x66351),x66354)))+P85(f341(f341(f241(x66351),x66352),x66353)) % 19.23/19.05 [6727]~P6(x67271)+~P85(f341(f341(f241(x67271),f52(x67271,x67274)),x67273))+P85(f341(f341(f241(x67271),x67272),x67273))+~P85(f341(f341(f343(x67271),x67272),x67274)) % 19.23/19.05 [6879]~P4(x68791)+P85(f341(f341(f288(x68791),x68792),f60(x68791,x68793,x68794)))+~P85(f341(f341(f288(x68791),x68792),x68794))+~P85(f341(f341(f288(x68791),x68792),x68793)) % 19.23/19.05 [7138]~P101(x71381)+E(f341(f341(f110(f864(x71381,a850)),f341(f303(x71381,x71382),x71383)),f341(f303(x71381,x71383),x71384)),f341(f303(x71381,x71382),x71384))+~P85(f341(f341(f241(x71381),x71383),x71384))+~P85(f341(f341(f241(x71381),x71382),x71383)) % 19.23/19.05 [7225]~P4(x72251)+~P85(f341(f341(f288(x72251),x72252),f60(x72251,x72253,x72254)))+P85(f341(f341(f288(x72251),x72252),x72253))+~P85(f341(f341(f288(x72251),x72252),x72254)) % 19.23/19.05 [7266]~P101(x72661)+E(f341(f341(f110(f864(x72661,a850)),f341(f303(x72661,x72662),x72663)),f304(x72661,x72663,x72664)),f304(x72661,x72662,x72664))+~P85(f341(f341(f241(x72661),x72663),x72664))+~P85(f341(f341(f241(x72661),x72662),x72663)) % 19.23/19.05 [7280]~P100(x72801)+~P49(a857,x72801,f288(a857),x72802)+P85(f341(f341(f241(x72801),f341(x72802,x72803)),f341(x72802,x72804)))+~P85(f341(f341(f288(a857),x72803),x72804)) % 19.23/19.05 [7334]~P101(x73341)+E(f341(f341(f110(f864(x73341,a850)),f307(x73341,x73342,x73343)),f341(f303(x73341,x73343),x73344)),f307(x73341,x73342,x73344))+~P85(f341(f341(f242(x73341),x73342),x73343))+~P85(f341(f341(f241(x73341),x73343),x73344)) % 19.23/19.05 [7357]~P101(x73571)+E(f341(f341(f110(f864(x73571,a850)),f304(x73571,x73572,x73573)),f307(x73571,x73573,x73574)),f341(f303(x73571,x73572),x73574))+~P85(f341(f341(f242(x73571),x73573),x73574))+~P85(f341(f341(f241(x73571),x73572),x73573)) % 19.23/19.05 [7392]~P101(x73921)+E(f341(f341(f110(f864(x73921,a850)),f307(x73921,x73922,x73923)),f304(x73921,x73923,x73924)),f306(x73921,x73922,x73924))+~P85(f341(f341(f242(x73921),x73922),x73923))+~P85(f341(f341(f241(x73921),x73923),x73924)) % 19.23/19.05 [7393]~P101(x73931)+E(f341(f341(f110(f864(x73931,a850)),f306(x73931,x73932,x73933)),f307(x73931,x73933,x73934)),f307(x73931,x73932,x73934))+~P85(f341(f341(f242(x73931),x73933),x73934))+~P85(f341(f341(f241(x73931),x73932),x73933)) % 19.23/19.05 [7394]~P101(x73941)+E(f341(f341(f110(f864(x73941,a850)),f306(x73941,x73942,x73943)),f306(x73941,x73943,x73944)),f306(x73941,x73942,x73944))+~P85(f341(f341(f241(x73941),x73943),x73944))+~P85(f341(f341(f241(x73941),x73942),x73943)) % 19.23/19.05 [7395]~P101(x73951)+E(f341(f341(f110(f864(x73951,a850)),f304(x73951,x73952,x73953)),f306(x73951,x73953,x73954)),f304(x73951,x73952,x73954))+~P85(f341(f341(f241(x73951),x73953),x73954))+~P85(f341(f341(f241(x73951),x73952),x73953)) % 19.23/19.05 [8181]P26(x81811,x81812,f452(x81813,x81812,x81814,x81811),x81814)+~P85(f341(f71(x81812),x81813))+~P85(f341(f71(x81811),x81814))+~P85(f341(f341(f241(a857),f341(f50(x81811),x81814)),f341(f50(x81812),x81813))) % 19.23/19.05 [8251]~P71(x82511)+~E(f341(x82513,f631(x82513,x82514,x82512,x82511)),f87(x82511))+E(f341(f341(f341(f75(x82511,x82512,f90(x82511)),x82513),f87(x82511)),x82514),f87(x82511))+~P85(f341(f71(x82512),x82514)) % 19.23/19.05 [8524]~P120(x85241)+~P85(f341(f341(f241(x85241),f2(x85241)),x85243))+P85(f341(f341(f241(x85241),x85242),x85243))+~P85(f341(f341(f241(x85241),f341(f341(f251(x85241),x85242),f341(a121,x85244))),f341(f341(f251(x85241),x85243),f341(a121,x85244)))) % 19.23/19.05 [8857]~P71(x88571)+E(f341(f341(f341(f75(x88571,x88572,f90(x88571)),x88573),f87(x88571)),x88574),f87(x88571))+~P85(f341(f71(x88572),x88574))+P85(f341(f341(f343(x88572),f631(x88573,x88574,x88572,x88571)),x88574)) % 19.23/19.05 [9110]~P9(x91102,x91103,x91104)+~P85(f341(f71(x91102),x91103))+~P85(f341(f341(f288(a857),x91101),f341(f50(x91102),f404(x91101,x91104,x91103,x91102))))+P85(f341(f341(f288(a857),x91101),f341(f50(x91102),x91103))) % 19.23/19.05 [9308]~P85(f341(f341(f288(a857),x93081),x93083))+~P85(f341(f341(f288(a857),x93081),x93082))+~P85(f341(f341(f288(a857),x93084),x93083))+~P85(f341(f341(f242(f864(a857,a850)),f291(a857,f288(a857),x93081,x93083)),f291(a857,f288(a857),x93082,x93084))) % 19.23/19.05 [9313]~P85(f341(f341(f241(a1),x93134),f2(a1)))+P85(f341(f341(f241(a1),f341(f341(f89(a1),f341(f341(f90(a1),x93131),f60(a1,x93132,x93133))),x93134)),f2(a1)))+~P85(f341(f341(f242(a1),f2(a1)),x93133))+~P85(f341(f341(f242(a1),x93131),x93134)) % 19.23/19.05 [9727]~P85(f341(f71(x97271),x97272))+~P85(f341(f341(f343(x97271),x97274),x97272))+~P85(f341(f341(f343(x97271),x97273),x97272))+P85(f341(f341(f242(a857),f341(f50(x97271),f341(f341(f3(f864(x97271,a850)),f341(f341(f3(f864(x97271,a850)),x97272),f341(f341(f311(x97271),x97273),f185(f864(x97271,a850))))),f341(f341(f311(x97271),x97274),f185(f864(x97271,a850)))))),f341(f50(x97271),x97272))) % 19.23/19.05 [6789]~P139(x67893)+~P115(x67893)+P85(f341(x67891,f350(x67892,x67891,x67893)))+~P85(f341(x67891,f341(f341(f90(x67893),x67892),x67894))) % 19.23/19.05 [6849]~P101(x68491)+~P85(f341(f341(f242(x68491),x68492),x68494))+~P85(f341(f341(f242(x68491),x68492),x68493))+P85(f341(f341(f242(x68491),x68492),f341(f341(f245(x68491),x68493),x68494))) % 19.23/19.05 [6852]~P101(x68521)+~P85(f341(f341(f241(x68521),x68522),x68524))+~P85(f341(f341(f241(x68521),x68522),x68523))+P85(f341(f341(f241(x68521),x68522),f341(f341(f245(x68521),x68523),x68524))) % 19.23/19.05 [6855]~P99(x68551)+~P85(f341(f341(f241(x68551),x68552),x68554))+~P85(f341(f341(f241(x68551),x68552),x68553))+P85(f341(f341(f241(x68551),x68552),f341(f341(f111(x68551),x68553),x68554))) % 19.23/19.05 [6856]~P86(x68561)+~P85(f341(f341(f288(x68561),x68562),x68564))+~P85(f341(f341(f288(x68561),x68562),x68563))+P85(f341(f341(f288(x68561),x68562),f341(f341(f89(x68561),x68563),x68564))) % 19.23/19.05 [6857]~P105(x68571)+~P85(f341(f341(f288(x68571),x68572),x68574))+~P85(f341(f341(f288(x68571),x68572),x68573))+P85(f341(f341(f288(x68571),x68572),f341(f341(f3(x68571),x68573),x68574))) % 19.23/19.05 [6877]~P60(x68772)+E(x68771,f2(x68772))+E(f341(f341(f292(x68772),f341(f341(f251(x68772),x68771),x68773)),f341(f341(f251(x68772),x68771),x68774)),f341(f341(f251(x68772),x68771),f341(f341(f3(a857),x68773),x68774)))+~P85(f341(f341(f241(a857),x68774),x68773)) % 19.23/19.05 [6922]~P101(x69221)+~P15(x69221,f341(f341(f146(x69221),x69223),x69224))+P15(x69221,f341(f341(f146(x69221),x69222),f341(f341(f146(x69221),x69223),x69224)))+~P85(f341(f341(f241(x69221),x69222),x69223)) % 19.23/19.05 [6961]~P81(x69611)+~P85(f341(f341(f241(x69611),f2(x69611)),x69613))+~P85(f341(f341(f242(x69611),x69612),x69614))+P85(f341(f341(f242(x69611),x69612),f341(f341(f89(x69611),x69613),x69614))) % 19.23/19.05 [6962]~P81(x69621)+~P85(f341(f341(f241(x69621),x69622),x69624))+~P85(f341(f341(f242(x69621),f2(x69621)),x69623))+P85(f341(f341(f242(x69621),x69622),f341(f341(f89(x69621),x69623),x69624))) % 19.23/19.05 [6963]~P120(x69631)+~P85(f341(f341(f242(x69631),f2(x69631)),x69633))+~P85(f341(f341(f242(x69631),x69632),x69634))+P85(f341(f341(f242(x69631),x69632),f341(f341(f89(x69631),x69633),x69634))) % 19.23/19.05 [6964]~P81(x69641)+~P85(f341(f341(f241(x69641),f2(x69641)),x69644))+~P85(f341(f341(f241(x69641),x69642),x69643))+P85(f341(f341(f241(x69641),x69642),f341(f341(f89(x69641),x69643),x69644))) % 19.23/19.05 [6965]~P81(x69651)+~P85(f341(f341(f241(x69651),f2(x69651)),x69653))+~P85(f341(f341(f241(x69651),x69652),x69654))+P85(f341(f341(f241(x69651),x69652),f341(f341(f89(x69651),x69653),x69654))) % 19.23/19.05 [6999]~P101(x69991)+P85(f341(f341(f242(x69991),x69992),x69993))+P85(f341(f341(f242(x69991),x69992),x69994))+~P85(f341(f341(f242(x69991),x69992),f341(f341(f240(x69991),x69994),x69993))) % 19.23/19.05 [7000]~P101(x70001)+P85(f341(f341(f241(x70001),x70002),x70003))+P85(f341(f341(f241(x70001),x70002),x70004))+~P85(f341(f341(f241(x70001),x70002),f341(f341(f240(x70001),x70004),x70003))) % 19.23/19.05 [7682]~P62(x76821)+~P85(f341(f341(f242(x76821),x76824),f2(x76821)))+~P85(f341(f341(f242(x76821),x76823),f341(f341(f292(x76821),x76822),x76824)))+P85(f341(f341(f242(x76821),x76822),f341(f341(f90(x76821),x76823),x76824))) % 19.23/19.05 [7683]~P62(x76831)+~P85(f341(f341(f242(x76831),x76834),f2(x76831)))+~P85(f341(f341(f242(x76831),x76833),f341(f341(f90(x76831),x76832),x76834)))+P85(f341(f341(f242(x76831),x76832),f341(f341(f292(x76831),x76833),x76834))) % 19.23/19.05 [7684]~P62(x76841)+~P85(f341(f341(f242(x76841),x76844),f2(x76841)))+~P85(f341(f341(f241(x76841),x76843),f341(f341(f292(x76841),x76842),x76844)))+P85(f341(f341(f241(x76841),x76842),f341(f341(f90(x76841),x76843),x76844))) % 19.23/19.05 [7685]~P62(x76851)+~P85(f341(f341(f242(x76851),x76854),f2(x76851)))+~P85(f341(f341(f241(x76851),x76853),f341(f341(f90(x76851),x76852),x76854)))+P85(f341(f341(f241(x76851),x76852),f341(f341(f292(x76851),x76853),x76854))) % 19.23/19.05 [7798]~P122(x77981)+~P85(f341(f341(f242(x77981),x77983),f2(x77981)))+~P85(f341(f341(f242(x77981),x77984),x77982))+P85(f341(f341(f242(x77981),f341(f341(f90(x77981),x77982),x77983)),f341(f341(f90(x77981),x77984),x77983))) % 19.23/19.05 [7799]~P122(x77991)+~P85(f341(f341(f242(x77991),x77992),f2(x77991)))+~P85(f341(f341(f242(x77991),x77994),x77993))+P85(f341(f341(f242(x77991),f341(f341(f90(x77991),x77992),x77993)),f341(f341(f90(x77991),x77992),x77994))) % 19.23/19.05 [7800]~P62(x78001)+~P85(f341(f341(f242(x78001),x78003),f2(x78001)))+~P85(f341(f341(f242(x78001),x78004),x78002))+P85(f341(f341(f242(x78001),f341(f341(f292(x78001),x78002),x78003)),f341(f341(f292(x78001),x78004),x78003))) % 19.23/19.05 [7801]~P122(x78011)+~P85(f341(f341(f242(x78011),x78012),f2(x78011)))+~P85(f341(f341(f241(x78011),x78014),x78013))+P85(f341(f341(f241(x78011),f341(f341(f90(x78011),x78012),x78013)),f341(f341(f90(x78011),x78012),x78014))) % 19.23/19.05 [7802]~P131(x78021)+~P85(f341(f341(f241(x78021),x78022),f2(x78021)))+~P85(f341(f341(f241(x78021),x78024),x78023))+P85(f341(f341(f241(x78021),f341(f341(f90(x78021),x78022),x78023)),f341(f341(f90(x78021),x78022),x78024))) % 19.23/19.05 [7803]~P131(x78031)+~P85(f341(f341(f241(x78031),x78033),f2(x78031)))+~P85(f341(f341(f241(x78031),x78034),x78032))+P85(f341(f341(f241(x78031),f341(f341(f90(x78031),x78032),x78033)),f341(f341(f90(x78031),x78034),x78033))) % 19.23/19.05 [7804]~P61(x78041)+~P85(f341(f341(f241(x78041),x78043),f2(x78041)))+~P85(f341(f341(f241(x78041),x78044),x78042))+P85(f341(f341(f241(x78041),f341(f341(f292(x78041),x78042),x78043)),f341(f341(f292(x78041),x78044),x78043))) % 19.23/19.05 [7806]~P120(x78061)+~P85(f341(f341(f242(x78061),f87(x78061)),x78062))+~P85(f341(f341(f242(a857),x78063),x78064))+P85(f341(f341(f242(x78061),f341(f341(f251(x78061),x78062),x78063)),f341(f341(f251(x78061),x78062),x78064))) % 19.23/19.05 [7807]~P120(x78071)+~P85(f341(f341(f242(x78071),f87(x78071)),x78072))+~P85(f341(f341(f241(a857),x78073),x78074))+P85(f341(f341(f241(x78071),f341(f341(f251(x78071),x78072),x78073)),f341(f341(f251(x78071),x78072),x78074))) % 19.23/19.05 [7808]~P120(x78081)+~P85(f341(f341(f241(x78081),f87(x78081)),x78082))+~P85(f341(f341(f241(a857),x78083),x78084))+P85(f341(f341(f241(x78081),f341(f341(f251(x78081),x78082),x78083)),f341(f341(f251(x78081),x78082),x78084))) % 19.23/19.05 [7835]P85(f341(f341(f242(a857),f2(a857)),f341(x78351,x78352)))+~P85(f341(f71(x78353),x78354))+~P85(f341(f341(f343(x78353),x78352),x78354))+~P85(f341(f341(f242(a857),f2(a857)),f341(f341(f11(x78353,a857),x78351),x78354))) % 19.23/19.05 [7847]~P125(x78471)+~P85(f341(f341(f242(x78471),x78473),x78474))+~P85(f341(f341(f242(x78471),f2(x78471)),x78472))+P85(f341(f341(f242(x78471),f341(f341(f90(x78471),x78472),x78473)),f341(f341(f90(x78471),x78472),x78474))) % 19.23/19.05 [7848]~P118(x78481)+~P85(f341(f341(f242(x78481),x78483),x78484))+~P85(f341(f341(f242(x78481),f2(x78481)),x78482))+P85(f341(f341(f242(x78481),f341(f341(f90(x78481),x78482),x78483)),f341(f341(f90(x78481),x78482),x78484))) % 19.23/19.05 [7849]~P122(x78491)+~P85(f341(f341(f242(x78491),x78492),x78494))+~P85(f341(f341(f242(x78491),f2(x78491)),x78493))+P85(f341(f341(f242(x78491),f341(f341(f90(x78491),x78492),x78493)),f341(f341(f90(x78491),x78494),x78493))) % 19.23/19.05 [7850]~P125(x78501)+~P85(f341(f341(f242(x78501),x78502),x78504))+~P85(f341(f341(f242(x78501),f2(x78501)),x78503))+P85(f341(f341(f242(x78501),f341(f341(f90(x78501),x78502),x78503)),f341(f341(f90(x78501),x78504),x78503))) % 19.23/19.05 [7851]~P122(x78511)+~P85(f341(f341(f242(x78511),x78513),x78514))+~P85(f341(f341(f242(x78511),f2(x78511)),x78512))+P85(f341(f341(f242(x78511),f341(f341(f90(x78511),x78512),x78513)),f341(f341(f90(x78511),x78512),x78514))) % 19.23/19.05 [7852]~P62(x78521)+~P85(f341(f341(f242(x78521),x78522),x78524))+~P85(f341(f341(f242(x78521),f2(x78521)),x78523))+P85(f341(f341(f242(x78521),f341(f341(f292(x78521),x78522),x78523)),f341(f341(f292(x78521),x78524),x78523))) % 19.23/19.05 [7853]~P122(x78531)+~P85(f341(f341(f242(x78531),f2(x78531)),x78532))+~P85(f341(f341(f241(x78531),x78533),x78534))+P85(f341(f341(f241(x78531),f341(f341(f90(x78531),x78532),x78533)),f341(f341(f90(x78531),x78532),x78534))) % 19.23/19.05 [7854]~P133(x78541)+~P85(f341(f341(f241(x78541),x78543),x78544))+~P85(f341(f341(f241(x78541),f2(x78541)),x78542))+P85(f341(f341(f241(x78541),f341(f341(f90(x78541),x78542),x78543)),f341(f341(f90(x78541),x78542),x78544))) % 19.23/19.05 [7855]~P132(x78551)+~P85(f341(f341(f241(x78551),x78553),x78554))+~P85(f341(f341(f241(x78551),f2(x78551)),x78552))+P85(f341(f341(f241(x78551),f341(f341(f90(x78551),x78552),x78553)),f341(f341(f90(x78551),x78552),x78554))) % 19.23/19.05 [7856]~P133(x78561)+~P85(f341(f341(f241(x78561),x78562),x78564))+~P85(f341(f341(f241(x78561),f2(x78561)),x78563))+P85(f341(f341(f241(x78561),f341(f341(f90(x78561),x78562),x78563)),f341(f341(f90(x78561),x78564),x78563))) % 19.23/19.05 [7857]~P120(x78571)+~P85(f341(f341(f241(x78571),x78572),x78574))+~P85(f341(f341(f241(x78571),f2(x78571)),x78572))+P85(f341(f341(f241(x78571),f341(f341(f251(x78571),x78572),x78573)),f341(f341(f251(x78571),x78574),x78573))) % 19.23/19.05 [7858]~P61(x78581)+~P85(f341(f341(f241(x78581),x78582),x78584))+~P85(f341(f341(f241(x78581),f2(x78581)),x78583))+P85(f341(f341(f241(x78581),f341(f341(f292(x78581),x78582),x78583)),f341(f341(f292(x78581),x78584),x78583))) % 19.23/19.05 [7897]~P103(x78972)+P85(f341(f341(f241(f864(x78971,x78972)),x78974),x78973))+~P85(f341(f341(f241(f864(x78971,x78972)),x78973),x78974))+P85(f341(f341(f242(f864(x78971,x78972)),x78973),x78974)) % 19.23/19.05 [7941]P85(f341(f341(f343(x79411),x79412),x79413))+P85(f341(f341(f343(x79411),x79412),x79414))+~P85(f341(f341(f241(f864(x79411,a850)),x79414),x79413))+P85(f341(f341(f242(f864(x79411,a850)),x79414),f341(f341(f311(x79411),x79412),x79413))) % 19.23/19.05 [8047]~P114(x80472)+E(x80471,f2(x80472))+P85(f341(f341(f288(x80472),x80473),x80474))+~P85(f341(f341(f288(x80472),f341(f341(f90(x80472),x80473),x80471)),f341(f341(f90(x80472),x80474),x80471))) % 19.23/19.05 [8048]~P114(x80482)+E(x80481,f2(x80482))+P85(f341(f341(f288(x80482),x80483),x80484))+~P85(f341(f341(f288(x80482),f341(f341(f90(x80482),x80481),x80483)),f341(f341(f90(x80482),x80481),x80484))) % 19.23/19.05 [8092]P85(f341(f341(f343(x80921),x80922),x80923))+P85(f341(f341(f343(x80921),x80922),x80924))+~P85(f341(f341(f242(f864(x80921,a850)),x80924),f341(f341(f311(x80921),x80922),x80923)))+P85(f341(f341(f241(f864(x80921,a850)),x80924),x80923)) % 19.23/19.05 [8159]~P122(x81591)+P85(f341(f341(f242(x81591),x81593),x81592))+P85(f341(f341(f242(x81591),x81592),x81593))+~P85(f341(f341(f242(x81591),f341(f341(f90(x81591),x81594),x81592)),f341(f341(f90(x81591),x81594),x81593))) % 19.23/19.05 [8160]~P122(x81601)+P85(f341(f341(f242(x81601),x81603),x81602))+P85(f341(f341(f242(x81601),x81602),x81603))+~P85(f341(f341(f242(x81601),f341(f341(f90(x81601),x81602),x81604)),f341(f341(f90(x81601),x81603),x81604))) % 19.23/19.05 [8171]~P122(x81711)+P85(f341(f341(f242(x81711),x81714),f2(x81711)))+P85(f341(f341(f242(x81711),x81712),x81713))+~P85(f341(f341(f242(x81711),f341(f341(f90(x81711),x81712),x81714)),f341(f341(f90(x81711),x81713),x81714))) % 19.23/19.05 [8172]~P122(x81721)+P85(f341(f341(f242(x81721),x81724),f2(x81721)))+P85(f341(f341(f242(x81721),x81722),x81723))+~P85(f341(f341(f242(x81721),f341(f341(f90(x81721),x81724),x81722)),f341(f341(f90(x81721),x81724),x81723))) % 19.23/19.05 [8175]~P122(x81751)+P85(f341(f341(f242(x81751),x81752),x81753))+P85(f341(f341(f242(x81751),f2(x81751)),x81754))+~P85(f341(f341(f242(x81751),f341(f341(f90(x81751),x81754),x81753)),f341(f341(f90(x81751),x81754),x81752))) % 19.23/19.05 [8176]~P122(x81761)+P85(f341(f341(f242(x81761),x81762),x81763))+P85(f341(f341(f242(x81761),f2(x81761)),x81764))+~P85(f341(f341(f242(x81761),f341(f341(f90(x81761),x81763),x81764)),f341(f341(f90(x81761),x81762),x81764))) % 19.23/19.05 [8189]~P122(x81891)+P85(f341(f341(f242(x81891),x81892),f2(x81891)))+P85(f341(f341(f242(x81891),f2(x81891)),x81892))+~P85(f341(f341(f242(x81891),f341(f341(f90(x81891),x81893),x81892)),f341(f341(f90(x81891),x81894),x81892))) % 19.23/19.05 [8190]~P122(x81901)+P85(f341(f341(f242(x81901),x81902),f2(x81901)))+P85(f341(f341(f242(x81901),f2(x81901)),x81902))+~P85(f341(f341(f242(x81901),f341(f341(f90(x81901),x81902),x81903)),f341(f341(f90(x81901),x81902),x81904))) % 19.23/19.05 [8214]~P122(x82141)+~P85(f341(f341(f242(x82141),x82144),f2(x82141)))+P85(f341(f341(f242(x82141),x82142),x82143))+~P85(f341(f341(f242(x82141),f341(f341(f90(x82141),x82144),x82143)),f341(f341(f90(x82141),x82144),x82142))) % 19.23/19.05 [8215]~P122(x82151)+~P85(f341(f341(f242(x82151),x82154),f2(x82151)))+P85(f341(f341(f241(x82151),x82152),x82153))+~P85(f341(f341(f241(x82151),f341(f341(f90(x82151),x82154),x82153)),f341(f341(f90(x82151),x82154),x82152))) % 19.23/19.05 [8227]~P120(x82273)+~P85(f341(f341(f242(x82273),f87(x82273)),x82274))+P85(f341(f341(f242(a857),x82271),x82272))+~P85(f341(f341(f242(x82273),f341(f341(f251(x82273),x82274),x82271)),f341(f341(f251(x82273),x82274),x82272))) % 19.23/19.05 [8229]~P120(x82293)+~P85(f341(f341(f242(x82293),f87(x82293)),x82294))+P85(f341(f341(f241(a857),x82291),x82292))+~P85(f341(f341(f241(x82293),f341(f341(f251(x82293),x82294),x82291)),f341(f341(f251(x82293),x82294),x82292))) % 19.23/19.05 [8239]~P122(x82391)+P85(f341(f341(f242(x82391),x82392),x82393))+~P85(f341(f341(f242(x82391),f2(x82391)),x82394))+~P85(f341(f341(f242(x82391),f341(f341(f90(x82391),x82394),x82392)),f341(f341(f90(x82391),x82394),x82393))) % 19.23/19.05 [8240]~P125(x82401)+P85(f341(f341(f242(x82401),x82402),x82403))+~P85(f341(f341(f241(x82401),f2(x82401)),x82404))+~P85(f341(f341(f242(x82401),f341(f341(f90(x82401),x82404),x82402)),f341(f341(f90(x82401),x82404),x82403))) % 19.23/19.05 [8241]~P127(x82411)+P85(f341(f341(f242(x82411),x82412),x82413))+~P85(f341(f341(f241(x82411),f2(x82411)),x82414))+~P85(f341(f341(f242(x82411),f341(f341(f90(x82411),x82414),x82412)),f341(f341(f90(x82411),x82414),x82413))) % 19.23/19.05 [8242]~P120(x82421)+~P85(f341(f341(f241(x82421),f2(x82421)),x82423))+P85(f341(f341(f242(x82421),x82422),x82423))+~P85(f341(f341(f242(x82421),f341(f341(f251(x82421),x82422),x82424)),f341(f341(f251(x82421),x82423),x82424))) % 19.23/19.05 [8243]~P125(x82431)+P85(f341(f341(f242(x82431),x82432),x82433))+~P85(f341(f341(f241(x82431),f2(x82431)),x82434))+~P85(f341(f341(f242(x82431),f341(f341(f90(x82431),x82432),x82434)),f341(f341(f90(x82431),x82433),x82434))) % 19.23/19.05 [8244]~P127(x82441)+P85(f341(f341(f242(x82441),x82442),x82443))+~P85(f341(f341(f241(x82441),f2(x82441)),x82444))+~P85(f341(f341(f242(x82441),f341(f341(f90(x82441),x82442),x82444)),f341(f341(f90(x82441),x82443),x82444))) % 19.23/19.05 [8245]~P122(x82451)+P85(f341(f341(f241(x82451),x82452),x82453))+~P85(f341(f341(f242(x82451),f2(x82451)),x82454))+~P85(f341(f341(f241(x82451),f341(f341(f90(x82451),x82454),x82452)),f341(f341(f90(x82451),x82454),x82453))) % 19.23/19.05 [8246]~P125(x82461)+P85(f341(f341(f241(x82461),x82462),x82463))+~P85(f341(f341(f242(x82461),f2(x82461)),x82464))+~P85(f341(f341(f241(x82461),f341(f341(f90(x82461),x82464),x82462)),f341(f341(f90(x82461),x82464),x82463))) % 19.23/19.05 [8247]~P125(x82471)+P85(f341(f341(f241(x82471),x82472),x82473))+~P85(f341(f341(f242(x82471),f2(x82471)),x82474))+~P85(f341(f341(f241(x82471),f341(f341(f90(x82471),x82472),x82474)),f341(f341(f90(x82471),x82473),x82474))) % 19.23/19.05 [8288]P85(f341(f341(f343(x82881),x82882),x82883))+~P85(f341(f341(f241(f864(x82881,a850)),x82883),x82884))+~P85(f341(f341(f242(f864(x82881,a850)),x82883),x82884))+P85(f341(f341(f242(f864(x82881,a850)),x82883),f341(f341(f311(x82881),x82882),x82884))) % 19.23/19.05 [8323]~P139(x83231)+~P115(x83231)+P85(f341(f341(f288(x83231),x83232),f341(f341(f89(x83231),f350(x83232,x83233,x83231)),f2(x83231))))+~P85(f341(x83233,f341(f341(f90(x83231),x83232),x83234))) % 19.23/19.05 [8648]E(f341(f341(f3(a1),f476(x86481,x86482,x86483,x86484)),f477(x86481,x86482,x86483,x86484)),x86484)+~P85(f341(f341(f242(a1),f2(a1)),x86483))+~P85(f341(f341(f241(a1),x86481),x86484))+P85(f341(f341(f241(a1),x86481),f341(f341(f89(a1),x86484),x86483))) % 19.23/19.05 [8649]E(f341(f341(f3(a1),f486(x86491,x86492,x86493,x86494)),f487(x86491,x86492,x86493,x86494)),x86494)+~P85(f341(f341(f242(a1),f2(a1)),x86493))+~P85(f341(f341(f242(a1),x86491),x86494))+P85(f341(f341(f242(a1),x86491),f341(f341(f89(a1),x86494),x86493))) % 19.23/19.05 [8775]~E(f341(f341(f158(x87751),x87753),f768(x87754,x87753,x87751,x87752)),f341(f341(f158(x87751),x87754),f768(x87754,x87753,x87751,x87752)))+E(f341(f341(f164(x87751),x87752),x87753),f341(f341(f164(x87751),x87752),x87754))+~P85(f341(f341(f241(a857),x87752),f341(f186(f858(x87751)),x87753)))+~P85(f341(f341(f241(a857),x87752),f341(f186(f858(x87751)),x87754))) % 19.23/19.05 [8829]~P85(f341(f341(f242(a1),f2(a1)),x88293))+~P85(f341(f341(f241(a1),x88291),x88294))+P85(f341(f341(f343(a1),f476(x88291,x88292,x88293,x88294)),x88292))+P85(f341(f341(f241(a1),x88291),f341(f341(f89(a1),x88294),x88293))) % 19.23/19.05 [8830]~P85(f341(f341(f242(a1),f2(a1)),x88303))+~P85(f341(f341(f242(a1),x88301),x88304))+P85(f341(f341(f343(a1),f486(x88301,x88302,x88303,x88304)),x88302))+P85(f341(f341(f242(a1),x88301),f341(f341(f89(a1),x88304),x88303))) % 19.23/19.05 [8866]~P101(x88661)+~P85(f341(f71(x88661),x88663))+~P85(f341(f341(f343(x88661),x88664),x88663))+P85(f341(f341(f241(x88661),f341(f341(f74(x88661,x88661,f245(x88661)),x88662),x88663)),f341(f341(f245(x88661),x88664),x88662))) % 19.23/19.05 [8867]~P99(x88671)+~P85(f341(f71(x88671),x88673))+~P85(f341(f341(f343(x88671),x88674),x88673))+P85(f341(f341(f241(x88671),f341(f341(f74(x88671,x88671,f111(x88671)),x88672),x88673)),f341(f341(f111(x88671),x88674),x88672))) % 19.23/19.05 [8876]~P9(x88762,x88763,x88764)+~P85(f341(f71(x88762),x88763))+P85(f341(f341(f288(a857),x88761),f341(f50(x88762),x88763)))+P85(f341(f341(f343(f864(x88762,a850)),f404(x88761,x88764,x88763,x88762)),f341(f341(f69(x88762),x88763),x88764))) % 19.23/19.05 [8915]E(f341(f341(f164(x89151),x89152),x89153),f341(f341(f164(x89151),x89152),x89154))+P85(f341(f341(f242(a857),f768(x89153,x89154,x89151,x89152)),x89152))+~P85(f341(f341(f241(a857),x89152),f341(f186(f858(x89151)),x89153)))+~P85(f341(f341(f241(a857),x89152),f341(f186(f858(x89151)),x89154))) % 19.23/19.05 [8920]~P85(f341(f341(f242(a1),f2(a1)),x89203))+~P85(f341(f341(f242(a1),x89201),x89202))+P85(f341(f341(f343(a1),f487(x89201,x89204,x89203,x89202)),f304(a1,f87(a1),x89203)))+P85(f341(f341(f242(a1),x89201),f341(f341(f89(a1),x89202),x89203))) % 19.23/19.05 [8921]~P85(f341(f341(f242(a1),f2(a1)),x89213))+~P85(f341(f341(f241(a1),x89211),x89212))+P85(f341(f341(f343(a1),f477(x89211,x89214,x89213,x89212)),f304(a1,f87(a1),x89213)))+P85(f341(f341(f241(a1),x89211),f341(f341(f89(a1),x89212),x89213))) % 19.23/19.05 [9086]~E(f171(x90861,x90862,x90863),f171(x90861,x90862,x90864))+E(f341(f163(f863(x90861,x90862)),x90863),f341(f163(f863(x90861,x90862)),x90864))+~P85(f341(f134(x90861),f341(f341(f149(f863(x90861,x90862),x90861),f249(x90861,x90862)),x90864)))+~P85(f341(f134(x90861),f341(f341(f149(f863(x90861,x90862),x90861),f249(x90861,x90862)),x90863))) % 19.23/19.05 [9089]E(f171(x90891,x90892,x90893),f171(x90891,x90892,x90894))+~E(f341(f163(f863(x90891,x90892)),x90893),f341(f163(f863(x90891,x90892)),x90894))+~P85(f341(f134(x90891),f341(f341(f149(f863(x90891,x90892),x90891),f249(x90891,x90892)),x90894)))+~P85(f341(f134(x90891),f341(f341(f149(f863(x90891,x90892),x90891),f249(x90891,x90892)),x90893))) % 19.23/19.05 [9204]~P101(x92041)+~P85(f341(f71(x92041),x92044))+P85(f341(f341(f343(x92041),f696(x92042,x92043,x92044,x92041)),x92044))+P85(f341(f341(f241(x92041),f341(f341(f74(x92041,x92041,f240(x92041)),x92042),x92044)),f341(f341(f240(x92041),x92043),x92042))) % 19.23/19.05 [9205]~P98(x92051)+~P85(f341(f71(x92051),x92054))+P85(f341(f341(f343(x92051),f700(x92052,x92053,x92054,x92051)),x92054))+P85(f341(f341(f241(x92051),f341(f341(f74(x92051,x92051,f110(x92051)),x92052),x92054)),f341(f341(f110(x92051),x92053),x92052))) % 19.23/19.05 [9330]~P101(x93301)+~P85(f341(f71(x93301),x93303))+~P85(f341(f341(f241(x93301),f696(x93302,x93304,x93303,x93301)),x93304))+P85(f341(f341(f241(x93301),f341(f341(f74(x93301,x93301,f240(x93301)),x93302),x93303)),f341(f341(f240(x93301),x93304),x93302))) % 19.23/19.05 [9331]~P98(x93311)+~P85(f341(f71(x93311),x93313))+~P85(f341(f341(f241(x93311),f700(x93312,x93314,x93313,x93311)),x93314))+P85(f341(f341(f241(x93311),f341(f341(f74(x93311,x93311,f110(x93311)),x93312),x93313)),f341(f341(f110(x93311),x93314),x93312))) % 19.23/19.05 [9334]~P85(f341(f341(f242(a1),f2(a1)),x93343))+~P85(f341(f341(f241(a1),f2(a1)),x93344))+~P85(f341(f341(f242(a1),x93344),x93341))+P85(f341(f341(f242(a1),f341(f341(f89(a1),f341(f341(f90(a1),x93341),f60(a1,x93342,x93343))),x93344)),f341(f341(f90(a1),x93341),x93343))) % 19.23/19.05 [9601]~P100(x96011)+P85(f341(f341(f242(x96011),f341(x96012,x96013)),f341(x96012,x96014)))+~P85(f341(f341(f242(a857),x96013),x96014))+~P85(f341(f341(f242(x96011),f341(x96012,f736(x96014,x96013,x96012,x96011))),f341(x96012,f341(a121,f736(x96014,x96013,x96012,x96011))))) % 19.23/19.05 [9602]~P100(x96021)+P85(f341(f341(f242(x96021),f341(x96022,x96023)),f341(x96022,x96024)))+~P85(f341(f341(f242(a857),x96023),x96024))+~P85(f341(f341(f242(x96021),f341(x96022,f724(x96024,x96023,x96022,x96021))),f341(x96022,f341(a121,f724(x96024,x96023,x96022,x96021))))) % 19.23/19.05 [9603]~P100(x96033)+~P85(f341(f341(f242(x96033),f341(x96034,x96031)),f341(x96034,x96032)))+P85(f341(f341(f242(a857),x96031),x96032))+~P85(f341(f341(f242(x96033),f341(x96034,f736(x96032,x96031,x96034,x96033))),f341(x96034,f341(a121,f736(x96032,x96031,x96034,x96033))))) % 19.23/19.05 [9697]E(x96971,x96972)+P85(f341(f341(f343(f863(f858(x96973),f858(x96973))),f341(f341(f250(f858(x96973),f858(x96973)),x96972),x96971)),f143(x96973,x96974)))+P85(f341(f341(f343(f863(f858(x96973),f858(x96973))),f341(f341(f250(f858(x96973),f858(x96973)),x96971),x96972)),f143(x96973,x96974)))+~P85(f341(f341(f343(f863(x96973,x96973)),f341(f341(f250(x96973,x96973),f762(x96971,x96972,x96974,x96973)),f764(x96971,x96972,x96974,x96973))),x96974)) % 19.23/19.05 [9698]E(x96981,x96982)+P85(f341(f341(f343(f863(f858(x96983),f858(x96983))),f341(f341(f250(f858(x96983),f858(x96983)),x96982),x96981)),f143(x96983,x96984)))+P85(f341(f341(f343(f863(f858(x96983),f858(x96983))),f341(f341(f250(f858(x96983),f858(x96983)),x96981),x96982)),f143(x96983,x96984)))+~P85(f341(f341(f343(f863(x96983,x96983)),f341(f341(f250(x96983,x96983),f764(x96981,x96982,x96984,x96983)),f762(x96981,x96982,x96984,x96983))),x96984)) % 19.23/19.05 [7381]~P101(x73811)+~P85(f341(f341(f242(x73811),x73813),x73814))+~P85(f341(f341(f242(x73811),x73812),x73814))+P85(f341(f341(f242(x73811),f341(f341(f240(x73811),x73812),x73813)),x73814)) % 19.23/19.05 [7384]~P101(x73841)+~P85(f341(f341(f241(x73841),x73843),x73844))+~P85(f341(f341(f241(x73841),x73842),x73844))+P85(f341(f341(f241(x73841),f341(f341(f240(x73841),x73842),x73843)),x73844)) % 19.23/19.05 [7387]~P98(x73871)+~P85(f341(f341(f241(x73871),x73873),x73874))+~P85(f341(f341(f241(x73871),x73872),x73874))+P85(f341(f341(f241(x73871),f341(f341(f110(x73871),x73872),x73873)),x73874)) % 19.23/19.05 [7627]~P4(x76271)+E(f341(f341(f89(x76271),f341(f341(f51(x76271),x76272),x76273)),f341(f341(f51(x76271),x76274),x76273)),f341(f341(f51(x76271),f341(f341(f89(x76271),x76272),x76274)),x76273))+~P85(f341(f341(f288(x76271),x76273),x76274))+~P85(f341(f341(f288(x76271),x76273),x76272)) % 19.23/19.05 [7705]~E(x77051,x77053)+E(f136(a857,f341(f303(a857,x77051),x77052)),f341(f341(f146(a857),x77053),x77054))+~E(f136(a857,f341(f303(a857,f341(f341(f89(a857),x77051),f87(a857))),x77052)),x77054)+~P85(f341(f341(f242(a857),x77051),x77052)) % 19.23/19.05 [7716]~P101(x77161)+P85(f341(f341(f242(x77161),x77162),x77163))+P85(f341(f341(f242(x77161),x77164),x77163))+~P85(f341(f341(f242(x77161),f341(f341(f245(x77161),x77164),x77162)),x77163)) % 19.23/19.05 [7717]~P101(x77171)+P85(f341(f341(f241(x77171),x77172),x77173))+P85(f341(f341(f241(x77171),x77174),x77173))+~P85(f341(f341(f241(x77171),f341(f341(f245(x77171),x77174),x77172)),x77173)) % 19.23/19.05 [7998]~P61(x79981)+~P85(f341(f341(f242(x79981),f2(x79981)),x79983))+~P85(f341(f341(f242(x79981),x79982),f341(f341(f292(x79981),x79984),x79983)))+P85(f341(f341(f242(x79981),f341(f341(f90(x79981),x79982),x79983)),x79984)) % 19.23/19.05 [7999]~P62(x79991)+~P85(f341(f341(f242(x79991),f2(x79991)),x79993))+~P85(f341(f341(f242(x79991),x79992),f341(f341(f292(x79991),x79994),x79993)))+P85(f341(f341(f242(x79991),f341(f341(f90(x79991),x79992),x79993)),x79994)) % 19.23/19.05 [8000]~P61(x80001)+~P85(f341(f341(f242(x80001),f2(x80001)),x80003))+~P85(f341(f341(f242(x80001),x80002),f341(f341(f90(x80001),x80004),x80003)))+P85(f341(f341(f242(x80001),f341(f341(f292(x80001),x80002),x80003)),x80004)) % 19.23/19.05 [8002]~P62(x80021)+~P85(f341(f341(f242(x80021),f2(x80021)),x80023))+~P85(f341(f341(f242(x80021),x80022),f341(f341(f90(x80021),x80024),x80023)))+P85(f341(f341(f242(x80021),f341(f341(f292(x80021),x80022),x80023)),x80024)) % 19.23/19.05 [8003]~P61(x80031)+~P85(f341(f341(f242(x80031),f2(x80031)),x80033))+~P85(f341(f341(f241(x80031),x80032),f341(f341(f292(x80031),x80034),x80033)))+P85(f341(f341(f241(x80031),f341(f341(f90(x80031),x80032),x80033)),x80034)) % 19.23/19.05 [8004]~P62(x80041)+~P85(f341(f341(f242(x80041),f2(x80041)),x80043))+~P85(f341(f341(f241(x80041),x80042),f341(f341(f292(x80041),x80044),x80043)))+P85(f341(f341(f241(x80041),f341(f341(f90(x80041),x80042),x80043)),x80044)) % 19.23/19.05 [8005]~P61(x80051)+~P85(f341(f341(f242(x80051),f2(x80051)),x80053))+~P85(f341(f341(f241(x80051),x80052),f341(f341(f90(x80051),x80054),x80053)))+P85(f341(f341(f241(x80051),f341(f341(f292(x80051),x80052),x80053)),x80054)) % 19.23/19.05 [8007]~P62(x80071)+~P85(f341(f341(f242(x80071),f2(x80071)),x80073))+~P85(f341(f341(f241(x80071),x80072),f341(f341(f90(x80071),x80074),x80073)))+P85(f341(f341(f241(x80071),f341(f341(f292(x80071),x80072),x80073)),x80074)) % 19.23/19.05 [8129]~P61(x81291)+~P85(f341(f341(f242(x81291),f2(x81291)),x81294))+P85(f341(f341(f242(x81291),x81292),f341(f341(f90(x81291),x81293),x81294)))+~P85(f341(f341(f242(x81291),f341(f341(f292(x81291),x81292),x81294)),x81293)) % 19.23/19.05 [8130]~P61(x81301)+~P85(f341(f341(f242(x81301),f2(x81301)),x81304))+P85(f341(f341(f242(x81301),x81302),f341(f341(f292(x81301),x81303),x81304)))+~P85(f341(f341(f242(x81301),f341(f341(f90(x81301),x81302),x81304)),x81303)) % 19.23/19.05 [8132]~P62(x81321)+~P85(f341(f341(f242(x81321),f2(x81321)),x81324))+P85(f341(f341(f242(x81321),x81322),f341(f341(f90(x81321),x81323),x81324)))+~P85(f341(f341(f242(x81321),f341(f341(f292(x81321),x81322),x81324)),x81323)) % 19.23/19.05 [8133]~P62(x81331)+~P85(f341(f341(f242(x81331),f2(x81331)),x81334))+P85(f341(f341(f242(x81331),x81332),f341(f341(f292(x81331),x81333),x81334)))+~P85(f341(f341(f242(x81331),f341(f341(f90(x81331),x81332),x81334)),x81333)) % 19.23/19.05 [8134]~P61(x81341)+~P85(f341(f341(f242(x81341),f2(x81341)),x81344))+P85(f341(f341(f241(x81341),x81342),f341(f341(f90(x81341),x81343),x81344)))+~P85(f341(f341(f241(x81341),f341(f341(f292(x81341),x81342),x81344)),x81343)) % 19.23/19.05 [8135]~P61(x81351)+~P85(f341(f341(f242(x81351),f2(x81351)),x81354))+P85(f341(f341(f241(x81351),x81352),f341(f341(f292(x81351),x81353),x81354)))+~P85(f341(f341(f241(x81351),f341(f341(f90(x81351),x81352),x81354)),x81353)) % 19.23/19.05 [8137]~P62(x81371)+~P85(f341(f341(f242(x81371),f2(x81371)),x81374))+P85(f341(f341(f241(x81371),x81372),f341(f341(f90(x81371),x81373),x81374)))+~P85(f341(f341(f241(x81371),f341(f341(f292(x81371),x81372),x81374)),x81373)) % 19.23/19.05 [8138]~P62(x81381)+~P85(f341(f341(f242(x81381),f2(x81381)),x81384))+P85(f341(f341(f241(x81381),x81382),f341(f341(f292(x81381),x81383),x81384)))+~P85(f341(f341(f241(x81381),f341(f341(f90(x81381),x81382),x81384)),x81383)) % 19.23/19.05 [8293]~P62(x82931)+~P85(f341(f341(f242(x82931),x82933),f2(x82931)))+~P85(f341(f341(f242(x82931),f341(f341(f292(x82931),x82934),x82933)),x82932))+P85(f341(f341(f242(x82931),f341(f341(f90(x82931),x82932),x82933)),x82934)) % 19.23/19.05 [8294]~P62(x82941)+~P85(f341(f341(f242(x82941),x82943),f2(x82941)))+~P85(f341(f341(f242(x82941),f341(f341(f90(x82941),x82944),x82943)),x82942))+P85(f341(f341(f242(x82941),f341(f341(f292(x82941),x82942),x82943)),x82944)) % 19.23/19.05 [8295]~P62(x82951)+~P85(f341(f341(f242(x82951),x82953),f2(x82951)))+~P85(f341(f341(f241(x82951),f341(f341(f292(x82951),x82954),x82953)),x82952))+P85(f341(f341(f241(x82951),f341(f341(f90(x82951),x82952),x82953)),x82954)) % 19.23/19.05 [8296]~P62(x82961)+~P85(f341(f341(f242(x82961),x82963),f2(x82961)))+~P85(f341(f341(f241(x82961),f341(f341(f90(x82961),x82964),x82963)),x82962))+P85(f341(f341(f241(x82961),f341(f341(f292(x82961),x82962),x82963)),x82964)) % 19.23/19.05 [8309]~P85(f341(x83091,x83094))+~P85(f341(f341(f242(a857),x83092),f341(f341(f90(a857),x83093),f341(a121,x83094))))+P85(f341(x83091,f341(f341(f51(a857),x83092),x83093)))+~P85(f341(f341(f241(a857),f341(f341(f90(a857),x83093),x83094)),x83092)) % 19.23/19.05 [8522]~P101(x85221)+~P85(f341(f71(x85221),x85224))+~P85(f341(f341(f343(x85221),x85222),x85224))+P85(f341(f341(f241(x85221),f341(f341(f240(x85221),x85222),x85223)),f341(f341(f74(x85221,x85221,f240(x85221)),x85223),x85224))) % 19.23/19.05 [8523]~P98(x85231)+~P85(f341(f71(x85231),x85234))+~P85(f341(f341(f343(x85231),x85232),x85234))+P85(f341(f341(f241(x85231),f341(f341(f110(x85231),x85232),x85233)),f341(f341(f74(x85231,x85231,f110(x85231)),x85233),x85234))) % 19.23/19.05 [8650]~P85(f341(f71(x86501),x86502))+E(f341(f50(x86501),f341(f341(f3(f864(x86501,a850)),x86502),f341(f341(f311(x86501),x86503),x86504))),f341(f341(f3(a857),f341(f50(x86501),f341(f341(f3(f864(x86501,a850)),x86502),x86504))),f87(a857)))+P85(f341(f341(f343(x86501),x86503),x86504))+~P85(f341(f341(f343(x86501),x86503),x86502)) % 19.23/19.05 [8714]E(f341(f341(f89(a1),f478(x87141,x87142,x87143,x87144)),f479(x87141,x87142,x87143,x87144)),x87144)+~P85(f341(f341(f242(a1),f2(a1)),x87143))+~P85(f341(f341(f241(a1),x87144),x87141))+P85(f341(f341(f241(a1),f341(f341(f3(a1),x87144),x87143)),x87141)) % 19.23/19.05 [8715]E(f341(f341(f89(a1),f488(x87151,x87152,x87153,x87154)),f489(x87151,x87152,x87153,x87154)),x87154)+~P85(f341(f341(f242(a1),f2(a1)),x87153))+~P85(f341(f341(f242(a1),x87154),x87151))+P85(f341(f341(f242(a1),f341(f341(f3(a1),x87154),x87153)),x87151)) % 19.23/19.05 [8900]~P85(f341(f341(f242(a1),f2(a1)),x89003))+~P85(f341(f341(f241(a1),x89004),x89001))+P85(f341(f341(f343(a1),f478(x89001,x89002,x89003,x89004)),x89002))+P85(f341(f341(f241(a1),f341(f341(f3(a1),x89004),x89003)),x89001)) % 19.23/19.05 [8901]~P85(f341(f341(f242(a1),f2(a1)),x89013))+~P85(f341(f341(f242(a1),x89014),x89011))+P85(f341(f341(f343(a1),f488(x89011,x89012,x89013,x89014)),x89012))+P85(f341(f341(f242(a1),f341(f341(f3(a1),x89014),x89013)),x89011)) % 19.23/19.05 [8979]~P85(f341(f341(f242(a1),f2(a1)),x89792))+~P85(f341(f341(f242(a1),x89791),x89793))+P85(f341(f341(f343(a1),f489(x89793,x89794,x89792,x89791)),f304(a1,f87(a1),x89792)))+P85(f341(f341(f242(a1),f341(f341(f3(a1),x89791),x89792)),x89793)) % 19.23/19.05 [8980]~P85(f341(f341(f242(a1),f2(a1)),x89802))+~P85(f341(f341(f241(a1),x89801),x89803))+P85(f341(f341(f343(a1),f479(x89803,x89804,x89802,x89801)),f304(a1,f87(a1),x89802)))+P85(f341(f341(f241(a1),f341(f341(f3(a1),x89801),x89802)),x89803)) % 19.23/19.05 [9001]~P85(f341(f341(f242(a1),f2(a1)),x90013))+~P85(f341(f341(f241(a1),f2(a1)),x90014))+~P85(f341(f341(f242(a1),x90014),x90011))+P85(f341(f341(f241(a1),f2(a1)),f341(f341(f89(a1),f341(f341(f90(a1),x90011),f60(a1,x90012,x90013))),x90014))) % 19.23/19.05 [9061]~P101(x90611)+~P85(f341(f71(x90611),x90614))+~P85(f341(f341(f241(x90611),x90612),f695(x90613,x90612,x90614,x90611)))+P85(f341(f341(f241(x90611),f341(f341(f245(x90611),x90612),x90613)),f341(f341(f74(x90611,x90611,f245(x90611)),x90613),x90614))) % 19.23/19.05 [9062]~P99(x90621)+~P85(f341(f71(x90621),x90624))+~P85(f341(f341(f241(x90621),x90622),f699(x90623,x90622,x90624,x90621)))+P85(f341(f341(f241(x90621),f341(f341(f111(x90621),x90622),x90623)),f341(f341(f74(x90621,x90621,f111(x90621)),x90623),x90624))) % 19.23/19.05 [9076]~P85(f341(f341(f241(a1),x90764),f2(a1)))+~P85(f341(f341(f242(a1),f2(a1)),x90762))+~P85(f341(f341(f242(a1),x90761),x90764))+P85(f341(f341(f242(a1),f341(f341(f90(a1),x90761),x90762)),f341(f341(f89(a1),f341(f341(f90(a1),x90761),f60(a1,x90763,x90762))),x90764))) % 19.23/19.05 [9098]P85(f341(f71(x90981),x90982))+~P85(f341(f71(x90981),x90983))+~P85(f341(f341(f343(f864(x90981,a850)),x90982),f341(f341(f69(x90981),x90983),x90984)))+~P85(f341(f341(f241(f864(f863(x90981,x90981),a850)),x90984),f341(f341(f257(x90981,x90981),x90983),f341(f18(f864(x90981,a850),x90981),x90983)))) % 19.23/19.05 [9120]~P101(x91201)+~P85(f341(f71(x91201),x91204))+P85(f341(f341(f343(x91201),f695(x91202,x91203,x91204,x91201)),x91204))+P85(f341(f341(f241(x91201),f341(f341(f245(x91201),x91203),x91202)),f341(f341(f74(x91201,x91201,f245(x91201)),x91202),x91204))) % 19.23/19.05 [9121]~P99(x91211)+~P85(f341(f71(x91211),x91214))+P85(f341(f341(f343(x91211),f699(x91212,x91213,x91214,x91211)),x91214))+P85(f341(f341(f241(x91211),f341(f341(f111(x91211),x91213),x91212)),f341(f341(f74(x91211,x91211,f111(x91211)),x91212),x91214))) % 19.23/19.05 [9493]~P85(f341(f71(x94932),x94934))+~P85(f341(f71(x94931),x94933))+~P85(f341(f341(f241(a857),f341(f50(x94932),x94934)),f341(f50(x94931),x94933)))+P85(f341(f341(f241(f864(x94931,a850)),f341(f312(x94932,x94931,f452(x94933,x94931,x94934,x94932)),x94934)),x94933)) % 19.23/19.05 [9159]~P85(f341(f341(f343(x91591),x91592),x91594))+P85(f341(f341(f343(x91591),x91592),x91593))+~P85(f341(f341(f242(f864(x91591,a850)),x91594),f341(f341(f311(x91591),x91592),x91593)))+P85(f341(f341(f242(f864(x91591,a850)),f341(f341(f3(f864(x91591,a850)),x91594),f341(f341(f311(x91591),x91592),f185(f864(x91591,a850))))),x91593)) % 19.23/19.05 [9310]~P85(f341(f341(f343(x93101),x93102),x93104))+P85(f341(f341(f343(x93101),x93102),x93103))+P85(f341(f341(f242(f864(x93101,a850)),x93104),f341(f341(f311(x93101),x93102),x93103)))+~P85(f341(f341(f242(f864(x93101,a850)),f341(f341(f3(f864(x93101,a850)),x93104),f341(f341(f311(x93101),x93102),f185(f864(x93101,a850))))),x93103)) % 19.23/19.05 [9337]P85(f341(f341(f343(x93371),x93372),x93373))+~P85(f341(f341(f241(f864(x93371,a850)),x93374),x93373))+P85(f341(f341(f242(f864(x93371,a850)),x93374),f341(f341(f311(x93371),x93372),x93373)))+~P85(f341(f341(f242(f864(x93371,a850)),f341(f341(f3(f864(x93371,a850)),x93374),f341(f341(f311(x93371),x93372),f185(f864(x93371,a850))))),x93373)) % 19.23/19.05 [9342]~P85(f341(f341(f343(x93421),x93423),x93422))+~P85(f341(f341(f242(f864(x93421,a850)),x93422),x93424))+P85(f341(f341(f242(f864(x93421,a850)),x93422),f341(f341(f311(x93421),x93423),x93424)))+~P85(f341(f341(f242(f864(x93421,a850)),f341(f341(f3(f864(x93421,a850)),x93422),f341(f341(f311(x93421),x93423),f185(f864(x93421,a850))))),x93424)) % 19.23/19.05 [9354]~P85(f341(f341(f241(f864(x93541,a850)),x93542),x93544))+~P85(f341(f341(f242(f864(x93541,a850)),x93542),x93544))+P85(f341(f341(f242(f864(x93541,a850)),x93542),f341(f341(f311(x93541),x93543),x93544)))+~P85(f341(f341(f242(f864(x93541,a850)),f341(f341(f3(f864(x93541,a850)),x93542),f341(f341(f311(x93541),x93543),f185(f864(x93541,a850))))),x93544)) % 19.23/19.05 [9689]E(f341(f341(f158(x96891),f341(f341(f158(f858(x96891)),f169(x96891,x96892)),x96893)),x96894),f341(f341(f158(x96891),f341(f341(f158(f858(x96891)),x96892),x96894)),x96893))+~P85(f341(f341(f242(a857),x96893),f341(f186(f858(f858(x96891))),f169(x96891,x96892))))+~P15(a857,f341(f148(a857),f341(f341(f149(f858(x96891),a857),f186(f858(x96891))),x96892)))+~P85(f341(f341(f242(a857),x96894),f341(f186(f858(f858(x96891))),f341(f133(f858(x96891),f341(f341(f10(a857,a850,f858(x96891)),f341(f242(a857),x96893)),f186(f858(x96891)))),x96892)))) % 19.23/19.05 [9710]~P85(f341(f341(f343(f863(a857,a857)),x97104),x97101))+~P85(f341(f341(f343(f863(f863(a857,a857),f863(a857,a857))),f341(f341(f250(f863(a857,a857),f863(a857,a857)),x97104),x97102)),a47))+~P85(f341(f341(f343(f863(f864(f863(a857,a857),a850),f864(f863(a857,a857),a850))),f341(f341(f250(f864(f863(a857,a857),a850),f864(f863(a857,a857),a850)),x97101),x97103)),a48))+P85(f341(f341(f343(f863(f864(f863(a857,a857),a850),f864(f863(a857,a857),a850))),f341(f341(f250(f864(f863(a857,a857),a850),f864(f863(a857,a857),a850)),x97101),f341(f341(f311(f863(a857,a857)),x97102),x97103))),a48)) % 19.23/19.05 [9711]~P85(f341(f341(f343(f863(a857,a857)),x97114),x97111))+~P85(f341(f341(f343(f863(f863(a857,a857),f863(a857,a857))),f341(f341(f250(f863(a857,a857),f863(a857,a857)),x97114),x97112)),a79))+~P85(f341(f341(f343(f863(f864(f863(a857,a857),a850),f864(f863(a857,a857),a850))),f341(f341(f250(f864(f863(a857,a857),a850),f864(f863(a857,a857),a850)),x97111),x97113)),a80))+P85(f341(f341(f343(f863(f864(f863(a857,a857),a850),f864(f863(a857,a857),a850))),f341(f341(f250(f864(f863(a857,a857),a850),f864(f863(a857,a857),a850)),x97111),f341(f341(f311(f863(a857,a857)),x97112),x97113))),a80)) % 19.23/19.05 [9723]~P85(f341(f341(f343(f863(a857,a857)),x97234),x97233))+~P85(f341(f341(f343(f863(f863(a857,a857),f863(a857,a857))),f341(f341(f250(f863(a857,a857),f863(a857,a857)),x97231),x97234)),a47))+~P85(f341(f341(f343(f863(f864(f863(a857,a857),a850),f864(f863(a857,a857),a850))),f341(f341(f250(f864(f863(a857,a857),a850),f864(f863(a857,a857),a850)),x97232),x97233)),a49))+P85(f341(f341(f343(f863(f864(f863(a857,a857),a850),f864(f863(a857,a857),a850))),f341(f341(f250(f864(f863(a857,a857),a850),f864(f863(a857,a857),a850)),f341(f341(f311(f863(a857,a857)),x97231),x97232)),x97233)),a49)) % 19.23/19.05 [9724]~P85(f341(f341(f343(f863(a857,a857)),x97244),x97243))+~P85(f341(f341(f343(f863(f863(a857,a857),f863(a857,a857))),f341(f341(f250(f863(a857,a857),f863(a857,a857)),x97241),x97244)),a79))+~P85(f341(f341(f343(f863(f864(f863(a857,a857),a850),f864(f863(a857,a857),a850))),f341(f341(f250(f864(f863(a857,a857),a850),f864(f863(a857,a857),a850)),x97242),x97243)),a78))+P85(f341(f341(f343(f863(f864(f863(a857,a857),a850),f864(f863(a857,a857),a850))),f341(f341(f250(f864(f863(a857,a857),a850),f864(f863(a857,a857),a850)),f341(f341(f311(f863(a857,a857)),x97241),x97242)),x97243)),a78)) % 19.23/19.05 [5918]~P8(x59184,x59181)+~P85(f341(f341(x59181,x59182),x59185))+P85(f341(f341(x59181,x59182),x59183))+~P85(f341(f341(x59181,x59185),x59183)) % 19.23/19.05 [5185]~P3(x51855)+E(x51851,x51852)+~E(x51853,x51854)+~E(f341(f341(f3(x51855),x51853),x51854),f341(f341(f3(x51855),x51851),x51852)) % 19.23/19.05 [6029]~P18(x60295,x60291,x60293)+E(f341(f341(x60291,x60292),f341(x60293,x60294)),f341(x60293,x60294))+~P85(f341(f71(x60295),x60294))+~P85(f341(f341(f343(x60295),x60292),x60294)) % 19.23/19.05 [6226]~P77(x62261)+~E(f341(f341(f3(x62261),x62264),x62265),f341(f341(f3(x62261),x62262),x62263))+~P85(f341(f341(f242(x62261),x62264),x62265))+P85(f341(f341(f242(x62261),x62262),x62263)) % 19.23/19.05 [6228]~P77(x62281)+~E(f341(f341(f3(x62281),x62284),x62285),f341(f341(f3(x62281),x62282),x62283))+~P85(f341(f341(f241(x62281),x62284),x62285))+P85(f341(f341(f241(x62281),x62282),x62283)) % 19.23/19.05 [7226]~E(x72262,f341(f341(f146(x72261),x72264),x72265))+P85(f341(f341(f343(f858(x72261)),x72262),f155(x72261,x72263)))+~P85(f341(f341(f343(f858(x72261)),x72265),f155(x72261,x72263)))+~P85(f341(f341(f343(x72261),x72264),x72263)) % 19.23/19.05 [7659]~E(f341(f186(f858(x76591)),x76593),f341(f186(f858(x76592)),x76594))+~E(f341(f341(f149(f863(x76591,x76592),x76592),f259(x76591,x76592)),x76595),x76594)+~E(f341(f341(f149(f863(x76591,x76592),x76591),f249(x76591,x76592)),x76595),x76593)+E(f341(f341(f172(x76591,x76592),x76593),x76594),x76595) % 19.23/19.05 [7995]~P100(x79951)+P85(f341(f341(f242(f864(x79951,a850)),f304(x79951,x79952,x79953)),f304(x79951,x79954,x79955)))+~P85(f341(f341(f241(x79951),x79954),x79955))+P85(f341(f341(f241(x79951),x79952),x79953)) % 19.23/19.05 [8086]~P100(x80861)+P85(f341(f341(f241(f864(x80861,a850)),f304(x80861,x80862,x80863)),f304(x80861,x80864,x80865)))+~P85(f341(f341(f241(x80861),x80863),x80865))+~P85(f341(f341(f241(x80861),x80864),x80862)) % 19.23/19.05 [8202]~P101(x82021)+P85(f341(f341(f241(x82021),x82022),x82023))+P85(f341(f341(f241(x82021),x82024),x82023))+~P85(f341(f341(f241(f864(x82021,a850)),f341(f303(x82021,x82023),x82022)),f341(f303(x82021,x82024),x82025))) % 19.23/19.05 [8203]~P101(x82031)+P85(f341(f341(f241(x82031),x82032),x82033))+P85(f341(f341(f241(x82031),x82032),x82034))+~P85(f341(f341(f241(f864(x82031,a850)),f341(f303(x82031,x82033),x82032)),f341(f303(x82031,x82035),x82034))) % 19.23/19.05 [8443]~P100(x84431)+~P85(f341(f341(f242(f864(x84431,a850)),f304(x84431,x84434,x84432)),f304(x84431,x84435,x84433)))+P85(f341(f341(f241(x84431),x84432),x84433))+~P85(f341(f341(f241(x84431),x84434),x84432)) % 19.23/19.05 [8444]~P100(x84441)+~P85(f341(f341(f241(f864(x84441,a850)),f304(x84441,x84444,x84442)),f304(x84441,x84445,x84443)))+P85(f341(f341(f241(x84441),x84442),x84443))+~P85(f341(f341(f241(x84441),x84444),x84442)) % 19.23/19.05 [8445]~P100(x84451)+~P85(f341(f341(f242(f864(x84451,a850)),f304(x84451,x84453,x84454)),f304(x84451,x84452,x84455)))+P85(f341(f341(f241(x84451),x84452),x84453))+~P85(f341(f341(f241(x84451),x84453),x84454)) % 19.23/19.05 [8446]~P100(x84461)+~P85(f341(f341(f241(f864(x84461,a850)),f304(x84461,x84463,x84464)),f304(x84461,x84462,x84465)))+P85(f341(f341(f241(x84461),x84462),x84463))+~P85(f341(f341(f241(x84461),x84463),x84464)) % 19.23/19.05 [5917]~P18(x59172,x59175,x59173)+E(x59171,f185(f864(x59172,a850)))+~P85(f341(f71(x59172),x59171))+E(f341(x59173,f341(f341(f311(x59172),x59174),x59171)),f341(f341(x59175,x59174),f341(x59173,x59171))) % 19.23/19.05 [6716]~E(x67161,x67162)+~E(f341(f341(f111(f864(x67163,a850)),x67164),x67165),f185(f864(x67163,a850)))+~P85(f341(f341(f343(x67163),x67162),x67165))+~P85(f341(f341(f343(x67163),x67161),x67164)) % 19.23/19.05 [6802]~P19(x68022,x68025,x68021)+~P85(f341(f71(x68022),x68024))+E(f341(x68021,f341(f341(f311(x68022),x68023),x68024)),f341(f341(f74(x68022,x68022,x68025),x68023),x68024))+P85(f341(f341(f343(x68022),x68023),x68024)) % 19.23/19.05 [6873]~P71(x68732)+~P85(f341(f71(x68731),x68735))+E(f341(f341(f11(x68731,x68732),x68733),f341(f341(f311(x68731),x68734),x68735)),f341(f341(f90(x68732),f341(x68733,x68734)),f341(f341(f11(x68731,x68732),x68733),x68735)))+P85(f341(f341(f343(x68731),x68734),x68735)) % 19.23/19.05 [6875]~P68(x68752)+~P85(f341(f71(x68751),x68755))+E(f341(f341(f8(x68751,x68752),x68753),f341(f341(f311(x68751),x68754),x68755)),f341(f341(f89(x68752),f341(x68753,x68754)),f341(f341(f8(x68751,x68752),x68753),x68755)))+P85(f341(f341(f343(x68751),x68754),x68755)) % 19.23/19.05 [7284]~P86(x72841)+~P85(f341(f71(x72844),x72845))+~P85(f341(f341(f343(x72844),x72843),x72845))+P85(f341(f341(f288(x72841),f341(x72842,x72843)),f341(f341(f11(x72844,x72841),x72842),x72845))) % 19.23/19.05 [7397]~P19(x73972,x73975,x73971)+~P85(f341(f71(x73972),x73974))+E(f341(x73971,f341(f341(f311(x73972),x73973),x73974)),x73973)+~E(f341(f341(f3(f864(x73972,a850)),x73974),f341(f341(f311(x73972),x73973),f185(f864(x73972,a850)))),f185(f864(x73972,a850))) % 19.23/19.05 [7709]~P85(f341(x77091,x77093))+~P85(f341(f341(f192(x77092),x77093),x77095))+~P85(f341(f341(f192(f37(x77091,x77092)),x77095),x77094))+P85(f341(f341(f192(f37(x77091,x77092)),x77093),x77094)) % 19.23/19.05 [7727]~P86(x77271)+~P85(f341(f341(f288(x77271),x77272),x77274))+~P85(f341(f341(f241(a857),x77273),x77275))+P85(f341(f341(f288(x77271),f341(f341(f251(x77271),x77272),x77273)),f341(f341(f251(x77271),x77274),x77275))) % 19.23/19.05 [7761]~P4(x77611)+E(f341(f341(f51(x77611),f341(f341(f90(x77611),x77612),x77613)),f341(f341(f90(x77611),x77614),x77615)),f341(f341(f90(x77611),f341(f341(f51(x77611),x77612),x77614)),f341(f341(f51(x77611),x77613),x77615)))+~P85(f341(f341(f288(x77611),x77615),x77613))+~P85(f341(f341(f288(x77611),x77614),x77612)) % 19.23/19.05 [7765]~P80(x77651)+~P85(f341(f341(f242(x77651),x77653),x77655))+~P85(f341(f341(f242(x77651),x77652),x77654))+P85(f341(f341(f242(x77651),f341(f341(f89(x77651),x77652),x77653)),f341(f341(f89(x77651),x77654),x77655))) % 19.23/19.05 [7766]~P80(x77661)+~P85(f341(f341(f241(x77661),x77662),x77664))+~P85(f341(f341(f242(x77661),x77663),x77665))+P85(f341(f341(f242(x77661),f341(f341(f89(x77661),x77662),x77663)),f341(f341(f89(x77661),x77664),x77665))) % 19.23/19.05 [7767]~P80(x77671)+~P85(f341(f341(f241(x77671),x77673),x77675))+~P85(f341(f341(f242(x77671),x77672),x77674))+P85(f341(f341(f242(x77671),f341(f341(f89(x77671),x77672),x77673)),f341(f341(f89(x77671),x77674),x77675))) % 19.23/19.05 [7768]~P78(x77681)+~P85(f341(f341(f241(x77681),x77683),x77685))+~P85(f341(f341(f241(x77681),x77682),x77684))+P85(f341(f341(f241(x77681),f341(f341(f89(x77681),x77682),x77683)),f341(f341(f89(x77681),x77684),x77685))) % 19.23/19.05 [7769]~P101(x77691)+~P85(f341(f341(f241(x77691),x77693),x77695))+~P85(f341(f341(f241(x77691),x77692),x77694))+P85(f341(f341(f241(x77691),f341(f341(f245(x77691),x77692),x77693)),f341(f341(f245(x77691),x77694),x77695))) % 19.23/19.05 [7770]~P101(x77701)+~P85(f341(f341(f241(x77701),x77703),x77705))+~P85(f341(f341(f241(x77701),x77702),x77704))+P85(f341(f341(f241(x77701),f341(f341(f240(x77701),x77702),x77703)),f341(f341(f240(x77701),x77704),x77705))) % 19.23/19.05 [7771]~P98(x77711)+~P85(f341(f341(f241(x77711),x77713),x77715))+~P85(f341(f341(f241(x77711),x77712),x77714))+P85(f341(f341(f241(x77711),f341(f341(f110(x77711),x77712),x77713)),f341(f341(f110(x77711),x77714),x77715))) % 19.23/19.05 [7772]~P99(x77721)+~P85(f341(f341(f241(x77721),x77723),x77725))+~P85(f341(f341(f241(x77721),x77722),x77724))+P85(f341(f341(f241(x77721),f341(f341(f111(x77721),x77722),x77723)),f341(f341(f111(x77721),x77724),x77725))) % 19.23/19.05 [7773]~P86(x77731)+~P85(f341(f341(f288(x77731),x77733),x77735))+~P85(f341(f341(f288(x77731),x77732),x77734))+P85(f341(f341(f288(x77731),f341(f341(f90(x77731),x77732),x77733)),f341(f341(f90(x77731),x77734),x77735))) % 19.23/19.05 [7906]~P111(x79065)+E(x79061,x79062)+E(x79063,x79064)+~E(f341(f341(f89(x79065),f341(f341(f90(x79065),x79063),x79061)),f341(f341(f90(x79065),x79064),x79062)),f341(f341(f89(x79065),f341(f341(f90(x79065),x79063),x79062)),f341(f341(f90(x79065),x79064),x79061))) % 19.23/19.05 [8043]P30(x80431,x80432,x80433)+~P31(x80431,x80434,x80435)+~P30(x80431,x80432,f609(x80435,x80434,x80431,x80432))+~P85(f341(f341(f343(f856(x80431)),x80433),x80435)) % 19.23/19.05 [8106]~P101(x81064)+~P85(f341(f134(x81061),x81063))+P85(f341(f341(f343(x81061),x81062),f341(f163(x81061),x81063)))+P85(f341(f134(x81061),f341(f341(f144(x81061,x81064,x81065),x81062),x81063))) % 19.23/19.05 [8248]~P68(x82481)+E(f341(f341(f89(x82481),f341(f341(f8(a857,x82481),x82482),f341(f303(a857,x82483),x82484))),f341(f341(f8(a857,x82481),x82482),f341(f303(a857,x82484),x82485))),f341(f341(f8(a857,x82481),x82482),f341(f303(a857,x82483),x82485)))+~P85(f341(f341(f241(a857),x82484),x82485))+~P85(f341(f341(f241(a857),x82483),x82484)) % 19.23/19.05 [8249]~P3(x82491)+E(f341(f341(f3(x82491),f341(f341(f8(a857,x82491),x82492),f341(f303(a857,x82493),x82494))),f341(f341(f8(a857,x82491),x82492),f341(f303(a857,x82493),x82495))),f341(f341(f8(a857,x82491),x82492),f341(f303(a857,x82495),x82494)))+~P85(f341(f341(f241(a857),x82495),x82494))+~P85(f341(f341(f241(a857),x82493),x82495)) % 19.23/19.05 [8567]~P60(x85672)+E(x85671,f2(x85672))+E(x85673,f2(x85672))+E(f341(f341(f292(x85672),f341(f341(f89(x85672),f341(f341(f90(x85672),x85674),x85671)),f341(f341(f90(x85672),x85675),x85673))),f341(f341(f90(x85672),x85673),x85671)),f341(f341(f89(x85672),f341(f341(f292(x85672),x85674),x85673)),f341(f341(f292(x85672),x85675),x85671))) % 19.23/19.05 [8568]~P60(x85682)+E(x85681,f2(x85682))+E(x85683,f2(x85682))+E(f341(f341(f292(x85682),f341(f341(f3(x85682),f341(f341(f90(x85682),x85684),x85681)),f341(f341(f90(x85682),x85685),x85683))),f341(f341(f90(x85682),x85683),x85681)),f341(f341(f3(x85682),f341(f341(f292(x85682),x85684),x85683)),f341(f341(f292(x85682),x85685),x85681))) % 19.23/19.05 [8577]~E(x85772,f341(x85773,x85771))+E(x85771,f527(x85772,x85773,x85774,x85775))+~P26(x85775,x85774,x85773,f248(f864(x85775,a850)))+~P85(f341(f341(f343(x85774),x85772),f341(f312(x85775,x85774,x85773),f248(f864(x85775,a850))))) % 19.23/19.05 [8762]~P113(x87621)+~P85(f341(f341(f242(x87621),f341(f84(x87621),x87622)),x87624))+P85(f341(f341(f242(x87621),f341(f341(f90(x87621),f341(f84(x87621),x87622)),f341(f84(x87621),x87623))),f341(f341(f90(x87621),x87624),x87625)))+~P85(f341(f341(f242(x87621),f341(f84(x87621),x87623)),x87625)) % 19.23/19.05 [8776]~P31(x87761,x87765,x87764)+P30(x87761,x87762,x87763)+P85(f341(f341(f343(f856(x87761)),f609(x87764,x87765,x87761,x87762)),x87765))+~P85(f341(f341(f343(f856(x87761)),x87763),x87764)) % 19.23/19.05 [8858]~P26(x88581,x88583,x88585,x88582)+~P85(f341(f71(x88583),x88584))+P85(f341(f341(f241(a857),f341(f50(x88581),x88582)),f341(f50(x88583),x88584)))+~P85(f341(f341(f241(f864(x88583,a850)),f341(f312(x88581,x88583,x88585),x88582)),x88584)) % 19.23/19.05 [8927]~P71(x89272)+~P26(x89271,x89271,x89274,x89275)+~P85(f341(f71(x89271),x89275))+E(f341(f341(f11(x89271,x89272),f341(f82(x89271,x89272,x89271,x89273),x89274)),x89275),f341(f341(f11(x89271,x89272),x89273),f341(f312(x89271,x89271,x89274),x89275))) % 19.23/19.05 [8928]~P68(x89282)+~P26(x89281,x89281,x89284,x89285)+~P85(f341(f71(x89281),x89285))+E(f341(f341(f8(x89281,x89282),f341(f82(x89281,x89282,x89281,x89283),x89284)),x89285),f341(f341(f8(x89281,x89282),x89283),f341(f312(x89281,x89281,x89284),x89285))) % 19.23/19.05 [9040]~P35(x90401,x90402)+~P85(f341(f341(f343(x90401),x90403),x90404))+~P85(f341(f341(f343(x90401),x90405),x90404))+~P85(f341(f341(f343(f863(x90401,x90401)),f341(f341(f250(x90401,x90401),x90405),f703(x90402,x90401,x90404))),x90402)) % 19.23/19.05 [9075]~P26(x90752,x90753,x90755,x90751)+E(x90751,f185(f864(x90752,a850)))+E(f341(f312(x90753,x90752,f454(x90754,x90753,x90752,x90751)),x90754),x90751)+~P85(f341(f341(f241(f864(x90753,a850)),f341(f312(x90752,x90753,x90755),x90751)),x90754)) % 19.23/19.05 [9516]~P101(x95165)+~P6(x95165)+P85(f341(f341(f343(x95161),f420(x95162,x95163,x95161,x95164,x95165)),x95163))+~P85(f341(f341(f242(x95165),x95164),f341(f341(f54(x95161,x95165),x95163),x95162))) % 19.23/19.05 [9521]~P101(x95211)+~P6(x95211)+P85(f341(f341(f242(x95211),x95212),f341(x95213,f420(x95213,x95214,x95215,x95212,x95211))))+~P85(f341(f341(f242(x95211),x95212),f341(f341(f54(x95215,x95211),x95214),x95213))) % 19.23/19.05 [9596]~P65(x95961)+~P85(f341(f76(x95961,x95961,f90(x95961),x95962,x95963),x95965))+P85(f341(f341(f343(x95961),x95962),x95963))+P85(f341(f76(x95961,x95961,f90(x95961),x95964,f341(f341(f311(x95961),x95962),x95963)),f341(f341(f90(x95961),x95964),x95965))) % 19.23/19.05 [9806]~P71(x98062)+~P85(f341(f71(x98061),x98065))+E(f341(f341(f11(x98061,x98062),f341(f341(f9(x98061,x98062,x98062),f341(f341(f20(x98061,x98062,f864(x98062,x98062)),f341(f341(f10(a850,f864(x98062,f864(x98062,x98062)),x98061),f105(x98062)),f341(a338,x98063))),x98064)),f87(x98062))),x98065),f87(x98062))+P85(f341(f341(f343(x98061),x98063),x98065)) % 19.23/19.05 [9807]~P68(x98072)+~P85(f341(f71(x98071),x98075))+E(f341(f341(f8(x98071,x98072),f341(f341(f9(x98071,x98072,x98072),f341(f341(f20(x98071,x98072,f864(x98072,x98072)),f341(f341(f10(a850,f864(x98072,f864(x98072,x98072)),x98071),f105(x98072)),f341(a338,x98073))),x98074)),f2(x98072))),x98075),f2(x98072))+P85(f341(f341(f343(x98071),x98073),x98075)) % 19.23/19.05 [9808]~P71(x98082)+~P85(f341(f71(x98081),x98085))+E(f341(f341(f11(x98081,x98082),f341(f341(f9(x98081,x98082,x98082),f341(f341(f20(x98081,x98082,f864(x98082,x98082)),f341(f341(f10(a850,f864(x98082,f864(x98082,x98082)),x98081),f105(x98082)),f341(a338,x98083))),x98084)),f87(x98082))),x98085),f341(x98084,x98083))+~P85(f341(f341(f343(x98081),x98083),x98085)) % 19.23/19.05 [9809]~P68(x98092)+~P85(f341(f71(x98091),x98095))+E(f341(f341(f8(x98091,x98092),f341(f341(f9(x98091,x98092,x98092),f341(f341(f20(x98091,x98092,f864(x98092,x98092)),f341(f341(f10(a850,f864(x98092,f864(x98092,x98092)),x98091),f105(x98092)),f341(a338,x98093))),x98094)),f2(x98092))),x98095),f341(x98094,x98093))+~P85(f341(f341(f343(x98091),x98093),x98095)) % 19.23/19.05 [9874]~P71(x98742)+~P85(f341(f71(x98741),x98745))+E(f341(f341(f11(x98741,x98742),f341(f341(f9(x98741,x98742,x98742),f341(f341(f20(x98741,x98742,f864(x98742,x98742)),f341(f341(f10(a850,f864(x98742,f864(x98742,x98742)),x98741),f105(x98742)),f341(f341(f9(x98741,x98741,a850),a338),x98743))),x98744)),f87(x98742))),x98745),f87(x98742))+P85(f341(f341(f343(x98741),x98743),x98745)) % 19.23/19.05 [9875]~P68(x98752)+~P85(f341(f71(x98751),x98755))+E(f341(f341(f8(x98751,x98752),f341(f341(f9(x98751,x98752,x98752),f341(f341(f20(x98751,x98752,f864(x98752,x98752)),f341(f341(f10(a850,f864(x98752,f864(x98752,x98752)),x98751),f105(x98752)),f341(f341(f9(x98751,x98751,a850),a338),x98753))),x98754)),f2(x98752))),x98755),f2(x98752))+P85(f341(f341(f343(x98751),x98753),x98755)) % 19.23/19.05 [9877]~P71(x98772)+~P85(f341(f71(x98771),x98775))+E(f341(f341(f11(x98771,x98772),f341(f341(f9(x98771,x98772,x98772),f341(f341(f20(x98771,x98772,f864(x98772,x98772)),f341(f341(f10(a850,f864(x98772,f864(x98772,x98772)),x98771),f105(x98772)),f341(f341(f9(x98771,x98771,a850),a338),x98773))),x98774)),f87(x98772))),x98775),f341(x98774,x98773))+~P85(f341(f341(f343(x98771),x98773),x98775)) % 19.23/19.05 [9878]~P68(x98782)+~P85(f341(f71(x98781),x98785))+E(f341(f341(f8(x98781,x98782),f341(f341(f9(x98781,x98782,x98782),f341(f341(f20(x98781,x98782,f864(x98782,x98782)),f341(f341(f10(a850,f864(x98782,f864(x98782,x98782)),x98781),f105(x98782)),f341(f341(f9(x98781,x98781,a850),a338),x98783))),x98784)),f2(x98782))),x98785),f341(x98784,x98783))+~P85(f341(f341(f343(x98781),x98783),x98785)) % 19.23/19.05 [7764]~P3(x77642)+~P85(f341(f71(x77641),x77644))+E(f341(f341(f8(x77641,x77642),x77643),f341(f341(f3(f864(x77641,a850)),x77644),f341(f341(f311(x77641),x77645),f185(f864(x77641,a850))))),f341(f341(f8(x77641,x77642),x77643),x77644))+P85(f341(f341(f343(x77641),x77645),x77644)) % 19.23/19.05 [8255]~P123(x82552)+~P85(f341(f71(x82551),x82554))+E(f341(f341(f8(x82551,x82552),x82553),f341(f341(f3(f864(x82551,a850)),x82554),f341(f341(f311(x82551),x82555),f185(f864(x82551,a850))))),f341(f341(f3(x82552),f341(f341(f8(x82551,x82552),x82553),x82554)),f341(x82553,x82555)))+~P85(f341(f341(f343(x82551),x82555),x82554)) % 19.23/19.05 [8256]~P3(x82562)+~P85(f341(f71(x82561),x82564))+E(f341(f341(f8(x82561,x82562),x82563),f341(f341(f3(f864(x82561,a850)),x82564),f341(f341(f311(x82561),x82565),f185(f864(x82561,a850))))),f341(f341(f3(x82562),f341(f341(f8(x82561,x82562),x82563),x82564)),f341(x82563,x82565)))+~P85(f341(f341(f343(x82561),x82565),x82564)) % 19.23/19.05 [8267]~P86(x82671)+~P85(f341(f341(f241(a857),x82673),x82675))+~P85(f341(f341(f288(x82671),f341(f341(f251(x82671),x82672),x82675)),x82674))+P85(f341(f341(f288(x82671),f341(f341(f251(x82671),x82672),x82673)),x82674)) % 19.23/19.05 [8284]~P3(x82841)+~P85(f341(f71(x82842),x82844))+E(f341(f341(f3(x82841),f341(f341(f8(x82842,x82841),x82843),x82844)),f341(f341(f8(x82842,x82841),x82843),x82845)),f341(f341(f8(x82842,x82841),x82843),f341(f341(f3(f864(x82842,a850)),x82844),x82845)))+~P85(f341(f341(f241(f864(x82842,a850)),x82845),x82844)) % 19.23/19.05 [8305]P85(f341(f71(x83051),f341(x83052,x83053)))+~P85(f341(f71(x83054),x83055))+~P85(f341(f341(f343(x83054),x83053),x83055))+~P85(f341(f71(x83051),f341(f341(f54(x83054,f864(x83051,a850)),x83055),x83052))) % 19.23/19.05 [8727]~P9(x87271,x87275,x87274)+~E(f341(f286(x87271,x87271,x87274),f341(f341(f311(x87271),x87272),f185(f864(x87271,a850)))),f341(f286(x87271,x87271,x87274),f341(f341(f311(x87271),x87273),f185(f864(x87271,a850)))))+~P85(f341(f341(f343(x87271),x87273),x87275))+P85(f341(f341(f343(f863(x87271,x87271)),f341(f341(f250(x87271,x87271),x87272),x87273)),x87274)) % 19.23/19.05 [8999]~P85(f341(x89991,x89995))+P85(f341(x89991,f364(x89991,x89992,x89993,x89994)))+P85(f341(x89991,f361(x89991,x89992,x89993,x89994)))+~P85(f341(f341(f343(x89994),x89995),f341(f341(f110(f864(x89994,a850)),x89993),x89992))) % 19.23/19.05 [9162]~P85(f341(x91621,x91625))+P85(f341(x91621,f361(x91621,x91622,x91623,x91624)))+P85(f341(f341(f343(x91624),f364(x91621,x91622,x91623,x91624)),x91622))+~P85(f341(f341(f343(x91624),x91625),f341(f341(f110(f864(x91624,a850)),x91623),x91622))) % 19.23/19.05 [9163]~P85(f341(x91631,x91635))+P85(f341(x91631,f364(x91631,x91632,x91633,x91634)))+P85(f341(f341(f343(x91634),f361(x91631,x91632,x91633,x91634)),x91633))+~P85(f341(f341(f343(x91634),x91635),f341(f341(f110(f864(x91634,a850)),x91633),x91632))) % 19.23/19.05 [9167]P85(f341(x91671,x91672))+~P85(f341(x91671,f363(x91671,x91673,x91674,x91675)))+~P85(f341(x91671,f362(x91671,x91673,x91674,x91675)))+~P85(f341(f341(f343(x91675),x91672),f341(f341(f110(f864(x91675,a850)),x91674),x91673))) % 19.23/19.05 [9199]E(x91991,x91992)+~P85(f341(f341(f343(f863(x91993,x91993)),f341(f341(f250(x91993,x91993),x91991),x91992)),f309(x91993,x91995)))+P85(f341(f341(f343(x91993),x91991),x91994))+~P85(f341(f341(f241(f864(f863(x91993,x91993),a850)),x91995),f341(f341(f257(x91993,x91993),x91994),f341(f18(f864(x91993,a850),x91993),x91994)))) % 19.23/19.05 [9216]P85(f341(x92161,x92162))+~P85(f341(x92161,f362(x92161,x92164,x92165,x92163)))+P85(f341(f341(f343(x92163),f363(x92161,x92164,x92165,x92163)),x92164))+~P85(f341(f341(f343(x92163),x92162),f341(f341(f110(f864(x92163,a850)),x92165),x92164))) % 19.23/19.05 [9217]P85(f341(x92171,x92172))+~P85(f341(x92171,f363(x92171,x92174,x92175,x92173)))+P85(f341(f341(f343(x92173),f362(x92171,x92174,x92175,x92173)),x92175))+~P85(f341(f341(f343(x92173),x92172),f341(f341(f110(f864(x92173,a850)),x92175),x92174))) % 19.23/19.05 [9279]P85(f341(x92791,x92792))+P85(f341(f341(f343(x92793),f363(x92791,x92794,x92795,x92793)),x92794))+P85(f341(f341(f343(x92793),f362(x92791,x92794,x92795,x92793)),x92795))+~P85(f341(f341(f343(x92793),x92792),f341(f341(f110(f864(x92793,a850)),x92795),x92794))) % 19.23/19.05 [9281]~P85(f341(x92812,x92815))+P85(f341(f341(f343(x92811),f364(x92812,x92813,x92814,x92811)),x92813))+P85(f341(f341(f343(x92811),f361(x92812,x92813,x92814,x92811)),x92814))+~P85(f341(f341(f343(x92811),x92815),f341(f341(f110(f864(x92811,a850)),x92814),x92813))) % 19.23/19.05 [9426]~P9(x94261,x94265,x94264)+~P85(f341(f341(f343(x94261),x94263),x94265))+P85(f341(f341(f343(f863(x94261,x94261)),f341(f341(f250(x94261,x94261),x94262),x94263)),x94264))+~P85(f341(f341(f241(f864(x94261,a850)),f341(f286(x94261,x94261,x94264),f341(f341(f311(x94261),x94263),f185(f864(x94261,a850))))),f341(f286(x94261,x94261,x94264),f341(f341(f311(x94261),x94262),f185(f864(x94261,a850)))))) % 19.23/19.05 [9546]~P101(x95465)+~P6(x95465)+P85(f341(f341(f343(x95461),f672(x95462,x95463,x95464,x95461,x95465)),x95464))+~P85(f341(f341(f242(x95465),f341(f341(f55(x95461,x95465),x95464),x95463)),x95462)) % 19.23/19.05 [9580]~P67(x95805)+~P78(x95805)+P85(f341(f341(f343(x95801),f763(x95802,x95803,x95804,x95801,x95805)),f341(f163(x95801),x95804)))+P85(f341(f341(f241(x95805),f341(f160(x95805),f341(f341(f149(x95801,x95805),x95803),x95804))),f341(f160(x95805),f341(f341(f149(x95801,x95805),x95802),x95804)))) % 19.23/19.05 [9679]~P101(x96791)+~P6(x96791)+P85(f341(f341(f242(x96791),f341(x96792,f672(x96793,x96792,x96794,x96795,x96791))),x96793))+~P85(f341(f341(f242(x96791),f341(f341(f55(x96795,x96791),x96794),x96792)),x96793)) % 19.23/19.05 [9823]~P67(x98231)+~P78(x98231)+~P85(f341(f341(f241(x98231),f341(x98233,f763(x98235,x98233,x98234,x98232,x98231))),f341(x98235,f763(x98235,x98233,x98234,x98232,x98231))))+P85(f341(f341(f241(x98231),f341(f160(x98231),f341(f341(f149(x98232,x98231),x98233),x98234))),f341(f160(x98231),f341(f341(f149(x98232,x98231),x98235),x98234)))) % 19.23/19.05 [8585]~P71(x85851)+~P85(f341(f71(x85854),x85855))+~P85(f341(f341(f343(x85854),x85853),x85855))+E(f341(f341(f90(x85851),f341(x85852,x85853)),f341(f341(f11(x85854,x85851),x85852),f341(f341(f3(f864(x85854,a850)),x85855),f341(f341(f311(x85854),x85853),f185(f864(x85854,a850)))))),f341(f341(f11(x85854,x85851),x85852),x85855)) % 19.23/19.05 [8587]~P68(x85871)+~P85(f341(f71(x85874),x85875))+~P85(f341(f341(f343(x85874),x85873),x85875))+E(f341(f341(f89(x85871),f341(x85872,x85873)),f341(f341(f8(x85874,x85871),x85872),f341(f341(f3(f864(x85874,a850)),x85875),f341(f341(f311(x85874),x85873),f185(f864(x85874,a850)))))),f341(f341(f8(x85874,x85871),x85872),x85875)) % 19.23/19.05 [8640]~P19(x86401,x86404,x86405)+~P85(f341(f71(x86401),x86402))+E(f341(f341(f3(f864(x86401,a850)),x86402),f341(f341(f311(x86401),x86403),f185(f864(x86401,a850)))),f185(f864(x86401,a850)))+E(f341(f341(x86404,x86403),f341(x86405,f341(f341(f3(f864(x86401,a850)),x86402),f341(f341(f311(x86401),x86403),f185(f864(x86401,a850)))))),f341(x86405,f341(f341(f311(x86401),x86403),x86402))) % 19.23/19.05 [8974]~P68(x89741)+~P85(f341(f71(x89742),x89745))+~P85(f341(f71(x89742),x89744))+E(f341(f341(f89(x89741),f341(f341(f8(x89742,x89741),x89743),f341(f341(f110(f864(x89742,a850)),x89744),x89745))),f341(f341(f8(x89742,x89741),x89743),f341(f341(f111(f864(x89742,a850)),x89744),x89745))),f341(f341(f89(x89741),f341(f341(f8(x89742,x89741),x89743),x89744)),f341(f341(f8(x89742,x89741),x89743),x89745))) % 19.23/19.05 [8976]~P71(x89761)+~P85(f341(f71(x89762),x89765))+~P85(f341(f71(x89762),x89764))+E(f341(f341(f90(x89761),f341(f341(f11(x89762,x89761),x89763),f341(f341(f110(f864(x89762,a850)),x89764),x89765))),f341(f341(f11(x89762,x89761),x89763),f341(f341(f111(f864(x89762,a850)),x89764),x89765))),f341(f341(f90(x89761),f341(f341(f11(x89762,x89761),x89763),x89764)),f341(f341(f11(x89762,x89761),x89763),x89765))) % 19.23/19.05 [9112]~P3(x91121)+~P85(f341(f71(x91122),x91125))+~P85(f341(f71(x91122),x91124))+E(f341(f341(f3(x91121),f341(f341(f89(x91121),f341(f341(f8(x91122,x91121),x91123),x91124)),f341(f341(f8(x91122,x91121),x91123),x91125))),f341(f341(f8(x91122,x91121),x91123),f341(f341(f111(f864(x91122,a850)),x91124),x91125))),f341(f341(f8(x91122,x91121),x91123),f341(f341(f110(f864(x91122,a850)),x91124),x91125))) % 19.23/19.05 [9293]~P26(x92931,x92932,x92933,x92935)+~P26(x92931,x92932,x92933,x92934)+P26(x92931,x92932,x92933,f341(f341(f110(f864(x92931,a850)),x92934),x92935))+~E(f341(f341(f111(f864(x92932,a850)),f341(f312(x92931,x92932,x92933),f341(f341(f3(f864(x92931,a850)),x92934),x92935))),f341(f312(x92931,x92932,x92933),f341(f341(f3(f864(x92931,a850)),x92935),x92934))),f185(f864(x92932,a850))) % 19.23/19.05 [9399]E(x93991,f2(a1))+~P85(f341(f341(f242(a1),f2(a1)),x93993))+~P85(f341(f64(x93992,x93991),f341(f341(f250(a1,a1),x93994),x93995)))+P85(f341(f64(x93992,f341(f341(f90(a1),x93991),x93993)),f341(f341(f250(a1,a1),f341(f341(f51(a1),x93994),x93993)),f341(f341(f89(a1),f341(f341(f90(a1),x93991),f60(a1,x93994,x93993))),x93995)))) % 19.23/19.05 [9408]~P85(f341(f341(f242(a857),f2(a857)),x94083))+~P85(f341(f341(f242(a857),f2(a857)),x94082))+~P85(f341(f63(x94081,x94082),f341(f341(f250(a857,a857),x94084),x94085)))+P85(f341(f63(x94081,f341(f341(f90(a857),x94082),x94083)),f341(f341(f250(a857,a857),f341(f341(f51(a857),x94084),x94083)),f341(f341(f89(a857),f341(f341(f90(a857),x94082),f60(a857,x94084,x94083))),x94085)))) % 19.23/19.05 [9458]E(f341(f341(f89(a1),f500(x94581,x94582,x94583,x94584,x94585)),f501(x94581,x94582,x94583,x94584,x94585)),x94585)+~P85(f341(f341(f288(a1),x94584),x94583))+~P85(f341(f341(f288(a1),x94584),f341(f341(f89(a1),x94585),x94581)))+P85(f341(f341(f288(a1),x94584),f341(f341(f89(a1),f341(f341(f3(a1),x94585),x94583)),x94581))) % 19.23/19.05 [9459]E(f341(f341(f3(a1),f502(x94591,x94592,x94593,x94594,x94595)),f503(x94591,x94592,x94593,x94594,x94595)),x94595)+~P85(f341(f341(f288(a1),x94594),x94593))+~P85(f341(f341(f288(a1),x94594),f341(f341(f89(a1),x94595),x94591)))+P85(f341(f341(f288(a1),x94594),f341(f341(f89(a1),f341(f341(f89(a1),x94595),x94593)),x94591))) % 19.23/19.05 [9460]~P71(x94601)+~P85(f341(f71(x94602),x94605))+~P85(f341(f71(x94602),x94604))+E(f341(f341(f90(x94601),f341(f341(f341(f75(x94601,x94602,f90(x94601)),x94603),f87(x94601)),f341(f341(f110(f864(x94602,a850)),x94604),x94605))),f341(f341(f341(f75(x94601,x94602,f90(x94601)),x94603),f87(x94601)),f341(f341(f111(f864(x94602,a850)),x94604),x94605))),f341(f341(f90(x94601),f341(f341(f341(f75(x94601,x94602,f90(x94601)),x94603),f87(x94601)),x94604)),f341(f341(f341(f75(x94601,x94602,f90(x94601)),x94603),f87(x94601)),x94605))) % 19.23/19.05 [9462]~E(f341(f341(f164(x94621),x94625),x94622),f341(f341(f164(x94621),x94625),x94623))+P85(f341(f341(f343(f863(f858(x94621),f858(x94621))),f341(f341(f250(f858(x94621),f858(x94621)),x94622),x94623)),f143(x94621,x94624)))+~P85(f341(f341(f242(a857),x94625),f341(f341(f245(a857),f341(f186(f858(x94621)),x94622)),f341(f186(f858(x94621)),x94623))))+~P85(f341(f341(f343(f863(x94621,x94621)),f341(f341(f250(x94621,x94621),f341(f341(f158(x94621),x94622),x94625)),f341(f341(f158(x94621),x94623),x94625))),x94624)) % 19.23/19.05 [9471]E(f341(f341(f89(a1),f504(x94711,x94712,x94713,x94714,x94715)),f505(x94711,x94712,x94713,x94714,x94715)),x94715)+~P85(f341(f341(f288(a1),x94714),x94713))+P85(f341(f341(f288(a1),x94714),f341(f341(f89(a1),x94715),x94711)))+~P85(f341(f341(f288(a1),x94714),f341(f341(f89(a1),f341(f341(f3(a1),x94715),x94713)),x94711))) % 19.23/19.05 [9472]E(f341(f341(f3(a1),f494(x94721,x94722,x94723,x94724,x94725)),f495(x94721,x94722,x94723,x94724,x94725)),x94725)+~P85(f341(f341(f288(a1),x94724),x94723))+P85(f341(f341(f288(a1),x94724),f341(f341(f89(a1),x94725),x94721)))+~P85(f341(f341(f288(a1),x94724),f341(f341(f89(a1),f341(f341(f89(a1),x94725),x94723)),x94721))) % 19.23/19.05 [9555]~P85(f341(f341(f288(a1),x95554),x95553))+P85(f341(f341(f343(a1),f500(x95551,x95552,x95553,x95554,x95555)),x95552))+~P85(f341(f341(f288(a1),x95554),f341(f341(f89(a1),x95555),x95551)))+P85(f341(f341(f288(a1),x95554),f341(f341(f89(a1),f341(f341(f3(a1),x95555),x95553)),x95551))) % 19.23/19.05 [9556]~P85(f341(f341(f288(a1),x95564),x95563))+P85(f341(f341(f343(a1),f502(x95561,x95562,x95563,x95564,x95565)),x95562))+~P85(f341(f341(f288(a1),x95564),f341(f341(f89(a1),x95565),x95561)))+P85(f341(f341(f288(a1),x95564),f341(f341(f89(a1),f341(f341(f89(a1),x95565),x95563)),x95561))) % 19.23/19.05 [9564]~P85(f341(f341(f288(a1),x95644),x95643))+P85(f341(f341(f343(a1),f501(x95641,x95642,x95643,x95644,x95645)),f304(a1,f87(a1),x95643)))+~P85(f341(f341(f288(a1),x95644),f341(f341(f89(a1),x95645),x95641)))+P85(f341(f341(f288(a1),x95644),f341(f341(f89(a1),f341(f341(f3(a1),x95645),x95643)),x95641))) % 19.23/19.05 [9565]~P85(f341(f341(f288(a1),x95654),x95653))+P85(f341(f341(f343(a1),f503(x95651,x95652,x95653,x95654,x95655)),f304(a1,f87(a1),x95653)))+~P85(f341(f341(f288(a1),x95654),f341(f341(f89(a1),x95655),x95651)))+P85(f341(f341(f288(a1),x95654),f341(f341(f89(a1),f341(f341(f89(a1),x95655),x95653)),x95651))) % 19.23/19.05 [9566]~P112(x95665)+~P78(x95665)+P85(f341(f341(f343(x95661),f507(x95662,x95663,x95664,x95661,x95665)),x95664))+P85(f341(f341(f241(x95665),f341(f341(f8(x95661,x95665),x95663),x95664)),f341(f341(f90(x95665),f341(f109(x95665),f341(f50(x95661),x95664))),x95662))) % 19.23/19.05 [9567]~P85(f341(f341(f288(a1),x95674),x95673))+P85(f341(f341(f343(a1),f494(x95671,x95672,x95673,x95674,x95675)),x95672))+P85(f341(f341(f288(a1),x95674),f341(f341(f89(a1),x95675),x95671)))+~P85(f341(f341(f288(a1),x95674),f341(f341(f89(a1),f341(f341(f89(a1),x95675),x95673)),x95671))) % 19.23/19.05 [9568]~P85(f341(f341(f288(a1),x95684),x95683))+P85(f341(f341(f343(a1),f504(x95681,x95682,x95683,x95684,x95685)),x95682))+P85(f341(f341(f288(a1),x95684),f341(f341(f89(a1),x95685),x95681)))+~P85(f341(f341(f288(a1),x95684),f341(f341(f89(a1),f341(f341(f3(a1),x95685),x95683)),x95681))) % 19.23/19.05 [9570]~P85(f341(f341(f288(a1),x95701),x95705))+P85(f341(f341(f343(a1),f495(x95703,x95704,x95705,x95701,x95702)),f304(a1,f87(a1),x95705)))+P85(f341(f341(f288(a1),x95701),f341(f341(f89(a1),x95702),x95703)))+~P85(f341(f341(f288(a1),x95701),f341(f341(f89(a1),f341(f341(f89(a1),x95702),x95705)),x95703))) % 19.23/19.05 [9571]~P85(f341(f341(f288(a1),x95711),x95715))+P85(f341(f341(f343(a1),f505(x95713,x95714,x95715,x95711,x95712)),f304(a1,f87(a1),x95715)))+P85(f341(f341(f288(a1),x95711),f341(f341(f89(a1),x95712),x95713)))+~P85(f341(f341(f288(a1),x95711),f341(f341(f89(a1),f341(f341(f3(a1),x95712),x95715)),x95713))) % 19.23/19.05 [9739]~P112(x97391)+~P78(x97391)+~P85(f341(f341(f241(x97391),f341(x97393,f507(x97395,x97393,x97394,x97392,x97391))),x97395))+P85(f341(f341(f241(x97391),f341(f341(f8(x97392,x97391),x97393),x97394)),f341(f341(f90(x97391),f341(f109(x97391),f341(f50(x97392),x97394))),x97395))) % 19.23/19.05 [8612]E(f341(f341(f132(x86121),x86122),x86123),f341(f341(f132(x86121),x86124),x86125))+~E(f341(f341(f164(x86121),f341(f186(f858(x86121)),x86122)),x86124),x86122)+~E(f341(f341(f132(x86121),f341(f341(f135(x86121),f341(f186(f858(x86121)),x86122)),x86124)),x86125),x86123)+P85(f341(f341(f241(a857),f341(f186(f858(x86121)),x86124)),f341(f186(f858(x86121)),x86122))) % 19.23/19.05 [8725]E(f341(f341(f132(x87251),x87252),x87253),f341(f341(f132(x87251),x87254),x87255))+~E(f341(f341(f164(x87251),f341(f186(f858(x87251)),x87252)),x87254),x87252)+~E(x87253,f341(f341(f132(x87251),f341(f341(f135(x87251),f341(f186(f858(x87251)),x87252)),x87254)),x87255))+~P85(f341(f341(f241(a857),f341(f186(f858(x87251)),x87252)),f341(f186(f858(x87251)),x87254))) % 19.23/19.05 [9893]~P85(f341(x98935,x98934))+~P85(f341(f71(x98932),f341(f265(x98932),x98935)))+P85(f341(f71(x98931),f341(f265(x98931),f341(f341(f9(x98931,x98932,a850),x98933),x98934))))+~P85(f341(f71(x98931),f341(f265(x98931),f341(f341(f10(f864(x98932,a850),a850,x98931),f96(x98932)),f341(f341(f10(f864(x98932,a850),f864(x98932,a850),x98931),f341(f20(x98932,a850,a850),f341(f341(f10(a850,f864(a850,a850),x98932),a339),x98935))),x98933))))) % 19.23/19.05 [7910]~P38(x79102,x79103,x79104,x79106)+~P38(f37(x79101,x79102),x79106,x79104,x79105)+P38(f37(x79101,x79102),x79103,x79104,x79105)+~P85(f341(x79101,x79103)) % 19.23/19.05 [8419]~P20(x84195,x84191,x84196,x84192)+E(f341(f82(x84191,x84191,x84191,f341(x84192,x84193)),f341(x84192,x84194)),f341(f82(x84191,x84191,x84191,f341(x84192,x84194)),f341(x84192,x84193)))+~P85(f341(f71(x84195),x84194))+~P85(f341(f71(x84195),x84193)) % 19.23/19.05 [7820]~P26(x78201,x78202,x78204,x78203)+~E(f341(x78204,x78206),x78205)+E(f341(f86(x78201,x78202,x78203,x78204),x78205),x78206)+~P85(f341(f341(f343(x78201),x78206),x78203)) % 19.23/19.05 [8013]~P21(x80136,x80131,x80134,x80132)+E(f341(f82(x80131,x80131,x80131,f341(x80132,x80133)),f341(x80134,x80135)),f341(x80132,x80133))+~P85(f341(f71(x80136),x80133))+~P85(f341(f341(f343(x80136),x80135),x80133)) % 19.23/19.05 [9151]~P20(x91513,x91511,x91516,x91512)+E(f341(f82(x91511,x91511,x91511,f341(x91512,f341(f341(f3(f864(x91513,a850)),x91514),f341(f341(f311(x91513),x91515),f185(f864(x91513,a850)))))),f341(x91516,x91515)),f341(x91512,x91514))+~P85(f341(f71(x91513),x91514))+~P85(f341(f341(f343(x91513),x91515),x91514)) % 19.23/19.05 [6880]~P4(x68801)+~E(f60(x68801,x68803,x68804),f60(x68801,x68806,x68804))+~E(f60(x68801,x68802,x68804),f60(x68801,x68805,x68804))+E(f60(x68801,f341(f341(f89(x68801),x68802),x68803),x68804),f60(x68801,f341(f341(f89(x68801),x68805),x68806),x68804)) % 19.23/19.05 [6881]~P4(x68811)+~E(f60(x68811,x68813,x68814),f60(x68811,x68816,x68814))+~E(f60(x68811,x68812,x68814),f60(x68811,x68815,x68814))+E(f60(x68811,f341(f341(f90(x68811),x68812),x68813),x68814),f60(x68811,f341(f341(f90(x68811),x68815),x68816),x68814)) % 19.23/19.05 [6882]~P5(x68821)+~E(f60(x68821,x68823,x68824),f60(x68821,x68826,x68824))+~E(f60(x68821,x68822,x68824),f60(x68821,x68825,x68824))+E(f60(x68821,f341(f341(f3(x68821),x68822),x68823),x68824),f60(x68821,f341(f341(f3(x68821),x68825),x68826),x68824)) % 19.23/19.05 [7711]~P17(x77111,x77112,x77113)+~P85(f341(f71(x77111),x77116))+E(f341(f341(f74(x77111,x77112,x77113),x77114),f341(f341(f311(x77111),x77115),x77116)),f341(f341(f74(x77111,x77112,x77113),f341(f341(x77113,x77115),x77114)),x77116))+P85(f341(f341(f343(x77111),x77115),x77116)) % 19.23/19.05 [7778]~P6(x77781)+P85(f341(f341(f241(x77781),x77782),f341(x77783,x77784)))+~P85(f341(f341(f343(x77785),x77784),x77786))+~P85(f341(f341(f241(x77781),x77782),f341(f341(f55(x77785,x77781),x77786),x77783))) % 19.23/19.05 [7938]~P17(x79381,x79382,x79383)+~P85(f341(f71(x79381),x79386))+E(f341(f341(f74(x79381,x79382,x79383),x79384),f341(f341(f311(x79381),x79385),x79386)),f341(f341(x79383,x79385),f341(f341(f74(x79381,x79382,x79383),x79384),x79386)))+P85(f341(f341(f343(x79381),x79385),x79386)) % 19.23/19.05 [8028]~P101(x80283)+~P85(f341(x80282,x80285))+~P15(x80283,f341(f341(f149(x80281,x80283),x80284),x80286))+E(f341(f133(x80281,x80282),f341(f341(f144(x80281,x80283,x80284),x80285),x80286)),f341(f341(f144(x80281,x80283,x80284),x80285),f341(f133(x80281,x80282),x80286))) % 19.23/19.05 [8051]E(x80511,x80512)+E(x80513,f2(a1))+~P85(f341(f64(x80514,x80513),f341(f341(f250(a1,a1),x80515),x80512)))+~P85(f341(f64(x80514,x80513),f341(f341(f250(a1,a1),x80516),x80511))) % 19.23/19.05 [8052]E(x80521,x80522)+E(x80523,f2(a1))+~P85(f341(f64(x80524,x80523),f341(f341(f250(a1,a1),x80522),x80525)))+~P85(f341(f64(x80524,x80523),f341(f341(f250(a1,a1),x80521),x80526))) % 19.23/19.05 [8074]~P20(x80742,x80745,x80746,x80741)+~P85(f341(f71(x80742),x80744))+E(f341(x80741,f341(f341(f311(x80742),x80743),x80744)),f341(f82(x80745,x80745,x80745,f341(x80741,x80744)),f341(x80746,x80743)))+P85(f341(f341(f343(x80742),x80743),x80744)) % 19.23/19.05 [8287]~P21(x82875,x82871,x82876,x82872)+E(f341(f82(x82871,x82871,x82871,f341(x82872,x82873)),f341(x82872,x82874)),f341(x82872,x82873))+~P85(f341(f71(x82875),x82873))+~P85(f341(f341(f241(f864(x82875,a850)),x82874),x82873)) % 19.23/19.05 [9339]~P26(x93391,x93392,x93394,x93393)+~P85(f341(f341(f343(x93392),x93395),f341(f312(x93391,x93392,x93394),x93393)))+P85(f341(f341(f343(x93391),f341(f86(x93391,x93392,x93393,x93394),x93395)),x93396))+~P85(f341(f341(f241(f864(x93391,a850)),x93393),x93396)) % 19.23/19.05 [9690]~P68(x96902)+~E(f530(x96901,x96903,x96905,x96906,x96904,x96902),f531(x96901,x96903,x96905,x96906,x96904,x96902))+~P85(f341(f71(x96904),x96906))+E(f341(f341(f8(x96901,x96902),x96903),f341(f312(x96904,x96901,x96905),x96906)),f341(f341(f8(x96904,x96902),f341(f82(x96901,x96902,x96904,x96903),x96905)),x96906)) % 19.23/19.05 [9719]~P68(x97196)+E(f341(x97191,f530(x97192,x97193,x97191,x97194,x97195,x97196)),f341(x97191,f531(x97192,x97193,x97191,x97194,x97195,x97196)))+E(f341(f341(f8(x97192,x97196),x97193),f341(f312(x97195,x97192,x97191),x97194)),f341(f341(f8(x97195,x97196),f341(f82(x97192,x97196,x97195,x97193),x97191)),x97194))+~P85(f341(f71(x97195),x97194)) % 19.23/19.05 [9773]~P68(x97732)+~E(f341(x97733,f341(x97735,f531(x97731,x97733,x97735,x97736,x97734,x97732))),f2(x97732))+~P85(f341(f71(x97734),x97736))+E(f341(f341(f8(x97731,x97732),x97733),f341(f312(x97734,x97731,x97735),x97736)),f341(f341(f8(x97734,x97732),f341(f82(x97731,x97732,x97734,x97733),x97735)),x97736)) % 19.23/19.05 [9836]~P68(x98362)+~P85(f341(f71(x98364),x98366))+E(f341(f341(f8(x98361,x98362),x98363),f341(f312(x98364,x98361,x98365),x98366)),f341(f341(f8(x98364,x98362),f341(f82(x98361,x98362,x98364,x98363),x98365)),x98366))+P85(f341(f341(f343(x98364),f531(x98361,x98363,x98365,x98366,x98364,x98362)),x98366)) % 19.23/19.05 [9837]~P68(x98372)+~P85(f341(f71(x98374),x98376))+E(f341(f341(f8(x98371,x98372),x98373),f341(f312(x98374,x98371,x98375),x98376)),f341(f341(f8(x98374,x98372),f341(f82(x98371,x98372,x98374,x98373),x98375)),x98376))+P85(f341(f341(f343(x98374),f530(x98371,x98373,x98375,x98376,x98374,x98372)),x98376)) % 19.23/19.05 [9956]~P71(x99561)+~P85(f341(f71(x99562),x99566))+E(f341(f341(f341(f75(x99561,x99562,f90(x99561)),f341(f341(f20(x99562,f864(x99563,a850),x99561),f341(f341(f9(x99562,x99561,f864(f864(x99563,a850),x99561)),f341(f341(f10(f864(x99563,x99561),f864(x99561,f864(f864(x99563,a850),x99561)),x99562),f75(x99561,x99563,f90(x99561))),x99564)),f87(x99561))),x99565)),f87(x99561)),x99566),f341(f341(f341(f75(x99561,f863(x99562,x99563),f90(x99561)),f341(f260(x99562,x99563,x99561),x99564)),f87(x99561)),f341(f341(f257(x99562,x99563),x99566),x99565)))+P85(f341(f341(f343(x99562),f555(x99564,x99565,x99563,x99566,x99562,x99561)),x99566)) % 19.23/19.05 [9974]~P71(x99741)+~P85(f341(f71(x99742),x99746))+E(f341(f341(f341(f75(x99741,x99742,f90(x99741)),f341(f341(f20(x99742,f864(x99743,a850),x99741),f341(f341(f9(x99742,x99741,f864(f864(x99743,a850),x99741)),f341(f341(f10(f864(x99743,x99741),f864(x99741,f864(f864(x99743,a850),x99741)),x99742),f75(x99741,x99743,f90(x99741))),x99744)),f87(x99741))),x99745)),f87(x99741)),x99746),f341(f341(f341(f75(x99741,f863(x99742,x99743),f90(x99741)),f341(f260(x99742,x99743,x99741),x99744)),f87(x99741)),f341(f341(f257(x99742,x99743),x99746),x99745)))+~P85(f341(f71(x99743),f341(x99745,f555(x99744,x99745,x99743,x99746,x99742,x99741)))) % 19.23/19.05 [8201]~P21(x82012,x82015,x82016,x82011)+~P85(f341(f71(x82012),x82014))+~P85(f341(f71(x82012),x82013))+E(f341(x82011,f341(f341(f110(f864(x82012,a850)),x82013),x82014)),f341(f82(x82015,x82015,x82015,f341(x82011,x82013)),f341(x82011,x82014))) % 19.23/19.05 [8421]~P6(x84211)+P85(f341(f341(f241(x84211),f341(x84212,x84213)),x84214))+~P85(f341(f341(f343(x84215),x84213),x84216))+~P85(f341(f341(f241(x84211),f341(f341(f54(x84215,x84211),x84216),x84212)),x84214)) % 19.23/19.05 [8795]~P26(x87952,x87951,x87953,x87956)+E(f341(f341(f3(f864(x87951,a850)),f341(f312(x87952,x87951,x87953),x87954)),f341(f312(x87952,x87951,x87953),x87955)),f341(f312(x87952,x87951,x87953),f341(f341(f3(f864(x87952,a850)),x87954),x87955)))+~P85(f341(f341(f241(f864(x87952,a850)),x87955),x87956))+~P85(f341(f341(f241(f864(x87952,a850)),x87954),x87956)) % 19.23/19.05 [8796]~P26(x87962,x87961,x87963,x87966)+E(f341(f341(f111(f864(x87961,a850)),f341(f312(x87962,x87961,x87963),x87964)),f341(f312(x87962,x87961,x87963),x87965)),f341(f312(x87962,x87961,x87963),f341(f341(f111(f864(x87962,a850)),x87964),x87965)))+~P85(f341(f341(f241(f864(x87962,a850)),x87965),x87966))+~P85(f341(f341(f241(f864(x87962,a850)),x87964),x87966)) % 19.23/19.05 [9043]E(x90431,x90432)+~P52(x90433,x90434,x90435)+~P85(f341(f341(f343(f863(x90433,x90434)),f341(f341(f250(x90433,x90434),x90436),x90432)),x90435))+~P85(f341(f341(f343(f863(x90433,x90434)),f341(f341(f250(x90433,x90434),x90436),x90431)),x90435)) % 19.23/19.05 [9631]~P68(x96311)+~P85(f341(f71(x96313),x96316))+~P85(f341(f71(x96312),x96315))+E(f341(f341(f89(x96311),f341(f341(f8(x96312,x96311),f341(f82(f865(x96312,x96313),x96311,x96312,x96314),f313(x96312,x96313))),x96315)),f341(f341(f8(x96313,x96311),f341(f82(f865(x96312,x96313),x96311,x96313,x96314),f322(x96313,x96312))),x96316)),f341(f341(f8(f865(x96312,x96313),x96311),x96314),f323(x96312,x96313,x96315,x96316))) % 19.23/19.05 [9769]~P65(x97691)+~E(f341(x97693,f634(x97694,x97696,x97693,x97695,x97692,x97691)),f341(x97696,f634(x97694,x97696,x97693,x97695,x97692,x97691)))+~P85(f341(f71(x97692),x97695))+E(f341(f341(f341(f75(x97691,x97692,f90(x97691)),x97693),x97694),x97695),f341(f341(f341(f75(x97691,x97692,f90(x97691)),x97696),x97694),x97695)) % 19.23/19.05 [9831]~P65(x98311)+~P85(f341(f71(x98312),x98315))+E(f341(f341(f341(f75(x98311,x98312,f90(x98311)),x98313),x98314),x98315),f341(f341(f341(f75(x98311,x98312,f90(x98311)),x98316),x98314),x98315))+P85(f341(f341(f343(x98312),f634(x98314,x98313,x98316,x98315,x98312,x98311)),x98315)) % 19.23/19.05 [8625]~P65(x86251)+~P85(f341(f71(x86252),x86256))+P85(f341(f341(f343(x86252),x86255),x86256))+E(f341(f341(f341(f75(x86251,x86252,f90(x86251)),x86253),x86254),f341(f341(f311(x86252),x86255),x86256)),f341(f341(f90(x86251),f341(x86253,x86255)),f341(f341(f341(f75(x86251,x86252,f90(x86251)),x86253),x86254),x86256))) % 19.23/19.05 [8669]~P9(x86691,x86696,x86693)+~P13(x86691,f864(x86692,a850),x86693,x86695)+~P85(f341(f341(f343(x86691),x86694),x86696))+E(f341(f341(f54(x86691,f864(x86692,a850)),f341(f286(x86691,x86691,x86693),f341(f341(f311(x86691),x86694),f185(f864(x86691,a850))))),x86695),f341(x86695,x86694)) % 19.23/19.05 [8777]~P17(x87773,x87774,x87771)+~P85(f341(f71(x87773),x87776))+~P85(f341(f341(f343(x87773),x87772),x87776))+E(f341(f341(x87771,x87772),f341(f341(f74(x87773,x87774,x87771),x87775),f341(f341(f3(f864(x87773,a850)),x87776),f341(f341(f311(x87773),x87772),f185(f864(x87773,a850)))))),f341(f341(f74(x87773,x87774,x87771),x87775),x87776)) % 19.23/19.05 [9053]~P20(x90533,x90531,x90536,x90532)+~P85(f341(f71(x90533),x90535))+~P85(f341(f71(x90533),x90534))+E(f341(f82(x90531,x90531,x90531,f341(x90532,f341(f341(f110(f864(x90533,a850)),x90534),x90535))),f341(x90532,f341(f341(f111(f864(x90533,a850)),x90534),x90535))),f341(f82(x90531,x90531,x90531,f341(x90532,x90534)),f341(x90532,x90535))) % 19.23/19.05 [9358]~E(x93583,f341(f341(f154(x93581,x93582),x93585),x93586))+P85(f341(f341(f343(f863(f858(x93581),f858(x93581))),f341(f341(f250(f858(x93581),f858(x93581)),x93582),x93583)),f152(x93581,x93584)))+~P85(f341(f341(f242(a857),x93585),f341(f186(f858(x93581)),x93582)))+~P85(f341(f341(f343(f863(x93581,x93581)),f341(f341(f250(x93581,x93581),f341(f341(f158(x93581),x93582),x93585)),x93586)),x93584)) % 19.23/19.05 [9853]~P71(x98532)+~P85(f341(f71(x98531),x98536))+P85(f341(f341(f343(x98531),f554(x98534,x98535,x98533,x98536,x98531,x98532)),x98536))+E(f341(f341(f11(x98531,x98532),f341(f341(f20(x98531,f864(x98533,a850),x98532),f341(f341(f10(f864(x98533,x98532),f864(f864(x98533,a850),x98532),x98531),f11(x98533,x98532)),x98534)),x98535)),x98536),f341(f341(f11(f863(x98531,x98533),x98532),f341(f260(x98531,x98533,x98532),x98534)),f341(f341(f257(x98531,x98533),x98536),x98535))) % 19.23/19.05 [9854]~P68(x98542)+~P85(f341(f71(x98541),x98546))+P85(f341(f341(f343(x98541),f558(x98544,x98545,x98543,x98546,x98541,x98542)),x98546))+E(f341(f341(f8(x98541,x98542),f341(f341(f20(x98541,f864(x98543,a850),x98542),f341(f341(f10(f864(x98543,x98542),f864(f864(x98543,a850),x98542),x98541),f8(x98543,x98542)),x98544)),x98545)),x98546),f341(f341(f8(f863(x98541,x98543),x98542),f341(f260(x98541,x98543,x98542),x98544)),f341(f341(f257(x98541,x98543),x98546),x98545))) % 19.23/19.05 [9891]~P71(x98912)+~P85(f341(f71(x98911),x98916))+~P85(f341(f71(x98913),f341(x98915,f554(x98914,x98915,x98913,x98916,x98911,x98912))))+E(f341(f341(f11(x98911,x98912),f341(f341(f20(x98911,f864(x98913,a850),x98912),f341(f341(f10(f864(x98913,x98912),f864(f864(x98913,a850),x98912),x98911),f11(x98913,x98912)),x98914)),x98915)),x98916),f341(f341(f11(f863(x98911,x98913),x98912),f341(f260(x98911,x98913,x98912),x98914)),f341(f341(f257(x98911,x98913),x98916),x98915))) % 19.23/19.05 [9892]~P68(x98922)+~P85(f341(f71(x98921),x98926))+~P85(f341(f71(x98923),f341(x98925,f558(x98924,x98925,x98923,x98926,x98921,x98922))))+E(f341(f341(f8(x98921,x98922),f341(f341(f20(x98921,f864(x98923,a850),x98922),f341(f341(f10(f864(x98923,x98922),f864(f864(x98923,a850),x98922),x98921),f8(x98923,x98922)),x98924)),x98925)),x98926),f341(f341(f8(f863(x98921,x98923),x98922),f341(f260(x98921,x98923,x98922),x98924)),f341(f341(f257(x98921,x98923),x98926),x98925))) % 19.23/19.05 [9876]~P71(x98762)+~P85(f341(f71(x98761),x98766))+P85(f341(f341(f343(x98761),x98763),x98766))+E(f341(f341(f11(x98761,x98762),f341(f341(f9(x98761,x98762,x98762),f341(f341(f20(x98761,x98762,f864(x98762,x98762)),f341(f341(f10(a850,f864(x98762,f864(x98762,x98762)),x98761),f105(x98762)),f341(f341(f9(x98761,x98761,a850),a338),x98763))),x98764)),x98765)),x98766),f341(f341(f251(x98762),x98765),f341(f50(x98761),x98766))) % 19.23/19.05 [9879]~P71(x98792)+~P85(f341(f71(x98791),x98796))+~P85(f341(f341(f343(x98791),x98793),x98796))+E(f341(f341(f11(x98791,x98792),f341(f341(f9(x98791,x98792,x98792),f341(f341(f20(x98791,x98792,f864(x98792,x98792)),f341(f341(f10(a850,f864(x98792,f864(x98792,x98792)),x98791),f105(x98792)),f341(f341(f9(x98791,x98791,a850),a338),x98793))),x98794)),x98795)),x98796),f341(f341(f90(x98792),f341(x98794,x98793)),f341(f341(f251(x98792),x98795),f341(f341(f3(a857),f341(f50(x98791),x98796)),f87(a857))))) % 19.23/19.05 [9943]~P85(f341(f71(x99431),x99435))+~P85(f341(f71(x99432),x99433))+P85(f341(f341(f343(x99432),f584(x99436,x99434,x99433,x99432,x99435,x99431)),x99433))+E(f341(f341(f8(x99431,a857),f341(f341(f10(f864(x99432,a850),a857,x99431),f50(x99432)),f341(f341(f10(f864(x99432,a850),f864(x99432,a850),x99431),f265(x99432)),f341(f341(f10(f864(x99432,a850),f864(x99432,a850),x99431),f341(f20(x99432,a850,a850),f341(f341(f10(a850,f864(a850,a850),x99432),a339),f341(f341(f9(x99432,f864(x99432,a850),a850),f343(x99432)),x99433)))),x99434)))),x99435),f341(f341(f90(a857),x99436),f341(f50(x99432),x99433))) % 19.23/19.05 [9944]~P85(f341(f71(x99441),x99445))+~P85(f341(f71(x99442),x99443))+P85(f341(f341(f343(x99442),f585(x99446,x99444,x99443,x99442,x99445,x99441)),x99443))+E(f341(f341(f8(x99441,a857),f341(f341(f10(f864(x99442,a850),a857,x99441),f50(x99442)),f341(f341(f10(f864(x99442,a850),f864(x99442,a850),x99441),f265(x99442)),f341(f341(f10(f864(x99442,a850),f864(x99442,a850),x99441),f341(f20(x99442,a850,a850),f341(f341(f10(a850,f864(a850,a850),x99442),a339),f341(f341(f9(x99442,f864(x99442,a850),a850),f343(x99442)),x99443)))),x99444)))),x99445),f341(f341(f8(x99442,a857),x99446),x99443)) % 19.23/19.05 [9980]~P85(f341(f71(x99802),x99803))+~P85(f341(f71(x99801),x99805))+~E(f341(f50(x99801),f341(f265(x99801),f341(f341(f20(x99801,a850,a850),f341(f341(f10(a850,f864(a850,a850),x99801),a339),f341(f341(f9(x99801,f864(x99801,a850),a850),f343(x99801)),x99805))),f341(f341(f9(x99801,x99802,a850),x99804),f584(x99806,x99804,x99803,x99802,x99805,x99801))))),x99806)+E(f341(f341(f8(x99801,a857),f341(f341(f10(f864(x99802,a850),a857,x99801),f50(x99802)),f341(f341(f10(f864(x99802,a850),f864(x99802,a850),x99801),f265(x99802)),f341(f341(f10(f864(x99802,a850),f864(x99802,a850),x99801),f341(f20(x99802,a850,a850),f341(f341(f10(a850,f864(a850,a850),x99802),a339),f341(f341(f9(x99802,f864(x99802,a850),a850),f343(x99802)),x99803)))),x99804)))),x99805),f341(f341(f90(a857),x99806),f341(f50(x99802),x99803))) % 19.23/19.05 [9982]~P85(f341(f71(x99822),x99823))+~P85(f341(f71(x99821),x99825))+~E(f341(f50(x99821),f341(f265(x99821),f341(f341(f20(x99821,a850,a850),f341(f341(f10(a850,f864(a850,a850),x99821),a339),f341(f341(f9(x99821,f864(x99821,a850),a850),f343(x99821)),x99825))),f341(f341(f9(x99821,x99822,a850),x99824),f585(x99826,x99824,x99823,x99822,x99825,x99821))))),f341(x99826,f585(x99826,x99824,x99823,x99822,x99825,x99821)))+E(f341(f341(f8(x99821,a857),f341(f341(f10(f864(x99822,a850),a857,x99821),f50(x99822)),f341(f341(f10(f864(x99822,a850),f864(x99822,a850),x99821),f265(x99822)),f341(f341(f10(f864(x99822,a850),f864(x99822,a850),x99821),f341(f20(x99822,a850,a850),f341(f341(f10(a850,f864(a850,a850),x99822),a339),f341(f341(f9(x99822,f864(x99822,a850),a850),f343(x99822)),x99823)))),x99824)))),x99825),f341(f341(f8(x99822,a857),x99826),x99823)) % 19.23/19.05 [9630]E(x96301,x96302)+~P17(x96303,x96304,x96305)+~P85(f341(f76(x96303,x96304,x96305,x96306,x96307),x96302))+~P85(f341(f76(x96303,x96304,x96305,x96306,x96307),x96301)) % 19.23/19.05 [9429]P85(f341(x94291,x94292))+~P85(f341(f341(f343(x94297),x94292),f341(x94296,x94294)))+~P85(f341(x94291,f415(x94291,x94296,x94295,x94293,x94297)))+~P85(f341(f341(f343(x94293),x94294),x94295)) % 19.23/19.05 [9868]~P17(x98687,x98686,x98681)+E(f341(f341(x98681,x98682),f673(x98682,x98683,x98684,x98685,x98681,x98686,x98687)),x98683)+~P85(f341(f76(x98687,x98686,x98681,x98685,x98684),x98683))+~P85(f341(f341(f343(x98687),x98682),x98684)) % 19.23/19.05 [9928]~P17(x99281,x99282,x99283)+~P85(f341(f76(x99281,x99282,x99283,x99284,x99285),x99287))+P85(f341(f76(x99281,x99282,x99283,x99284,f341(f341(f3(f864(x99281,a850)),x99285),f341(f341(f311(x99281),x99286),f185(f864(x99281,a850))))),f673(x99286,x99287,x99285,x99284,x99283,x99282,x99281)))+~P85(f341(f341(f343(x99281),x99286),x99285)) % 19.23/19.05 [9335]~P65(x93351)+~P26(x93355,x93352,x93356,x93357)+~P85(f341(f71(x93355),x93357))+E(f341(f341(f341(f75(x93351,x93352,f90(x93351)),x93353),x93354),f341(f312(x93355,x93352,x93356),x93357)),f341(f341(f341(f75(x93351,x93355,f90(x93351)),f341(f82(x93352,x93351,x93355,x93353),x93356)),x93354),x93357)) % 19.23/19.05 [9452]~E(f341(f341(f311(x94521),x94525),x94526),f341(f341(f311(x94521),x94522),x94523))+~P85(f341(f76(x94521,x94521,x94524,x94522,x94523),x94527))+P85(f341(f341(f343(x94521),x94522),x94523))+P85(f341(f72(x94521,x94524,f341(f341(f311(x94521),x94525),x94526)),x94527)) % 19.23/19.05 [9534]P85(f341(x95341,x95342))+~P85(f341(f341(f343(x95343),x95342),f341(x95344,x95347)))+~P85(f341(f341(f343(x95346),x95347),x95345))+P85(f341(f341(f343(x95343),f415(x95341,x95344,x95345,x95346,x95343)),f341(f341(f54(x95346,f864(x95343,a850)),x95345),x95344))) % 19.23/19.05 [9547]~P26(x95472,x95471,x95475,x95474)+~P26(x95471,x95473,x95476,f341(f312(x95472,x95471,x95475),x95474))+E(f341(f341(f82(x95471,x95472,x95473,f86(x95472,x95471,x95474,x95475)),f86(x95471,x95473,f341(f312(x95472,x95471,x95475),x95474),x95476)),x95477),f341(f86(x95472,x95473,x95474,f341(f82(x95471,x95473,x95472,x95476),x95475)),x95477))+~P85(f341(f341(f343(x95473),x95477),f341(f312(x95471,x95473,x95476),f341(f312(x95472,x95471,x95475),x95474)))) % 19.23/19.05 [9869]~P17(x98697,x98696,x98691)+E(f341(f341(x98691,x98692),f698(x98693,x98694,x98692,x98695,x98691,x98696,x98697)),x98693)+P85(f341(f341(f343(x98697),x98692),x98694))+~P85(f341(f76(x98697,x98696,x98691,x98695,f341(f341(f311(x98697),x98692),x98694)),x98693)) % 19.23/19.05 [9927]~P17(x99271,x99274,x99275)+P85(f341(f76(x99271,x99274,x99275,x99276,x99273),f698(x99277,x99273,x99272,x99276,x99275,x99274,x99271)))+P85(f341(f341(f343(x99271),x99272),x99273))+~P85(f341(f76(x99271,x99274,x99275,x99276,f341(f341(f311(x99271),x99272),x99273)),x99277)) % 19.23/19.05 [9614]E(x96141,f2(a1))+~P85(f341(f64(x96143,x96141),f341(f341(f250(a1,a1),x96145),x96147)))+~P85(f341(f64(x96142,x96141),f341(f341(f250(a1,a1),x96144),x96146)))+P85(f341(f64(f341(f341(f89(a1),x96142),x96143),x96141),f341(f341(f250(a1,a1),f341(f341(f89(a1),f341(f341(f89(a1),x96144),x96145)),f341(f341(f51(a1),f341(f341(f89(a1),x96146),x96147)),x96141))),f60(a1,f341(f341(f89(a1),x96146),x96147),x96141)))) % 19.23/19.05 [9616]~P85(f341(f341(f242(a857),f2(a857)),x96163))+~P85(f341(f63(x96162,x96163),f341(f341(f250(a857,a857),x96165),x96167)))+~P85(f341(f63(x96161,x96163),f341(f341(f250(a857,a857),x96164),x96166)))+P85(f341(f63(f341(f341(f89(a857),x96161),x96162),x96163),f341(f341(f250(a857,a857),f341(f341(f89(a857),f341(f341(f89(a857),x96164),x96165)),f341(f341(f51(a857),f341(f341(f89(a857),x96166),x96167)),x96163))),f60(a857,f341(f341(f89(a857),x96166),x96167),x96163)))) % 19.23/19.05 [9979]~P68(x99792)+~P85(f341(f71(x99793),x99795))+~P85(f341(f71(x99791),x99797))+E(f341(f341(f8(x99791,x99792),f341(f341(f20(x99791,f864(x99793,a850),x99792),f341(f341(f10(f864(x99793,x99792),f864(f864(x99793,a850),x99792),x99791),f8(x99793,x99792)),x99794)),f341(f341(f10(f864(x99793,a850),f864(x99793,a850),x99791),f265(x99793)),f341(f341(f10(f864(x99793,a850),f864(x99793,a850),x99791),f341(f20(x99793,a850,a850),f341(f341(f10(a850,f864(a850,a850),x99793),a339),f341(f341(f9(x99793,f864(x99793,a850),a850),f343(x99793)),x99795)))),x99796)))),x99797),f341(f341(f8(x99793,x99792),f341(f341(f20(x99793,f864(x99791,a850),x99792),f341(f341(f10(f864(x99791,x99792),f864(f864(x99791,a850),x99792),x99793),f8(x99791,x99792)),f341(f9(x99791,x99793,x99792),x99794))),f341(f341(f10(f864(x99791,a850),f864(x99791,a850),x99793),f265(x99791)),f341(f341(f10(f864(x99791,a850),f864(x99791,a850),x99793),f341(f20(x99791,a850,a850),f341(f341(f10(a850,f864(a850,a850),x99791),a339),f341(f341(f9(x99791,f864(x99791,a850),a850),f343(x99791)),x99797)))),f341(f9(x99791,x99793,a850),x99796))))),x99795)) % 19.23/19.05 [9492]~P23(x94927,x94926,x94921,x94928,x94922,x94924)+E(f341(f341(x94921,f341(x94922,x94923)),f341(x94924,x94925)),f341(x94924,x94925))+~P85(f341(f71(x94926),x94925))+~P85(f341(f341(f343(x94926),x94923),x94925)) % 19.23/19.05 [9496]~P14(x94966,x94961,x94962,x94968,x94963,x94964)+~P9(x94966,x94967,x94968)+P13(x94961,x94962,x94963,f341(x94964,x94965))+~P85(f341(f341(f343(x94966),x94965),x94967)) % 19.23/19.05 [7738]~P38(x77384,x77385,x77386,x77383)+~P30(x77388,x77386,f341(f341(f341(f100(x77388),x77387),x77384),x77381))+P85(f341(f341(x77381,x77382),x77383))+~P85(f341(f341(x77387,x77382),x77385)) % 19.23/19.05 [9140]~P20(x91407,x91401,x91408,x91403)+~P85(f341(f71(x91407),x91405))+~P85(f341(f71(x91407),x91404))+E(f341(f82(x91401,x91401,x91402,f341(x91403,x91404)),f341(f82(x91401,x91401,x91402,f341(x91403,x91405)),x91406)),f341(f82(x91401,x91401,x91402,f341(x91403,x91405)),f341(f82(x91401,x91401,x91402,f341(x91403,x91404)),x91406))) % 19.23/19.05 [9206]~P26(x92062,x92062,x92065,x92066)+~P22(x92063,x92062,x92067,x92068,x92061)+~P85(f341(f71(x92062),x92066))+E(f341(f341(x92061,f341(f82(x92062,x92063,x92062,x92064),x92065)),x92066),f341(f341(x92061,x92064),f341(f312(x92062,x92062,x92065),x92066))) % 19.23/19.05 [9494]~P24(x94947,x94942,x94945,x94948,x94946,x94941)+~P85(f341(f71(x94942),x94944))+E(f341(x94941,f341(f341(f311(x94942),x94943),x94944)),f341(f341(x94945,f341(x94946,x94943)),f341(x94941,x94944)))+P85(f341(f341(f343(x94942),x94943),x94944)) % 19.23/19.05 [9501]~P23(x95016,x95015,x95011,x95017,x95018,x95012)+E(f341(f341(x95011,f341(x95012,x95013)),f341(x95012,x95014)),f341(x95012,x95014))+~P85(f341(f71(x95015),x95014))+~P85(f341(f341(f241(f864(x95015,a850)),x95013),x95014)) % 19.23/19.05 [9127]P85(f341(f341(f343(f863(f858(x91271),f858(x91271))),f341(f341(f250(f858(x91271),f858(x91271)),x91272),x91273)),f152(x91271,x91274)))+~E(x91273,f341(f341(f132(x91271),x91275),f341(f341(f146(x91271),x91276),x91277)))+~E(x91272,f341(f341(f132(x91271),x91275),f341(f341(f146(x91271),x91278),x91277)))+~P85(f341(f341(f343(f863(x91271,x91271)),f341(f341(f250(x91271,x91271),x91278),x91276)),x91274)) % 19.23/19.05 [9497]~P23(x94976,x94972,x94975,x94977,x94978,x94971)+~P85(f341(f71(x94972),x94974))+~P85(f341(f71(x94972),x94973))+E(f341(x94971,f341(f341(f110(f864(x94972,a850)),x94973),x94974)),f341(f341(x94975,f341(x94971,x94973)),f341(x94971,x94974))) % 19.23/19.05 [10018]~P26(x100184,x100182,x100185,x100188)+E(f341(f341(f55(x100181,f864(x100182,a850)),x100183),f341(f341(f10(f864(x100184,a850),f864(x100182,a850),x100181),f312(x100184,x100182,x100185)),x100186)),f341(f312(x100184,x100182,x100185),f341(f341(f55(x100181,f864(x100184,a850)),x100183),x100186)))+~P85(f341(f341(f343(x100181),x100187),x100183))+P85(f341(f341(f343(x100181),f689(x100187,x100186,x100183,x100181,x100188,x100185,x100182,x100184)),x100183)) % 19.23/19.05 [10036]~P26(x100364,x100362,x100365,x100367)+E(f341(f341(f55(x100361,f864(x100362,a850)),x100363),f341(f341(f10(f864(x100364,a850),f864(x100362,a850),x100361),f312(x100364,x100362,x100365)),x100366)),f341(f312(x100364,x100362,x100365),f341(f341(f55(x100361,f864(x100364,a850)),x100363),x100366)))+~P85(f341(f341(f343(x100361),x100368),x100363))+~P85(f341(f341(f241(f864(x100364,a850)),f341(x100366,f689(x100368,x100366,x100363,x100361,x100367,x100365,x100362,x100364))),x100367)) % 19.23/19.05 [9552]~P24(x95527,x95525,x95521,x95528,x95522,x95524)+~P85(f341(f71(x95525),x95526))+~P85(f341(f341(f343(x95525),x95523),x95526))+E(f341(f341(x95521,f341(x95522,x95523)),f341(x95524,f341(f341(f3(f864(x95525,a850)),x95526),f341(f341(f311(x95525),x95523),f185(f864(x95525,a850)))))),f341(x95524,x95526)) % 19.23/19.05 [9562]~P24(x95626,x95623,x95621,x95627,x95628,x95622)+~P85(f341(f71(x95623),x95625))+~P85(f341(f71(x95623),x95624))+E(f341(f341(x95621,f341(x95622,f341(f341(f110(f864(x95623,a850)),x95624),x95625))),f341(x95622,f341(f341(f111(f864(x95623,a850)),x95624),x95625))),f341(f341(x95621,f341(x95622,x95624)),f341(x95622,x95625))) % 19.23/19.05 [9650]P40(x96501,x96502,x96503,x96504,x96505,f341(f341(x96503,x96506),x96507))+~P40(x96501,x96502,x96503,x96504,f341(f341(f3(f864(x96501,a850)),x96505),f341(f341(f311(x96501),x96508),f185(f864(x96501,a850)))),x96509)+~E(f341(f341(x96503,x96506),x96507),f341(f341(x96503,x96508),x96509))+~P85(f341(f341(f343(x96501),x96508),x96505)) % 19.23/19.05 [9589]~P14(x95896,x95897,x95898,x95899,x958910,x95891)+E(f341(f341(x95891,x95892),x95893),f341(f341(x95891,x95894),x95895))+~P85(f341(f341(f343(f863(x95897,x95897)),f341(f341(f250(x95897,x95897),x95893),x95895)),x958910))+~P85(f341(f341(f343(f863(x95896,x95896)),f341(f341(f250(x95896,x95896),x95892),x95894)),x95899)) % 19.23/19.05 [6809]E(x68091,x68092)+~P85(f341(f341(f241(a1),f2(a1)),x68092))+~P85(f341(f341(f241(a1),f2(a1)),x68091))+~P85(f341(f341(f288(a1),x68092),x68091))+~P85(f341(f341(f288(a1),x68091),x68092)) % 19.23/19.05 [9208]~P95(x92082)+E(x92081,f185(f864(x92082,a850)))+~P85(f341(f71(x92082),x92081))+P85(f341(f341(f343(x92082),f15(x92082,x92081)),x92081))+~P85(f341(f341(f343(x92082),f341(f341(f110(x92082),f386(x92081,x92082)),f387(x92081,x92082))),f341(f341(f311(x92082),f386(x92081,x92082)),f341(f341(f311(x92082),f387(x92081,x92082)),f185(f864(x92082,a850)))))) % 19.23/19.05 [9209]~P95(x92092)+E(x92091,f185(f864(x92092,a850)))+~P85(f341(f71(x92092),x92091))+P85(f341(f341(f343(x92092),f12(x92092,x92091)),x92091))+~P85(f341(f341(f343(x92092),f341(f341(f111(x92092),f394(x92091,x92092)),f396(x92091,x92092))),f341(f341(f311(x92092),f394(x92091,x92092)),f341(f341(f311(x92092),f396(x92091,x92092)),f185(f864(x92092,a850)))))) % 19.23/19.05 [9239]~P65(x92392)+E(x92391,f185(f864(x92392,a850)))+~P85(f341(f71(x92392),x92391))+P85(f341(f341(f343(x92392),f341(f73(x92392,f90(x92392)),x92391)),x92391))+~P85(f341(f341(f343(x92392),f341(f341(f90(x92392),f559(x92391,x92392)),f560(x92391,x92392))),f341(f341(f311(x92392),f559(x92391,x92392)),f341(f341(f311(x92392),f560(x92391,x92392)),f185(f864(x92392,a850)))))) % 19.23/19.05 [9245]~P101(x92452)+E(x92451,f185(f864(x92452,a850)))+~P85(f341(f71(x92452),x92451))+P85(f341(f341(f343(x92452),f13(x92452,f240(x92452),x92451)),x92451))+~P85(f341(f341(f343(x92452),f341(f341(f240(x92452),f389(x92451,x92452)),f390(x92451,x92452))),f341(f341(f311(x92452),f389(x92451,x92452)),f341(f341(f311(x92452),f390(x92451,x92452)),f185(f864(x92452,a850)))))) % 19.23/19.05 [9246]~P101(x92462)+E(x92461,f185(f864(x92462,a850)))+~P85(f341(f71(x92462),x92461))+P85(f341(f341(f343(x92462),f14(x92462,f245(x92462),x92461)),x92461))+~P85(f341(f341(f343(x92462),f341(f341(f245(x92462),f397(x92461,x92462)),f400(x92461,x92462))),f341(f341(f311(x92462),f397(x92461,x92462)),f341(f341(f311(x92462),f400(x92461,x92462)),f185(f864(x92462,a850)))))) % 19.23/19.05 [6425]~P81(x64252)+E(x64251,f2(x64252))+~E(f341(f341(f89(x64252),x64253),x64251),f2(x64252))+~P85(f341(f341(f241(x64252),f2(x64252)),x64253))+~P85(f341(f341(f241(x64252),f2(x64252)),x64251)) % 19.23/19.05 [6426]~P81(x64262)+E(x64261,f2(x64262))+~E(f341(f341(f89(x64262),x64261),x64263),f2(x64262))+~P85(f341(f341(f241(x64262),f2(x64262)),x64263))+~P85(f341(f341(f241(x64262),f2(x64262)),x64261)) % 19.23/19.05 [7140]~P101(x71401)+E(f17(x71401,x71402),x71403)+~P85(f341(f71(x71401),x71402))+~P85(f341(f341(f241(x71401),x71403),f635(x71403,x71402,x71401)))+~P85(f341(f341(f343(x71401),x71403),x71402)) % 19.23/19.05 [7175]~P101(x71751)+~P15(x71751,x71752)+~P15(x71751,x71753)+P15(x71751,f341(f341(f132(x71751),x71752),x71753))+P85(f341(f341(f343(x71751),f778(x71753,x71752,x71751)),f341(f163(x71751),x71752))) % 19.23/19.05 [7176]~P101(x71761)+~P15(x71761,x71762)+~P15(x71761,x71763)+P15(x71761,f341(f341(f132(x71761),x71762),x71763))+P85(f341(f341(f343(x71761),f779(x71763,x71762,x71761)),f341(f163(x71761),x71763))) % 19.23/19.05 [7242]~P101(x72421)+E(f16(x72421,x72422),x72423)+~P85(f341(f71(x72421),x72422))+P85(f341(f341(f343(x72421),f636(x72423,x72422,x72421)),x72422))+~P85(f341(f341(f343(x72421),x72423),x72422)) % 19.23/19.05 [7243]~P101(x72431)+E(f17(x72431,x72432),x72433)+~P85(f341(f71(x72431),x72432))+P85(f341(f341(f343(x72431),f635(x72433,x72432,x72431)),x72432))+~P85(f341(f341(f343(x72431),x72433),x72432)) % 19.23/19.05 [7841]~P101(x78411)+E(f16(x78411,x78412),x78413)+~P85(f341(f71(x78411),x78412))+~P85(f341(f341(f343(x78411),x78413),x78412))+~P85(f341(f341(f241(x78411),f636(x78413,x78412,x78411)),x78413)) % 19.23/19.05 [8152]~P101(x81521)+~P15(x81521,x81522)+~P15(x81521,x81523)+P15(x81521,f341(f341(f132(x81521),x81522),x81523))+~P85(f341(f341(f241(x81521),f778(x81523,x81522,x81521)),f779(x81523,x81522,x81521))) % 19.23/19.05 [8883]~P95(x88832)+E(x88831,f185(f864(x88832,a850)))+~E(f341(f341(f110(x88832),f341(x88833,f437(x88831,x88833,x88832))),f341(x88833,f447(x88831,x88833,x88832))),f341(x88833,f341(f341(f110(x88832),f437(x88831,x88833,x88832)),f447(x88831,x88833,x88832))))+E(f15(x88832,f341(f312(x88832,x88832,x88833),x88831)),f341(x88833,f15(x88832,x88831)))+~P85(f341(f71(x88832),x88831)) % 19.23/19.05 [8884]~P95(x88842)+E(x88841,f185(f864(x88842,a850)))+~E(f341(f341(f111(x88842),f341(x88843,f438(x88841,x88843,x88842))),f341(x88843,f446(x88841,x88843,x88842))),f341(x88843,f341(f341(f111(x88842),f438(x88841,x88843,x88842)),f446(x88841,x88843,x88842))))+E(f12(x88842,f341(f312(x88842,x88842,x88843),x88841)),f341(x88843,f12(x88842,x88841)))+~P85(f341(f71(x88842),x88841)) % 19.23/19.05 [8885]~P101(x88852)+E(x88851,f185(f864(x88852,a850)))+~E(f341(f341(f240(x88852),f341(x88853,f439(x88851,x88853,x88852))),f341(x88853,f443(x88851,x88853,x88852))),f341(x88853,f341(f341(f240(x88852),f439(x88851,x88853,x88852)),f443(x88851,x88853,x88852))))+E(f16(x88852,f341(f312(x88852,x88852,x88853),x88851)),f341(x88853,f16(x88852,x88851)))+~P85(f341(f71(x88852),x88851)) % 19.23/19.05 [8886]~P101(x88862)+E(x88861,f185(f864(x88862,a850)))+~E(f341(f341(f245(x88862),f341(x88863,f444(x88861,x88863,x88862))),f341(x88863,f445(x88861,x88863,x88862))),f341(x88863,f341(f341(f245(x88862),f444(x88861,x88863,x88862)),f445(x88861,x88863,x88862))))+E(f17(x88862,f341(f312(x88862,x88862,x88863),x88861)),f341(x88863,f17(x88862,x88861)))+~P85(f341(f71(x88862),x88861)) % 19.23/19.05 [8950]~P101(x89502)+E(x89501,f185(f864(x89502,a850)))+~E(f341(f341(f240(x89502),f341(x89503,f427(x89501,x89503,x89502))),f341(x89503,f433(x89501,x89503,x89502))),f341(x89503,f341(f341(f240(x89502),f427(x89501,x89503,x89502)),f433(x89501,x89503,x89502))))+E(f13(x89502,f240(x89502),f341(f312(x89502,x89502,x89503),x89501)),f341(x89503,f13(x89502,f240(x89502),x89501)))+~P85(f341(f71(x89502),x89501)) % 19.23/19.05 [8951]~P101(x89512)+E(x89511,f185(f864(x89512,a850)))+~E(f341(f341(f245(x89512),f341(x89513,f440(x89511,x89513,x89512))),f341(x89513,f441(x89511,x89513,x89512))),f341(x89513,f341(f341(f245(x89512),f440(x89511,x89513,x89512)),f441(x89511,x89513,x89512))))+E(f14(x89512,f245(x89512),f341(f312(x89512,x89512,x89513),x89511)),f341(x89513,f14(x89512,f245(x89512),x89511)))+~P85(f341(f71(x89512),x89511)) % 19.23/19.05 [6442]~P65(x64422)+E(x64421,f185(f864(x64422,a850)))+~P85(f341(f71(x64422),x64421))+E(f341(f73(x64422,f90(x64422)),f341(f341(f311(x64422),x64423),x64421)),f341(f341(f90(x64422),x64423),f341(f73(x64422,f90(x64422)),x64421)))+P85(f341(f341(f343(x64422),x64423),x64421)) % 19.23/19.05 [6979]~P101(x69792)+E(f341(f341(f245(x69792),f17(x69792,x69791)),f17(x69792,x69793)),f17(x69792,x69793))+E(x69791,f185(f864(x69792,a850)))+~P85(f341(f71(x69792),x69793))+~P85(f341(f341(f241(f864(x69792,a850)),x69791),x69793)) % 19.23/19.05 [6980]~P101(x69802)+E(f341(f341(f240(x69802),f16(x69802,x69801)),f16(x69802,x69803)),f16(x69802,x69803))+E(x69801,f185(f864(x69802,a850)))+~P85(f341(f71(x69802),x69803))+~P85(f341(f341(f241(f864(x69802,a850)),x69801),x69803)) % 19.23/19.05 [6981]~P95(x69812)+E(f341(f341(f110(x69812),f15(x69812,x69811)),f15(x69812,x69813)),f15(x69812,x69813))+E(x69811,f185(f864(x69812,a850)))+~P85(f341(f71(x69812),x69813))+~P85(f341(f341(f241(f864(x69812,a850)),x69811),x69813)) % 19.23/19.05 [6982]~P95(x69822)+E(f341(f341(f111(x69822),f12(x69822,x69821)),f12(x69822,x69823)),f12(x69822,x69823))+E(x69821,f185(f864(x69822,a850)))+~P85(f341(f71(x69822),x69823))+~P85(f341(f341(f241(f864(x69822,a850)),x69821),x69823)) % 19.23/19.05 [7298]~P101(x72982)+E(x72981,f185(f864(x72982,a850)))+~P85(f341(f71(x72982),x72983))+P85(f341(f341(f241(x72982),f16(x72982,x72981)),f16(x72982,x72983)))+~P85(f341(f341(f241(f864(x72982,a850)),x72981),x72983)) % 19.23/19.05 [7299]~P101(x72992)+E(x72991,f185(f864(x72992,a850)))+~P85(f341(f71(x72992),x72993))+P85(f341(f341(f241(x72992),f17(x72992,x72993)),f17(x72992,x72991)))+~P85(f341(f341(f241(f864(x72992,a850)),x72991),x72993)) % 19.23/19.05 [7361]~P95(x73611)+E(f15(x73611,x73612),x73613)+~P85(f341(f71(x73611),x73612))+~E(f341(f341(f3(f864(x73611,a850)),x73612),f341(f341(f311(x73611),x73613),f185(f864(x73611,a850)))),f185(f864(x73611,a850)))+~P85(f341(f341(f343(x73611),x73613),x73612)) % 19.23/19.05 [7362]~P95(x73621)+E(f12(x73621,x73622),x73623)+~P85(f341(f71(x73621),x73622))+~E(f341(f341(f3(f864(x73621,a850)),x73622),f341(f341(f311(x73621),x73623),f185(f864(x73621,a850)))),f185(f864(x73621,a850)))+~P85(f341(f341(f343(x73621),x73623),x73622)) % 19.23/19.05 [7363]~P101(x73631)+E(f16(x73631,x73632),x73633)+~P85(f341(f71(x73631),x73632))+~E(f341(f341(f3(f864(x73631,a850)),x73632),f341(f341(f311(x73631),x73633),f185(f864(x73631,a850)))),f185(f864(x73631,a850)))+~P85(f341(f341(f343(x73631),x73633),x73632)) % 19.23/19.05 [7364]~P101(x73641)+E(f17(x73641,x73642),x73643)+~P85(f341(f71(x73641),x73642))+~E(f341(f341(f3(f864(x73641,a850)),x73642),f341(f341(f311(x73641),x73643),f185(f864(x73641,a850)))),f185(f864(x73641,a850)))+~P85(f341(f341(f343(x73641),x73643),x73642)) % 19.23/19.05 [7463]~P101(x74631)+E(f13(x74631,f240(x74631),x74632),x74633)+~P85(f341(f71(x74631),x74632))+~E(f341(f341(f3(f864(x74631,a850)),x74632),f341(f341(f311(x74631),x74633),f185(f864(x74631,a850)))),f185(f864(x74631,a850)))+~P85(f341(f341(f343(x74631),x74633),x74632)) % 19.23/19.05 [7464]~P101(x74641)+E(f14(x74641,f245(x74641),x74642),x74643)+~P85(f341(f71(x74641),x74642))+~E(f341(f341(f3(f864(x74641,a850)),x74642),f341(f341(f311(x74641),x74643),f185(f864(x74641,a850)))),f185(f864(x74641,a850)))+~P85(f341(f341(f343(x74641),x74643),x74642)) % 19.23/19.05 [7501]~P101(x75012)+E(x75011,f185(f864(x75012,a850)))+~P85(f341(f71(x75012),x75011))+~P85(f341(f341(f242(x75012),x75013),f539(x75013,x75011,x75012)))+P85(f341(f341(f242(x75012),x75013),f341(f73(x75012,f245(x75012)),x75011))) % 19.23/19.05 [7502]~P101(x75022)+E(x75021,f185(f864(x75022,a850)))+~P85(f341(f71(x75022),x75021))+~P85(f341(f341(f241(x75022),x75023),f540(x75023,x75021,x75022)))+P85(f341(f341(f241(x75022),x75023),f341(f73(x75022,f245(x75022)),x75021))) % 19.23/19.05 [7503]~P99(x75032)+E(x75031,f185(f864(x75032,a850)))+~P85(f341(f71(x75032),x75031))+~P85(f341(f341(f241(x75032),x75033),f541(x75033,x75031,x75032)))+P85(f341(f341(f241(x75032),x75033),f341(f73(x75032,f111(x75032)),x75031))) % 19.23/19.05 [7591]~P99(x75912)+E(x75911,f185(f864(x75912,a850)))+~P85(f341(f71(x75912),x75911))+P85(f341(f341(f343(x75912),f541(x75913,x75911,x75912)),x75911))+P85(f341(f341(f241(x75912),x75913),f341(f73(x75912,f111(x75912)),x75911))) % 19.23/19.05 [7592]~P101(x75922)+E(x75921,f185(f864(x75922,a850)))+~P85(f341(f71(x75922),x75921))+P85(f341(f341(f343(x75922),f540(x75923,x75921,x75922)),x75921))+P85(f341(f341(f241(x75922),x75923),f341(f73(x75922,f245(x75922)),x75921))) % 19.23/19.05 [7593]~P101(x75932)+E(x75931,f185(f864(x75932,a850)))+~P85(f341(f71(x75932),x75931))+P85(f341(f341(f343(x75932),f539(x75933,x75931,x75932)),x75931))+P85(f341(f341(f242(x75932),x75933),f341(f73(x75932,f245(x75932)),x75931))) % 19.23/19.05 [7713]~P101(x77132)+E(x77131,f185(f864(x77132,a850)))+E(f341(f341(f245(x77132),f14(x77132,f245(x77132),x77131)),f14(x77132,f245(x77132),x77133)),f14(x77132,f245(x77132),x77133))+~P85(f341(f71(x77132),x77133))+~P85(f341(f341(f241(f864(x77132,a850)),x77131),x77133)) % 19.23/19.05 [7714]~P101(x77142)+E(x77141,f185(f864(x77142,a850)))+E(f341(f341(f240(x77142),f13(x77142,f240(x77142),x77141)),f13(x77142,f240(x77142),x77143)),f13(x77142,f240(x77142),x77143))+~P85(f341(f71(x77142),x77143))+~P85(f341(f341(f241(f864(x77142,a850)),x77141),x77143)) % 19.23/19.05 [7916]~E(f686(x79161,x79163,x79162),f687(x79161,x79163,x79162))+~E(f341(f50(x79162),f688(x79161,x79163,x79162)),x79161)+E(f341(f341(f90(a857),x79161),f341(f50(f864(x79162,a850)),x79163)),f341(f50(x79162),f52(f864(x79162,a850),x79163)))+~P85(f341(f71(x79162),f52(f864(x79162,a850),x79163)))+~P85(f341(f71(f864(x79162,a850)),x79163)) % 19.23/19.05 [8090]~P101(x80902)+E(x80901,f185(f864(x80902,a850)))+~P85(f341(f71(x80902),x80903))+P85(f341(f341(f241(x80902),f341(f73(x80902,f245(x80902)),x80903)),f341(f73(x80902,f245(x80902)),x80901)))+~P85(f341(f341(f241(f864(x80902,a850)),x80901),x80903)) % 19.23/19.05 [8393]~E(f686(x83931,x83933,x83932),f687(x83931,x83933,x83932))+E(f341(f341(f90(a857),x83931),f341(f50(f864(x83932,a850)),x83933)),f341(f50(x83932),f52(f864(x83932,a850),x83933)))+P85(f341(f341(f343(f864(x83932,a850)),f688(x83931,x83933,x83932)),x83933))+~P85(f341(f71(x83932),f52(f864(x83932,a850),x83933)))+~P85(f341(f71(f864(x83932,a850)),x83933)) % 19.23/19.05 [8417]~E(f341(f50(x84172),f688(x84171,x84173,x84172)),x84171)+E(f341(f341(f90(a857),x84171),f341(f50(f864(x84172,a850)),x84173)),f341(f50(x84172),f52(f864(x84172,a850),x84173)))+P85(f341(f341(f343(f864(x84172,a850)),f687(x84171,x84173,x84172)),x84173))+~P85(f341(f71(x84172),f52(f864(x84172,a850),x84173)))+~P85(f341(f71(f864(x84172,a850)),x84173)) % 19.23/19.05 [8418]~E(f341(f50(x84182),f688(x84181,x84183,x84182)),x84181)+E(f341(f341(f90(a857),x84181),f341(f50(f864(x84182,a850)),x84183)),f341(f50(x84182),f52(f864(x84182,a850),x84183)))+P85(f341(f341(f343(f864(x84182,a850)),f686(x84181,x84183,x84182)),x84183))+~P85(f341(f71(x84182),f52(f864(x84182,a850),x84183)))+~P85(f341(f71(f864(x84182,a850)),x84183)) % 19.23/19.05 [8447]~E(f341(f50(x84472),f688(x84471,x84473,x84472)),x84471)+~E(f341(f341(f111(f864(x84472,a850)),f687(x84471,x84473,x84472)),f686(x84471,x84473,x84472)),f185(f864(x84472,a850)))+E(f341(f341(f90(a857),x84471),f341(f50(f864(x84472,a850)),x84473)),f341(f50(x84472),f52(f864(x84472,a850),x84473)))+~P85(f341(f71(f864(x84472,a850)),x84473))+~P85(f341(f71(x84472),f52(f864(x84472,a850),x84473))) % 19.23/19.05 [8673]E(f341(f341(f90(a857),x86731),f341(f50(f864(x86732,a850)),x86733)),f341(f50(x86732),f52(f864(x86732,a850),x86733)))+P85(f341(f341(f343(f864(x86732,a850)),f688(x86731,x86733,x86732)),x86733))+P85(f341(f341(f343(f864(x86732,a850)),f687(x86731,x86733,x86732)),x86733))+~P85(f341(f71(f864(x86732,a850)),x86733))+~P85(f341(f71(x86732),f52(f864(x86732,a850),x86733))) % 19.23/19.05 [8674]E(f341(f341(f90(a857),x86741),f341(f50(f864(x86742,a850)),x86743)),f341(f50(x86742),f52(f864(x86742,a850),x86743)))+P85(f341(f341(f343(f864(x86742,a850)),f688(x86741,x86743,x86742)),x86743))+P85(f341(f341(f343(f864(x86742,a850)),f686(x86741,x86743,x86742)),x86743))+~P85(f341(f71(f864(x86742,a850)),x86743))+~P85(f341(f71(x86742),f52(f864(x86742,a850),x86743))) % 19.23/19.05 [8699]~E(f341(f341(f111(f864(x86992,a850)),f687(x86991,x86993,x86992)),f686(x86991,x86993,x86992)),f185(f864(x86992,a850)))+E(f341(f341(f90(a857),x86991),f341(f50(f864(x86992,a850)),x86993)),f341(f50(x86992),f52(f864(x86992,a850),x86993)))+~P85(f341(f71(f864(x86992,a850)),x86993))+P85(f341(f341(f343(f864(x86992,a850)),f688(x86991,x86993,x86992)),x86993))+~P85(f341(f71(x86992),f52(f864(x86992,a850),x86993))) % 19.23/19.05 [8929]~P92(x89292)+E(x89291,f185(f864(x89292,a850)))+~E(f341(f341(f90(x89292),f341(x89293,f561(x89291,x89293,x89292))),f341(x89293,f562(x89291,x89293,x89292))),f341(x89293,f341(f341(f90(x89292),f561(x89291,x89293,x89292)),f562(x89291,x89293,x89292))))+~P85(f341(f71(x89292),x89291))+E(f341(f73(x89292,f90(x89292)),f341(f312(x89292,x89292,x89293),x89291)),f341(x89293,f341(f73(x89292,f90(x89292)),x89291))) % 19.23/19.05 [9804]P85(f341(f341(x98041,x98042),x98043))+P85(f341(f341(f242(a1),f836(x98041,x98043,x98042)),f840(x98041,x98043,x98042)))+P85(f341(f341(f241(a1),f840(x98041,x98043,x98042)),f2(a1)))+P85(f341(f341(x98041,f836(x98041,x98043,x98042)),f341(f341(f90(a1),f341(f113(a1),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),f840(x98041,x98043,x98042))))+~P85(f341(f330(f863(a1,a1),a70),f341(f341(f250(a1,a1),x98042),x98043))) % 19.23/19.05 [9810]P85(f341(f341(x98101,x98102),x98103))+P85(f341(f341(f241(a1),f835(x98101,x98103,x98102)),f2(a1)))+P85(f341(f341(x98101,f834(x98101,x98103,x98102)),f341(f341(f90(a1),f341(f113(a1),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),f835(x98101,x98103,x98102))))+P85(f341(f341(f241(a1),f2(a1)),f341(f341(f89(a1),f834(x98101,x98103,x98102)),f835(x98101,x98103,x98102))))+~P85(f341(f330(f863(a1,a1),a67),f341(f341(f250(a1,a1),x98102),x98103))) % 19.23/19.05 [7886]~P113(x78861)+~P85(f341(f341(f241(x78861),x78862),f87(x78861)))+~P85(f341(f341(f241(x78861),f2(x78861)),x78862))+~P85(f341(f341(f241(x78861),f2(x78861)),x78863))+P85(f341(f341(f241(x78861),f341(f341(f90(x78861),x78862),x78863)),x78863)) % 19.23/19.05 [7887]~P113(x78871)+~P85(f341(f341(f241(x78871),x78873),f87(x78871)))+~P85(f341(f341(f241(x78871),f2(x78871)),x78873))+~P85(f341(f341(f241(x78871),f2(x78871)),x78872))+P85(f341(f341(f241(x78871),f341(f341(f90(x78871),x78872),x78873)),x78872)) % 19.23/19.05 [8233]~P101(x82332)+E(x82331,f185(f864(x82332,a850)))+~P85(f341(f71(x82332),x82331))+P85(f341(f341(f242(x82332),f551(x82333,x82331,x82332)),x82333))+~P85(f341(f341(f242(x82332),f341(f73(x82332,f245(x82332)),x82331)),x82333)) % 19.23/19.05 [8234]~P101(x82342)+E(x82341,f185(f864(x82342,a850)))+~P85(f341(f71(x82342),x82341))+P85(f341(f341(f241(x82342),f550(x82343,x82341,x82342)),x82343))+~P85(f341(f341(f241(x82342),f341(f73(x82342,f245(x82342)),x82341)),x82343)) % 19.23/19.05 [8235]~P101(x82352)+E(x82351,f185(f864(x82352,a850)))+~P85(f341(f71(x82352),x82351))+P85(f341(f341(f343(x82352),f550(x82353,x82351,x82352)),x82351))+~P85(f341(f341(f241(x82352),f341(f73(x82352,f245(x82352)),x82351)),x82353)) % 19.23/19.05 [8236]~P101(x82362)+E(x82361,f185(f864(x82362,a850)))+~P85(f341(f71(x82362),x82361))+P85(f341(f341(f343(x82362),f551(x82363,x82361,x82362)),x82361))+~P85(f341(f341(f242(x82362),f341(f73(x82362,f245(x82362)),x82361)),x82363)) % 19.23/19.05 [8322]~P85(f341(x83221,x83223))+P85(f341(x83221,f483(x83221,x83222)))+P85(f341(x83221,f475(x83221,x83222)))+~P85(f341(f341(f242(a1),f2(a1)),x83222))+P85(f341(x83221,f341(f341(f3(a1),f475(x83221,x83222)),f341(f341(f90(a1),f484(x83221,x83222)),x83222)))) % 19.23/19.05 [8538]~P85(f341(x85381,x85383))+P85(f341(x85381,f475(x85381,x85382)))+~P85(f341(f341(f242(a1),f2(a1)),x85382))+P85(f341(f341(f343(a1),f483(x85381,x85382)),f304(a1,f87(a1),x85382)))+P85(f341(x85381,f341(f341(f3(a1),f475(x85381,x85382)),f341(f341(f90(a1),f484(x85381,x85382)),x85382)))) % 19.23/19.05 [8717]~P85(f341(x87171,x87173))+~P85(f341(x87171,f475(x87171,x87172)))+P85(f341(x87171,f483(x87171,x87172)))+~P85(f341(f341(f242(a1),f2(a1)),x87172))+~P85(f341(x87171,f341(f341(f3(a1),f475(x87171,x87172)),f341(f341(f90(a1),f484(x87171,x87172)),x87172)))) % 19.23/19.05 [8823]~P85(f341(x88231,x88233))+~P85(f341(x88231,f475(x88231,x88232)))+~P85(f341(f341(f242(a1),f2(a1)),x88232))+P85(f341(f341(f343(a1),f483(x88231,x88232)),f304(a1,f87(a1),x88232)))+~P85(f341(x88231,f341(f341(f3(a1),f475(x88231,x88232)),f341(f341(f90(a1),f484(x88231,x88232)),x88232)))) % 19.23/19.05 [8636]~P95(x86361)+~P85(f341(f71(x86361),x86362))+E(f341(f341(f3(f864(x86361,a850)),x86362),f341(f341(f311(x86361),x86363),f185(f864(x86361,a850)))),f185(f864(x86361,a850)))+~P85(f341(f341(f343(x86361),x86363),x86362))+E(f341(f341(f110(x86361),x86363),f15(x86361,f341(f341(f3(f864(x86361,a850)),x86362),f341(f341(f311(x86361),x86363),f185(f864(x86361,a850)))))),f15(x86361,x86362)) % 19.23/19.05 [8637]~P95(x86371)+~P85(f341(f71(x86371),x86372))+E(f341(f341(f3(f864(x86371,a850)),x86372),f341(f341(f311(x86371),x86373),f185(f864(x86371,a850)))),f185(f864(x86371,a850)))+~P85(f341(f341(f343(x86371),x86373),x86372))+E(f341(f341(f111(x86371),x86373),f12(x86371,f341(f341(f3(f864(x86371,a850)),x86372),f341(f341(f311(x86371),x86373),f185(f864(x86371,a850)))))),f12(x86371,x86372)) % 19.23/19.05 [8638]~P101(x86381)+~P85(f341(f71(x86381),x86382))+E(f341(f341(f3(f864(x86381,a850)),x86382),f341(f341(f311(x86381),x86383),f185(f864(x86381,a850)))),f185(f864(x86381,a850)))+~P85(f341(f341(f343(x86381),x86383),x86382))+E(f341(f341(f240(x86381),x86383),f16(x86381,f341(f341(f3(f864(x86381,a850)),x86382),f341(f341(f311(x86381),x86383),f185(f864(x86381,a850)))))),f16(x86381,x86382)) % 19.23/19.05 [8639]~P101(x86391)+~P85(f341(f71(x86391),x86392))+E(f341(f341(f3(f864(x86391,a850)),x86392),f341(f341(f311(x86391),x86393),f185(f864(x86391,a850)))),f185(f864(x86391,a850)))+~P85(f341(f341(f343(x86391),x86393),x86392))+E(f341(f341(f245(x86391),x86393),f17(x86391,f341(f341(f3(f864(x86391,a850)),x86392),f341(f341(f311(x86391),x86393),f185(f864(x86391,a850)))))),f17(x86391,x86392)) % 19.23/19.05 [8694]~P101(x86941)+~P85(f341(f71(x86941),x86942))+E(f341(f341(f3(f864(x86941,a850)),x86942),f341(f341(f311(x86941),x86943),f185(f864(x86941,a850)))),f185(f864(x86941,a850)))+~P85(f341(f341(f343(x86941),x86943),x86942))+E(f341(f341(f240(x86941),x86943),f13(x86941,f240(x86941),f341(f341(f3(f864(x86941,a850)),x86942),f341(f341(f311(x86941),x86943),f185(f864(x86941,a850)))))),f13(x86941,f240(x86941),x86942)) % 19.23/19.05 [8695]~P101(x86951)+~P85(f341(f71(x86951),x86952))+E(f341(f341(f3(f864(x86951,a850)),x86952),f341(f341(f311(x86951),x86953),f185(f864(x86951,a850)))),f185(f864(x86951,a850)))+~P85(f341(f341(f343(x86951),x86953),x86952))+E(f341(f341(f245(x86951),x86953),f14(x86951,f245(x86951),f341(f341(f3(f864(x86951,a850)),x86952),f341(f341(f311(x86951),x86953),f185(f864(x86951,a850)))))),f14(x86951,f245(x86951),x86952)) % 19.23/19.05 [8705]~P101(x87051)+~P85(f341(f71(x87051),x87053))+~P85(f341(f71(x87051),x87052))+E(f341(f341(f111(f864(x87051,a850)),x87052),x87053),f185(f864(x87051,a850)))+E(f341(f341(f245(x87051),f17(x87051,f341(f341(f110(f864(x87051,a850)),x87052),x87053))),f17(x87051,f341(f341(f111(f864(x87051,a850)),x87052),x87053))),f341(f341(f245(x87051),f17(x87051,x87052)),f17(x87051,x87053))) % 19.23/19.05 [8706]~P101(x87061)+~P85(f341(f71(x87061),x87063))+~P85(f341(f71(x87061),x87062))+E(f341(f341(f111(f864(x87061,a850)),x87062),x87063),f185(f864(x87061,a850)))+E(f341(f341(f240(x87061),f16(x87061,f341(f341(f110(f864(x87061,a850)),x87062),x87063))),f16(x87061,f341(f341(f111(f864(x87061,a850)),x87062),x87063))),f341(f341(f240(x87061),f16(x87061,x87062)),f16(x87061,x87063))) % 19.23/19.05 [8707]~P95(x87071)+~P85(f341(f71(x87071),x87073))+~P85(f341(f71(x87071),x87072))+E(f341(f341(f111(f864(x87071,a850)),x87072),x87073),f185(f864(x87071,a850)))+E(f341(f341(f110(x87071),f15(x87071,f341(f341(f110(f864(x87071,a850)),x87072),x87073))),f15(x87071,f341(f341(f111(f864(x87071,a850)),x87072),x87073))),f341(f341(f110(x87071),f15(x87071,x87072)),f15(x87071,x87073))) % 19.23/19.05 [8708]~P95(x87081)+~P85(f341(f71(x87081),x87083))+~P85(f341(f71(x87081),x87082))+E(f341(f341(f111(f864(x87081,a850)),x87082),x87083),f185(f864(x87081,a850)))+E(f341(f341(f111(x87081),f12(x87081,f341(f341(f110(f864(x87081,a850)),x87082),x87083))),f12(x87081,f341(f341(f111(f864(x87081,a850)),x87082),x87083))),f341(f341(f111(x87081),f12(x87081,x87082)),f12(x87081,x87083))) % 19.23/19.05 [8903]~P101(x89031)+~P85(f341(f71(x89031),x89033))+~P85(f341(f71(x89031),x89032))+E(f341(f341(f111(f864(x89031,a850)),x89032),x89033),f185(f864(x89031,a850)))+E(f341(f341(f245(x89031),f14(x89031,f245(x89031),f341(f341(f110(f864(x89031,a850)),x89032),x89033))),f14(x89031,f245(x89031),f341(f341(f111(f864(x89031,a850)),x89032),x89033))),f341(f341(f245(x89031),f14(x89031,f245(x89031),x89032)),f14(x89031,f245(x89031),x89033))) % 19.23/19.05 [8904]~P101(x89041)+~P85(f341(f71(x89041),x89043))+~P85(f341(f71(x89041),x89042))+E(f341(f341(f111(f864(x89041,a850)),x89042),x89043),f185(f864(x89041,a850)))+E(f341(f341(f240(x89041),f13(x89041,f240(x89041),f341(f341(f110(f864(x89041,a850)),x89042),x89043))),f13(x89041,f240(x89041),f341(f341(f111(f864(x89041,a850)),x89042),x89043))),f341(f341(f240(x89041),f13(x89041,f240(x89041),x89042)),f13(x89041,f240(x89041),x89043))) % 19.23/19.05 [9647]~P120(x96473)+E(x96471,x96472)+~P85(f341(f341(f241(x96473),f2(x96473)),x96472))+~P85(f341(f341(f241(x96473),f2(x96473)),x96471))+~E(f341(f341(f251(x96473),x96471),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)))),f341(f341(f251(x96473),x96472),f341(f113(a857),f341(f341(f89(a1),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106)),f341(f341(f3(a1),f341(f341(f89(a1),a92),a92)),a106))))) % 19.23/19.05 [5766]~P4(x57662)+E(x57661,f2(x57662))+~E(f341(f341(f51(x57662),x57663),x57661),x57664)+E(x57663,f341(f341(f90(x57662),x57664),x57661))+~P85(f341(f341(f288(x57662),x57661),x57663)) % 19.23/19.05 [5767]~P4(x57672)+E(x57671,f2(x57672))+~E(x57673,f341(f341(f90(x57672),x57674),x57671))+E(f341(f341(f51(x57672),x57673),x57671),x57674)+~P85(f341(f341(f288(x57672),x57671),x57673)) % 19.23/19.05 [6229]E(f496(x62291,x62292,x62293),x62294)+E(f341(x62291,x62294),f2(a857))+~E(f341(f341(f8(x62293,a857),x62291),x62292),f87(a857))+~P85(f341(f71(x62293),x62292))+~P85(f341(f341(f343(x62293),x62294),x62292)) % 19.23/19.05 [6297]E(f509(x62971,x62972,x62973),x62974)+E(f341(x62971,x62974),f2(a857))+~E(f341(f341(f8(x62973,a857),x62971),x62972),f341(a121,f2(a857)))+~P85(f341(f71(x62973),x62972))+~P85(f341(f341(f343(x62973),x62974),x62972)) % 19.23/19.05 [6411]~P101(x64111)+~P6(x64111)+P85(f341(f341(f242(x64111),x64112),f52(x64111,x64113)))+~P85(f341(f341(f343(x64111),x64114),x64113))+~P85(f341(f341(f242(x64111),x64112),x64114)) % 19.23/19.05 [6588]~P101(x65881)+~P6(x65881)+~P85(f341(f341(f343(x65881),x65884),x65882))+P85(f341(f341(f242(x65881),f53(x65881,x65882)),x65883))+~P85(f341(f341(f242(x65881),x65884),x65883)) % 19.23/19.05 [6863]~P120(x68633)+E(x68631,x68632)+~E(f341(f341(f251(x68633),x68631),f341(a121,x68634)),f341(f341(f251(x68633),x68632),f341(a121,x68634)))+~P85(f341(f341(f241(x68633),f2(x68633)),x68632))+~P85(f341(f341(f241(x68633),f2(x68633)),x68631)) % 19.23/19.05 [7073]~E(f511(x70732,x70733,x70731,x70734),x70734)+~E(f341(x70732,x70734),f87(a857))+E(f341(f341(f8(x70731,a857),x70732),x70733),f87(a857))+~P85(f341(f71(x70731),x70733))+~P85(f341(f341(f343(x70731),x70734),x70733)) % 19.23/19.05 [7080]~P86(x70804)+~P129(x70804)+E(f341(x70801,f403(x70801,x70802,x70803,x70804)),f2(x70804))+~E(f341(f341(f11(x70803,x70804),x70801),x70802),f2(x70804))+~P85(f341(f71(x70803),x70802)) % 19.23/19.05 [7162]~E(f510(x71622,x71623,x71621,x71624),x71624)+~E(f341(x71622,x71624),f341(a121,f2(a857)))+E(f341(f341(f8(x71621,a857),x71622),x71623),f341(a121,f2(a857)))+~P85(f341(f71(x71621),x71623))+~P85(f341(f341(f343(x71621),x71624),x71623)) % 19.23/19.05 [7926]~E(f341(x79262,x79264),f87(a857))+~E(f341(x79262,f511(x79262,x79263,x79261,x79264)),f2(a857))+E(f341(f341(f8(x79261,a857),x79262),x79263),f87(a857))+~P85(f341(f71(x79261),x79263))+~P85(f341(f341(f343(x79261),x79264),x79263)) % 19.23/19.05 [7971]~E(f341(x79712,x79714),f341(a121,f2(a857)))+~E(f341(x79712,f510(x79712,x79713,x79711,x79714)),f2(a857))+E(f341(f341(f8(x79711,a857),x79712),x79713),f341(a121,f2(a857)))+~P85(f341(f71(x79711),x79713))+~P85(f341(f341(f343(x79711),x79714),x79713)) % 19.23/19.05 [8049]~P139(x80492)+~P115(x80492)+~P85(f341(x80491,x80494))+~P85(f341(f341(f288(x80492),x80493),f341(f341(f89(x80492),x80494),f2(x80492))))+P85(f341(x80491,f341(f341(f90(x80492),x80493),f351(x80493,x80491,x80492)))) % 19.23/19.05 [8541]E(x85411,x85412)+E(f341(f341(f89(a1),f468(x85413,x85412,x85414,x85411)),f469(x85413,x85412,x85414,x85411)),x85411)+~E(f341(f341(f3(a1),x85411),x85414),x85412)+~P85(f341(f341(f242(a1),f2(a1)),x85414))+~P85(f341(f341(f343(a1),x85412),x85413)) % 19.23/19.05 [8542]E(x85421,x85422)+E(f341(f341(f3(a1),f470(x85423,x85422,x85424,x85421)),f471(x85423,x85422,x85424,x85421)),x85421)+~E(f341(f341(f89(a1),x85421),x85424),x85422)+~P85(f341(f341(f242(a1),f2(a1)),x85424))+~P85(f341(f341(f343(a1),x85422),x85423)) % 19.23/19.05 [8704]E(f341(x87041,f829(x87042,x87041,x87043,x87044)),x87042)+P85(f341(f341(f241(a857),x87044),f830(x87042,x87041,x87043,x87044)))+~P85(f341(f341(f241(a1),x87042),f341(x87041,x87043)))+~P85(f341(f341(f242(a857),x87044),x87043))+~P85(f341(f341(f241(a1),f341(x87041,x87044)),x87042)) % 19.23/19.05 [8721]~P86(x87214)+~P129(x87214)+~E(f341(f341(f11(x87211,x87214),x87212),x87213),f2(x87214))+~P85(f341(f71(x87211),x87213))+P85(f341(f341(f343(x87211),f403(x87212,x87213,x87211,x87214)),x87213)) % 19.23/19.05 [8754]~E(f341(x87542,x87544),f87(a857))+E(f341(f341(f8(x87541,a857),x87542),x87543),f87(a857))+~P85(f341(f71(x87541),x87543))+~P85(f341(f341(f343(x87541),x87544),x87543))+P85(f341(f341(f343(x87541),f511(x87542,x87543,x87541,x87544)),x87543)) % 19.23/19.05 [8763]E(x87631,x87632)+~E(f341(f341(f89(a1),x87632),x87634),x87631)+~P85(f341(f341(f242(a1),f2(a1)),x87634))+~P85(f341(f341(f343(a1),x87631),x87633))+P85(f341(f341(f343(a1),f470(x87633,x87631,x87634,x87632)),x87633)) % 19.23/19.05 [8764]E(x87641,x87642)+~E(f341(f341(f3(a1),x87642),x87644),x87641)+~P85(f341(f341(f242(a1),f2(a1)),x87644))+~P85(f341(f341(f343(a1),x87641),x87643))+P85(f341(f341(f343(a1),f468(x87643,x87641,x87644,x87642)),x87643)) % 19.23/19.05 [8766]~E(f341(x87662,x87664),f341(a121,f2(a857)))+E(f341(f341(f8(x87661,a857),x87662),x87663),f341(a121,f2(a857)))+~P85(f341(f71(x87661),x87663))+~P85(f341(f341(f343(x87661),x87664),x87663))+P85(f341(f341(f343(x87661),f510(x87662,x87663,x87661,x87664)),x87663)) % 19.23/19.05 [8770]P56(x87702,x87703,x87704,x87701)+E(x87701,f185(f864(x87702,a850)))+~P85(f341(f71(x87702),x87704))+~P85(f341(f71(x87702),x87701))+P85(f341(f341(f343(x87702),f543(x87701,x87704,x87703,x87702)),x87704)) % 19.23/19.05 [8836]E(x88361,x88362)+~E(f341(f341(f89(a1),x88362),x88364),x88361)+~P85(f341(f341(f242(a1),f2(a1)),x88364))+~P85(f341(f341(f343(a1),x88361),x88363))+P85(f341(f341(f343(a1),f471(x88363,x88361,x88364,x88362)),f304(a1,f87(a1),x88364))) % 19.23/19.05 [8837]E(x88371,x88372)+~E(f341(f341(f3(a1),x88372),x88374),x88371)+~P85(f341(f341(f242(a1),f2(a1)),x88374))+~P85(f341(f341(f343(a1),x88371),x88373))+P85(f341(f341(f343(a1),f469(x88373,x88371,x88374,x88372)),f304(a1,f87(a1),x88374))) % 19.23/19.05 [8909]P85(f341(f341(f241(a857),x89091),f829(x89092,x89093,x89094,x89091)))+~P85(f341(f341(f241(a1),x89092),f341(x89093,x89094)))+P85(f341(f341(f241(a857),x89091),f830(x89092,x89093,x89094,x89091)))+~P85(f341(f341(f242(a857),x89091),x89094))+~P85(f341(f341(f241(a1),f341(x89093,x89091)),x89092)) % 19.23/19.05 [9016]E(f341(x90161,f829(x90162,x90161,x90163,x90164)),x90162)+~P85(f341(f341(f241(a1),x90162),f341(x90161,x90163)))+P85(f341(f341(f242(a857),f830(x90162,x90161,x90163,x90164)),x90163))+~P85(f341(f341(f242(a857),x90164),x90163))+~P85(f341(f341(f241(a1),f341(x90161,x90164)),x90162)) % 19.23/19.05 [9122]~P85(f341(f341(f288(a857),x91224),x91221))+~P85(f341(f341(f288(a857),x91224),x91223))+~P85(f341(f341(f288(a857),x91222),x91221))+P85(f341(f341(f288(a857),x91221),x91222))+P85(f341(f341(f242(f864(a857,a850)),f291(a857,f288(a857),x91223,x91222)),f291(a857,f288(a857),x91224,x91221))) % 19.23/19.05 [9123]~P85(f341(f341(f288(a857),x91232),x91231))+~P85(f341(f341(f288(a857),x91233),x91234))+~P85(f341(f341(f288(a857),x91232),x91234))+P85(f341(f341(f288(a857),x91231),x91232))+P85(f341(f341(f242(f864(a857,a850)),f291(a857,f288(a857),x91231,x91233)),f291(a857,f288(a857),x91232,x91234))) % 19.23/19.05 [9134]~P85(f341(f341(f241(a1),x91342),f341(x91343,x91344)))+P85(f341(f341(f241(a857),x91341),f830(x91342,x91343,x91344,x91341)))+P85(f341(f341(f241(a857),f829(x91342,x91343,x91344,x91341)),x91344))+~P85(f341(f341(f242(a857),x91341),x91344))+~P85(f341(f341(f241(a1),f341(x91343,x91341)),x91342)) % 19.23/19.05 [9135]~P85(f341(f341(f241(a1),x91352),f341(x91353,x91354)))+P85(f341(f341(f241(a857),x91351),f829(x91352,x91353,x91354,x91351)))+P85(f341(f341(f242(a857),f830(x91352,x91353,x91354,x91351)),x91354))+~P85(f341(f341(f242(a857),x91351),x91354))+~P85(f341(f341(f241(a1),f341(x91353,x91351)),x91352)) % 19.23/19.05 [9221]~P85(f341(f341(f241(a1),x92211),f341(x92212,x92213)))+P85(f341(f341(f241(a857),f829(x92211,x92212,x92213,x92214)),x92213))+~P85(f341(f341(f242(a857),x92214),x92213))+~P85(f341(f341(f241(a1),f341(x92212,x92214)),x92211))+P85(f341(f341(f242(a857),f830(x92211,x92212,x92213,x92214)),x92213)) % 19.23/19.05 [9306]E(x93061,f185(f864(x93062,a850)))+~P85(f341(f71(x93062),x93064))+~P85(f341(f71(x93062),x93061))+P85(f341(f341(f343(f863(f864(x93062,a850),f864(x93062,a850))),f341(f341(f250(f864(x93062,a850),f864(x93062,a850)),x93064),x93061)),f334(x93062,x93063)))+P85(f341(f341(f343(x93062),f545(x93063,x93061,x93064,x93062)),x93064)) % 19.23/19.05 [9307]E(x93071,f185(f864(x93072,a850)))+~P85(f341(f71(x93072),x93074))+~P85(f341(f71(x93072),x93071))+P85(f341(f341(f343(f863(f864(x93072,a850),f864(x93072,a850))),f341(f341(f250(f864(x93072,a850),f864(x93072,a850)),x93074),x93071)),f334(x93072,x93073)))+P85(f341(f341(f343(x93072),f632(x93073,x93071,x93074,x93072)),x93074)) % 19.23/19.05 [9957]E(f341(x99571,f829(x99572,x99571,x99573,x99574)),x99572)+~P85(f341(f341(f241(a1),x99572),f341(x99571,x99573)))+~P85(f341(f341(f241(a1),f341(f84(a1),f341(f341(f3(a1),f341(x99571,f341(f341(f89(a857),f830(x99572,x99571,x99573,x99574)),f87(a857)))),f341(x99571,f830(x99572,x99571,x99573,x99574))))),f87(a1)))+~P85(f341(f341(f242(a857),x99574),x99573))+~P85(f341(f341(f241(a1),f341(x99571,x99574)),x99572)) % 19.23/19.05 [9958]~P85(f341(f341(f241(a1),x99582),f341(x99583,x99584)))+P85(f341(f341(f241(a857),x99581),f829(x99582,x99583,x99584,x99581)))+~P85(f341(f341(f241(a1),f341(f84(a1),f341(f341(f3(a1),f341(x99583,f341(f341(f89(a857),f830(x99582,x99583,x99584,x99581)),f87(a857)))),f341(x99583,f830(x99582,x99583,x99584,x99581))))),f87(a1)))+~P85(f341(f341(f242(a857),x99581),x99584))+~P85(f341(f341(f241(a1),f341(x99583,x99581)),x99582)) % 19.23/19.05 [9959]~P85(f341(f341(f241(a1),x99591),f341(x99592,x99593)))+~P85(f341(f341(f241(a1),f341(f84(a1),f341(f341(f3(a1),f341(x99592,f341(f341(f89(a857),f830(x99591,x99592,x99593,x99594)),f87(a857)))),f341(x99592,f830(x99591,x99592,x99593,x99594))))),f87(a1)))+~P85(f341(f341(f242(a857),x99594),x99593))+~P85(f341(f341(f241(a1),f341(x99592,x99594)),x99591))+P85(f341(f341(f241(a857),f829(x99591,x99592,x99593,x99594)),x99593)) % 19.23/19.05 [7130]~P61(x71301)+P85(f341(f341(f242(x71301),x71302),f2(x71301)))+~P85(f341(f341(f242(x71301),x71303),f2(x71301)))+P85(f341(f341(f242(x71301),f2(x71301)),x71302))+P85(f341(f341(f242(x71301),x71303),f341(f341(f292(x71301),x71304),x71302))) % 19.23/19.05 [7131]~P61(x71311)+P85(f341(f341(f242(x71311),x71312),f2(x71311)))+~P85(f341(f341(f241(x71311),x71313),f2(x71311)))+P85(f341(f341(f242(x71311),f2(x71311)),x71312))+P85(f341(f341(f241(x71311),x71313),f341(f341(f292(x71311),x71314),x71312))) % 19.23/19.05 [7402]~P61(x74021)+P85(f341(f341(f242(x74021),x74022),f2(x74021)))+P85(f341(f341(f242(x74021),x74023),f2(x74021)))+P85(f341(f341(f242(x74021),f2(x74021)),x74023))+~P85(f341(f341(f242(x74021),x74022),f341(f341(f292(x74021),x74024),x74023))) % 19.23/19.05 [7403]~P61(x74031)+P85(f341(f341(f242(x74031),x74032),f2(x74031)))+P85(f341(f341(f241(x74031),x74033),f2(x74031)))+P85(f341(f341(f242(x74031),f2(x74031)),x74032))+~P85(f341(f341(f241(x74031),x74033),f341(f341(f292(x74031),x74034),x74032))) % 19.23/19.05 [7521]E(x75211,x75212)+~E(f341(f341(f158(x75213),x75214),x75211),f341(f341(f158(x75213),x75214),x75212))+~P85(f341(f134(x75213),x75214))+~P85(f341(f341(f242(a857),x75212),f341(f186(f858(x75213)),x75214)))+~P85(f341(f341(f242(a857),x75211),f341(f186(f858(x75213)),x75214))) % 19.23/19.05 [7888]~P61(x78881)+~P85(f341(f341(f242(x78881),x78883),f2(x78881)))+P85(f341(f341(f242(x78881),f2(x78881)),x78882))+~P85(f341(f341(f242(x78881),x78884),f341(f341(f90(x78881),x78883),x78882)))+P85(f341(f341(f242(x78881),x78883),f341(f341(f292(x78881),x78884),x78882))) % 19.23/19.05 [7889]~P61(x78891)+~P85(f341(f341(f241(x78891),x78893),f2(x78891)))+P85(f341(f341(f242(x78891),f2(x78891)),x78892))+~P85(f341(f341(f241(x78891),x78894),f341(f341(f90(x78891),x78893),x78892)))+P85(f341(f341(f241(x78891),x78893),f341(f341(f292(x78891),x78894),x78892))) % 19.23/19.05 [7890]~P61(x78901)+~P85(f341(f341(f242(x78901),x78902),f2(x78901)))+P85(f341(f341(f242(x78901),f2(x78901)),x78902))+~P85(f341(f341(f242(x78901),x78904),f341(f341(f90(x78901),x78903),x78902)))+P85(f341(f341(f242(x78901),x78903),f341(f341(f292(x78901),x78904),x78902))) % 19.23/19.05 [7891]~P61(x78911)+~P85(f341(f341(f242(x78911),x78912),f2(x78911)))+P85(f341(f341(f242(x78911),f2(x78911)),x78912))+~P85(f341(f341(f242(x78911),x78914),f341(f341(f292(x78911),x78913),x78912)))+P85(f341(f341(f242(x78911),x78913),f341(f341(f90(x78911),x78914),x78912))) % 19.23/19.05 [7892]~P61(x78921)+~P85(f341(f341(f242(x78921),x78922),f2(x78921)))+P85(f341(f341(f242(x78921),f2(x78921)),x78922))+~P85(f341(f341(f241(x78921),x78924),f341(f341(f90(x78921),x78923),x78922)))+P85(f341(f341(f241(x78921),x78923),f341(f341(f292(x78921),x78924),x78922))) % 19.23/19.05 [7893]~P61(x78931)+~P85(f341(f341(f242(x78931),x78932),f2(x78931)))+P85(f341(f341(f242(x78931),f2(x78931)),x78932))+~P85(f341(f341(f241(x78931),x78934),f341(f341(f292(x78931),x78933),x78932)))+P85(f341(f341(f241(x78931),x78933),f341(f341(f90(x78931),x78934),x78932))) % 19.23/19.05 [8017]~P4(x80171)+~P85(f341(f341(f288(x80171),x80173),x80174))+~P85(f341(f341(f288(x80171),x80173),x80172))+~P85(f341(f341(f288(x80171),x80172),x80174))+P85(f341(f341(f288(x80171),f341(f341(f51(x80171),x80172),x80173)),f341(f341(f51(x80171),x80174),x80173))) % 19.23/19.05 [8032]~P101(x80321)+~P15(x80321,x80322)+~P85(f341(f341(f241(a857),x80323),x80324))+P85(f341(f341(f241(x80321),f341(f341(f158(x80321),x80322),x80323)),f341(f341(f158(x80321),x80322),x80324)))+~P85(f341(f341(f242(a857),x80324),f341(f186(f858(x80321)),x80322))) % 19.23/19.05 [8082]~P120(x80821)+~P85(f341(f341(f242(x80821),x80822),f87(x80821)))+~P85(f341(f341(f242(x80821),f2(x80821)),x80822))+~P85(f341(f341(f242(a857),x80824),x80823))+P85(f341(f341(f242(x80821),f341(f341(f251(x80821),x80822),x80823)),f341(f341(f251(x80821),x80822),x80824))) % 19.23/19.05 [8083]~P120(x80831)+~P85(f341(f341(f241(x80831),x80832),f87(x80831)))+~P85(f341(f341(f241(x80831),f2(x80831)),x80832))+~P85(f341(f341(f241(a857),x80834),x80833))+P85(f341(f341(f241(x80831),f341(f341(f251(x80831),x80832),x80833)),f341(f341(f251(x80831),x80832),x80834))) % 19.23/19.05 [8084]~P120(x80841)+~P85(f341(f341(f241(x80841),f2(x80841)),x80842))+~P85(f341(f341(f242(a857),f2(a857)),x80843))+~P85(f341(f341(f242(x80841),x80842),x80844))+P85(f341(f341(f242(x80841),f341(f341(f251(x80841),x80842),x80843)),f341(f341(f251(x80841),x80844),x80843))) % 19.23/19.05 [8102]~P101(x81021)+~P15(x81021,f341(f148(x81021),x81022))+~P85(f341(f341(f241(a857),x81024),x81023))+P85(f341(f341(f241(x81021),f341(f341(f158(x81021),x81022),x81023)),f341(f341(f158(x81021),x81022),x81024)))+~P85(f341(f341(f242(a857),x81023),f341(f186(f858(x81021)),x81022))) % 19.23/19.05 [8329]~P4(x83291)+P85(f341(f341(f288(x83291),x83292),x83293))+~P85(f341(f341(f288(x83291),x83294),x83293))+~P85(f341(f341(f288(x83291),x83294),x83292))+~P85(f341(f341(f288(x83291),f341(f341(f51(x83291),x83292),x83294)),f341(f341(f51(x83291),x83293),x83294))) % 19.23/19.05 [8346]~P62(x83461)+~P85(f341(f341(f242(x83461),x83462),f2(x83461)))+~P85(f341(f341(f242(x83461),x83463),x83464))+~P85(f341(f341(f242(x83461),f2(x83461)),f341(f341(f90(x83461),x83463),x83464)))+P85(f341(f341(f242(x83461),f341(f341(f292(x83461),x83462),x83463)),f341(f341(f292(x83461),x83462),x83464))) % 19.23/19.05 [8347]~P61(x83471)+~P85(f341(f341(f241(x83471),x83472),f2(x83471)))+~P85(f341(f341(f241(x83471),x83473),x83474))+~P85(f341(f341(f242(x83471),f2(x83471)),f341(f341(f90(x83471),x83473),x83474)))+P85(f341(f341(f241(x83471),f341(f341(f292(x83471),x83472),x83473)),f341(f341(f292(x83471),x83472),x83474))) % 19.23/19.05 [8357]~P62(x83571)+~P85(f341(f341(f242(x83571),x83574),x83573))+~P85(f341(f341(f242(x83571),f2(x83571)),x83572))+~P85(f341(f341(f242(x83571),f2(x83571)),f341(f341(f90(x83571),x83573),x83574)))+P85(f341(f341(f242(x83571),f341(f341(f292(x83571),x83572),x83573)),f341(f341(f292(x83571),x83572),x83574))) % 19.23/19.05 [8358]~P62(x83581)+~P85(f341(f341(f241(x83581),x83584),x83583))+~P85(f341(f341(f241(x83581),f2(x83581)),x83582))+~P85(f341(f341(f242(x83581),f2(x83581)),f341(f341(f90(x83581),x83583),x83584)))+P85(f341(f341(f241(x83581),f341(f341(f292(x83581),x83582),x83583)),f341(f341(f292(x83581),x83582),x83584))) % 19.23/19.05 [8464]P85(f341(x84641,x84642))+~P85(f341(f71(x84644),x84642))+P85(f341(x84641,f512(x84641,x84643,x84642,x84644)))+~P85(f341(x84641,f185(f864(x84644,a850))))+~P85(f341(f341(f241(f864(x84644,a850)),x84642),x84643)) % 19.23/19.05 [8472]P85(f341(x84721,x84722))+P85(f341(f71(x84723),f512(x84721,x84724,x84722,x84723)))+~P85(f341(f71(x84723),x84722))+~P85(f341(x84721,f185(f864(x84723,a850))))+~P85(f341(f341(f241(f864(x84723,a850)),x84722),x84724)) % 19.23/19.05 [8701]E(f341(f341(f89(a1),f473(x87011,x87012,x87013,x87014)),f474(x87011,x87012,x87013,x87014)),x87014)+~P85(f341(f341(f242(a1),f2(a1)),x87013))+~P85(f341(f341(f242(a1),x87012),x87014))+~P85(f341(f341(f343(a1),x87012),x87011))+P85(f341(f341(f242(a1),x87012),f341(f341(f3(a1),x87014),x87013))) % 19.23/19.05 [8889]~P85(f341(f341(f242(a1),f2(a1)),x88893))+~P85(f341(f341(f242(a1),x88892),x88894))+~P85(f341(f341(f343(a1),x88892),x88891))+P85(f341(f341(f343(a1),f473(x88891,x88892,x88893,x88894)),x88891))+P85(f341(f341(f242(a1),x88892),f341(f341(f3(a1),x88894),x88893))) % 19.23/19.05 [8902]P85(f341(x89021,x89022))+~P85(f341(f71(x89023),x89022))+P85(f341(f341(f343(x89023),f515(x89021,x89024,x89022,x89023)),x89024))+~P85(f341(x89021,f185(f864(x89023,a850))))+~P85(f341(f341(f241(f864(x89023,a850)),x89022),x89024)) % 19.23/19.05 [8919]E(f341(f341(f89(a1),f464(x89191,x89192,x89193,x89194)),f465(x89191,x89192,x89193,x89194)),x89194)+~P85(f341(f341(f242(a1),f2(a1)),x89193))+~P85(f341(f341(f241(a1),x89192),x89194))+P85(f341(f341(f241(a1),x89192),f341(f341(f3(a1),x89194),x89193)))+~P85(f341(f341(f343(a1),f341(f341(f3(a1),x89192),f87(a1))),x89191)) % 19.23/19.05 [8965]~P85(f341(f341(f242(a1),f2(a1)),x89653))+~P85(f341(f341(f242(a1),x89651),x89652))+~P85(f341(f341(f343(a1),x89651),x89654))+P85(f341(f341(f343(a1),f474(x89654,x89651,x89653,x89652)),f304(a1,f87(a1),x89653)))+P85(f341(f341(f242(a1),x89651),f341(f341(f3(a1),x89652),x89653))) % 19.23/19.05 [9060]~P85(f341(f341(f242(a1),f2(a1)),x90603))+~P85(f341(f341(f241(a1),x90602),x90604))+P85(f341(f341(f343(a1),f464(x90601,x90602,x90603,x90604)),x90601))+P85(f341(f341(f241(a1),x90602),f341(f341(f3(a1),x90604),x90603)))+~P85(f341(f341(f343(a1),f341(f341(f3(a1),x90602),f87(a1))),x90601)) % 19.23/19.05 [9099]~P85(f341(f341(f242(a1),f2(a1)),x90993))+~P85(f341(f341(f241(a1),x90991),x90992))+P85(f341(f341(f343(a1),f465(x90994,x90991,x90993,x90992)),f304(a1,f87(a1),x90993)))+P85(f341(f341(f241(a1),x90991),f341(f341(f3(a1),x90992),x90993)))+~P85(f341(f341(f343(a1),f341(f341(f3(a1),x90991),f87(a1))),x90994)) % 19.23/19.05 [9309]P85(f341(x93091,x93092))+~P85(f341(f341(f343(x93093),f515(x93091,x93094,x93092,x93093)),f512(x93091,x93094,x93092,x93093)))+~P85(f341(f71(x93093),x93092))+~P85(f341(x93091,f185(f864(x93093,a850))))+~P85(f341(f341(f241(f864(x93093,a850)),x93092),x93094)) % 19.23/19.05 [9513]P85(f341(x95131,x95132))+~P85(f341(f71(x95133),x95132))+~P85(f341(x95131,f341(f341(f311(x95133),f515(x95131,x95134,x95132,x95133)),f512(x95131,x95134,x95132,x95133))))+~P85(f341(x95131,f185(f864(x95133,a850))))+~P85(f341(f341(f241(f864(x95133,a850)),x95132),x95134)) % 19.23/19.05 [9842]~P100(x98423)+~P51(a857,x98423,f341(f341(f20(a857,f864(a857,a850),f864(a857,a850)),f341(f341(f10(f864(a857,f864(a850,a850)),f864(f864(a857,a850),f864(a857,a850)),a857),f20(a857,a850,a850)),f341(f341(f10(f864(a857,a850),f864(a857,f864(a850,a850)),a857),f341(f10(a850,f864(a850,a850),a857),a339)),f288(a857)))),f341(f341(f10(f864(a857,a850),f864(a857,a850),a857),f341(f10(a850,a850,a857),a337)),f341(f9(a857,a857,a850),f288(a857)))),x98424)+P85(f341(f341(f242(x98423),f341(x98424,x98422)),f341(x98424,x98421)))+~P85(f341(f341(f288(a857),x98422),x98421))+P85(f341(f341(f288(a857),x98421),x98422)) % 19.23/19.05 [7660]~P61(x76601)+P85(f341(f341(f242(x76601),x76602),f2(x76601)))+P85(f341(f341(f242(x76601),f2(x76601)),x76602))+~P85(f341(f341(f242(x76601),f2(x76601)),x76604))+P85(f341(f341(f242(x76601),f341(f341(f292(x76601),x76603),x76602)),x76604)) % 19.23/19.05 [7661]~P61(x76611)+P85(f341(f341(f242(x76611),x76612),f2(x76611)))+~P85(f341(f341(f241(x76611),f2(x76611)),x76614))+P85(f341(f341(f242(x76611),f2(x76611)),x76612))+P85(f341(f341(f241(x76611),f341(f341(f292(x76611),x76613),x76612)),x76614)) % 19.23/19.05 [7944]~P85(f341(f341(f241(a1),x79444),f2(a1)))+~E(x79442,f341(f341(f89(a1),f341(f341(f90(a1),x79441),x79443)),x79444))+P85(f341(f341(f242(a1),f2(a1)),x79441))+~P85(f341(f341(f242(a1),x79441),x79444))+P85(f341(f64(x79442,x79441),f341(f341(f250(a1,a1),x79443),x79444))) % 19.23/19.05 [7981]~P85(f341(x79811,x79814))+P85(f341(x79811,f819(x79812,x79811,x79813)))+~P85(f341(f341(f242(a1),f2(a1)),x79813))+~P85(f341(f341(f241(a1),f2(a1)),x79812))+P85(f341(x79811,f341(f341(f89(a1),x79814),f341(f341(f90(a1),x79812),x79813)))) % 19.23/19.05 [7982]~P85(f341(x79821,x79824))+P85(f341(x79821,f823(x79822,x79821,x79823)))+~P85(f341(f341(f242(a1),f2(a1)),x79823))+~P85(f341(f341(f241(a1),f2(a1)),x79822))+P85(f341(x79821,f341(f341(f3(a1),x79824),f341(f341(f90(a1),x79822),x79823)))) % 19.23/19.05 [7983]~P61(x79831)+P85(f341(f341(f242(x79831),x79832),f2(x79831)))+P85(f341(f341(f242(x79831),f2(x79831)),x79832))+P85(f341(f341(f242(x79831),f2(x79831)),x79833))+~P85(f341(f341(f242(x79831),f341(f341(f292(x79831),x79834),x79832)),x79833)) % 19.23/19.05 [7984]~P61(x79841)+P85(f341(f341(f242(x79841),x79842),f2(x79841)))+P85(f341(f341(f242(x79841),f2(x79841)),x79842))+P85(f341(f341(f241(x79841),f2(x79841)),x79843))+~P85(f341(f341(f241(x79841),f341(f341(f292(x79841),x79844),x79842)),x79843)) % 19.23/19.05 [8027]~E(x80271,f341(f341(f89(a1),f341(f341(f90(a1),x80272),x80273)),x80274))+~P85(f341(f341(f242(a1),f2(a1)),x80272))+~P85(f341(f341(f241(a1),f2(a1)),x80274))+~P85(f341(f341(f242(a1),x80274),x80272))+P85(f341(f64(x80271,x80272),f341(f341(f250(a1,a1),x80273),x80274))) % 19.23/19.05 [8142]~P61(x81421)+P85(f341(f341(f242(x81421),x81422),f2(x81421)))+~P85(f341(f341(f242(x81421),f2(x81421)),x81424))+~P85(f341(f341(f242(x81421),x81423),f341(f341(f90(x81421),x81424),x81422)))+P85(f341(f341(f242(x81421),f341(f341(f292(x81421),x81423),x81422)),x81424)) % 19.23/19.05 [8143]~P61(x81431)+P85(f341(f341(f242(x81431),x81432),f2(x81431)))+~P85(f341(f341(f241(x81431),f2(x81431)),x81434))+~P85(f341(f341(f241(x81431),x81433),f341(f341(f90(x81431),x81434),x81432)))+P85(f341(f341(f241(x81431),f341(f341(f292(x81431),x81433),x81432)),x81434)) % 19.23/19.05 [8221]~P61(x82211)+P85(f341(f341(f242(x82211),x82212),f2(x82211)))+~P85(f341(f341(f242(x82211),x82213),f2(x82211)))+P85(f341(f341(f242(x82211),x82213),f341(f341(f292(x82211),x82214),x82212)))+~P85(f341(f341(f242(x82211),f341(f341(f90(x82211),x82213),x82212)),x82214)) % 19.23/19.05 [8222]~P61(x82221)+P85(f341(f341(f242(x82221),x82222),f2(x82221)))+~P85(f341(f341(f241(x82221),x82223),f2(x82221)))+P85(f341(f341(f241(x82221),x82223),f341(f341(f292(x82221),x82224),x82222)))+~P85(f341(f341(f241(x82221),f341(f341(f90(x82221),x82223),x82222)),x82224)) % 19.23/19.05 [8382]~P61(x83821)+~P85(f341(f341(f242(x83821),x83822),f2(x83821)))+P85(f341(f341(f242(x83821),f2(x83821)),x83822))+~P85(f341(f341(f242(x83821),f341(f341(f292(x83821),x83824),x83822)),x83823))+P85(f341(f341(f242(x83821),f341(f341(f90(x83821),x83823),x83822)),x83824)) % 19.23/19.05 [8383]~P61(x83831)+~P85(f341(f341(f242(x83831),x83832),f2(x83831)))+P85(f341(f341(f242(x83831),f2(x83831)),x83832))+~P85(f341(f341(f242(x83831),f341(f341(f90(x83831),x83834),x83832)),x83833))+P85(f341(f341(f242(x83831),f341(f341(f292(x83831),x83833),x83832)),x83834)) % 19.23/19.05 [8384]~P61(x83841)+~P85(f341(f341(f242(x83841),x83842),f2(x83841)))+P85(f341(f341(f242(x83841),f2(x83841)),x83842))+~P85(f341(f341(f241(x83841),f341(f341(f292(x83841),x83844),x83842)),x83843))+P85(f341(f341(f241(x83841),f341(f341(f90(x83841),x83843),x83842)),x83844)) % 19.23/19.05 [8385]~P61(x83851)+~P85(f341(f341(f242(x83851),x83852),f2(x83851)))+P85(f341(f341(f242(x83851),f2(x83851)),x83852))+~P85(f341(f341(f241(x83851),f341(f341(f90(x83851),x83854),x83852)),x83853))+P85(f341(f341(f241(x83851),f341(f341(f292(x83851),x83853),x83852)),x83854)) % 19.23/19.05 [8404]~P61(x84041)+~P85(f341(f341(f242(x84041),f2(x84041)),x84044))+P85(f341(f341(f242(x84041),f2(x84041)),x84042))+~P85(f341(f341(f242(x84041),f341(f341(f90(x84041),x84044),x84042)),x84043))+P85(f341(f341(f242(x84041),f341(f341(f292(x84041),x84043),x84042)),x84044)) % 19.23/19.05 [8405]~P61(x84051)+~P85(f341(f341(f241(x84051),f2(x84051)),x84054))+P85(f341(f341(f242(x84051),f2(x84051)),x84052))+~P85(f341(f341(f241(x84051),f341(f341(f90(x84051),x84054),x84052)),x84053))+P85(f341(f341(f241(x84051),f341(f341(f292(x84051),x84053),x84052)),x84054)) % 19.23/19.05 [8480]~P61(x84801)+~P85(f341(f341(f242(x84801),x84804),f2(x84801)))+~P85(f341(f341(f242(x84801),x84803),f341(f341(f90(x84801),x84802),x84804)))+P85(f341(f341(f242(x84801),x84802),f341(f341(f292(x84801),x84803),x84804)))+~P85(f341(f341(f242(x84801),f341(f341(f90(x84801),x84802),x84804)),x84803)) % 19.23/19.05 [8481]~P61(x84811)+~P85(f341(f341(f242(x84811),x84812),f2(x84811)))+~P85(f341(f341(f242(x84811),x84813),f341(f341(f90(x84811),x84812),x84814)))+P85(f341(f341(f242(x84811),x84812),f341(f341(f292(x84811),x84813),x84814)))+~P85(f341(f341(f242(x84811),f341(f341(f90(x84811),x84812),x84814)),x84813)) % 19.23/19.05 [8482]~P61(x84821)+~P85(f341(f341(f242(x84821),x84824),f2(x84821)))+~P85(f341(f341(f241(x84821),x84823),f341(f341(f90(x84821),x84822),x84824)))+P85(f341(f341(f241(x84821),x84822),f341(f341(f292(x84821),x84823),x84824)))+~P85(f341(f341(f241(x84821),f341(f341(f90(x84821),x84822),x84824)),x84823)) % 19.23/19.05 [8483]~P61(x84831)+~P85(f341(f341(f241(x84831),x84832),f2(x84831)))+~P85(f341(f341(f241(x84831),x84833),f341(f341(f90(x84831),x84832),x84834)))+P85(f341(f341(f241(x84831),x84832),f341(f341(f292(x84831),x84833),x84834)))+~P85(f341(f341(f241(x84831),f341(f341(f90(x84831),x84832),x84834)),x84833)) % 19.23/19.05 [8583]~P61(x85831)+~P85(f341(f341(f242(x85831),x85833),f2(x85831)))+~P85(f341(f341(f242(x85831),x85832),f341(f341(f90(x85831),x85834),x85833)))+~P85(f341(f341(f242(x85831),f341(f341(f90(x85831),x85834),x85833)),x85832))+P85(f341(f341(f242(x85831),f341(f341(f292(x85831),x85832),x85833)),x85834)) % 19.23/19.05 [8584]~P61(x85841)+~P85(f341(f341(f242(x85841),x85843),f2(x85841)))+~P85(f341(f341(f241(x85841),x85842),f341(f341(f90(x85841),x85844),x85843)))+~P85(f341(f341(f241(x85841),f341(f341(f90(x85841),x85844),x85843)),x85842))+P85(f341(f341(f241(x85841),f341(f341(f292(x85841),x85842),x85843)),x85844)) % 19.23/19.05 [8598]~P61(x85981)+~P85(f341(f341(f242(x85981),f2(x85981)),x85984))+~P85(f341(f341(f242(x85981),x85982),f341(f341(f90(x85981),x85984),x85983)))+~P85(f341(f341(f242(x85981),f341(f341(f90(x85981),x85984),x85983)),x85982))+P85(f341(f341(f242(x85981),f341(f341(f292(x85981),x85982),x85983)),x85984)) % 19.23/19.05 [8599]~P61(x85991)+~P85(f341(f341(f241(x85991),f2(x85991)),x85994))+~P85(f341(f341(f241(x85991),x85992),f341(f341(f90(x85991),x85994),x85993)))+~P85(f341(f341(f241(x85991),f341(f341(f90(x85991),x85994),x85993)),x85992))+P85(f341(f341(f241(x85991),f341(f341(f292(x85991),x85992),x85993)),x85994)) % 19.23/19.05 [8756]E(f341(f341(f3(a1),f480(x87561,x87562,x87563,x87564)),f481(x87561,x87562,x87563,x87564)),x87564)+~P85(f341(f341(f242(a1),f2(a1)),x87563))+~P85(f341(f341(f242(a1),x87564),x87562))+~P85(f341(f341(f343(a1),x87562),x87561))+P85(f341(f341(f242(a1),f341(f341(f89(a1),x87564),x87563)),x87562)) % 19.23/19.05 [8820]~P85(f341(x88201,x88202))+~P85(f341(f341(f242(a1),f2(a1)),x88204))+~P85(f341(f341(f241(a1),f2(a1)),x88203))+~P85(f341(x88201,f341(f341(f89(a1),f819(x88203,x88201,x88204)),x88204)))+P85(f341(x88201,f341(f341(f89(a1),x88202),f341(f341(f90(a1),x88203),x88204)))) % 19.23/19.05 [8821]~P85(f341(x88211,x88212))+~P85(f341(f341(f242(a1),f2(a1)),x88214))+~P85(f341(f341(f241(a1),f2(a1)),x88213))+~P85(f341(x88211,f341(f341(f3(a1),f823(x88213,x88211,x88214)),x88214)))+P85(f341(x88211,f341(f341(f3(a1),x88212),f341(f341(f90(a1),x88213),x88214)))) % 19.23/19.05 [8958]~P85(f341(f341(f242(a1),f2(a1)),x89583))+~P85(f341(f341(f242(a1),x89584),x89582))+~P85(f341(f341(f343(a1),x89582),x89581))+P85(f341(f341(f343(a1),f480(x89581,x89582,x89583,x89584)),x89581))+P85(f341(f341(f242(a1),f341(f341(f89(a1),x89584),x89583)),x89582)) % 19.23/19.05 [8978]E(f341(f341(f3(a1),f466(x89781,x89782,x89783,x89784)),f467(x89781,x89782,x89783,x89784)),x89784)+~P85(f341(f341(f242(a1),f2(a1)),x89783))+~P85(f341(f341(f241(a1),x89784),x89782))+~P85(f341(f341(f343(a1),f341(f341(f89(a1),x89782),f87(a1))),x89781))+P85(f341(f341(f241(a1),f341(f341(f89(a1),x89784),x89783)),x89782)) % 19.23/19.05 [9010]~P85(f341(f341(f242(a1),f2(a1)),x90102))+~P85(f341(f341(f242(a1),x90101),x90103))+~P85(f341(f341(f343(a1),x90103),x90104))+P85(f341(f341(f343(a1),f481(x90104,x90103,x90102,x90101)),f304(a1,f87(a1),x90102)))+P85(f341(f341(f242(a1),f341(f341(f89(a1),x90101),x90102)),x90103)) % 19.23/19.05 [9092]~P85(f341(f341(f242(a1),f2(a1)),x90923))+~P85(f341(f341(f241(a1),x90924),x90922))+P85(f341(f341(f343(a1),f466(x90921,x90922,x90923,x90924)),x90921))+~P85(f341(f341(f343(a1),f341(f341(f89(a1),x90922),f87(a1))),x90921))+P85(f341(f341(f241(a1),f341(f341(f89(a1),x90924),x90923)),x90922)) % 19.23/19.05 [9130]~P85(f341(f341(f242(a1),f2(a1)),x91302))+~P85(f341(f341(f241(a1),x91301),x91303))+P85(f341(f341(f343(a1),f467(x91304,x91303,x91302,x91301)),f304(a1,f87(a1),x91302)))+~P85(f341(f341(f343(a1),f341(f341(f89(a1),x91303),f87(a1))),x91304))+P85(f341(f341(f241(a1),f341(f341(f89(a1),x91301),x91302)),x91303)) % 19.23/19.05 [9394]~P35(x93941,x93943)+~P27(x93941,x93944)+P35(x93941,f341(f341(f110(f864(f863(x93941,x93941),a850)),x93942),x93943))+~P85(f341(f341(f241(f864(f863(x93941,x93941),a850)),x93942),f341(f249(f864(f863(x93941,x93941),a850),f864(f863(x93941,x93941),a850)),x93944)))+~P85(f341(f341(f241(f864(f863(x93941,x93941),a850)),x93943),f341(f259(f864(f863(x93941,x93941),a850),f864(f863(x93941,x93941),a850)),x93944))) % 19.23/19.05 [9671]~E(f341(f716(x96711,x96714,x96713,x96712),f720(x96711,x96714,x96713,x96712)),f188(f858(a849)))+P85(f341(f341(f242(a1),f719(x96711,x96714,x96713,x96712)),f720(x96711,x96714,x96713,x96712)))+P85(f341(f341(f341(x96711,x96712),x96713),x96714))+P85(f341(f341(f341(x96711,f716(x96711,x96714,x96713,x96712)),f719(x96711,x96714,x96713,x96712)),f341(f341(f89(a1),f720(x96711,x96714,x96713,x96712)),f87(a1))))+~P85(f341(f330(f863(f864(a1,f861(f858(a849))),f863(a1,a1)),a320),f341(f341(f250(f864(a1,f861(f858(a849))),f863(a1,a1)),x96712),f341(f341(f250(a1,a1),x96713),x96714)))) % 19.23/19.05 [9772]~P19(x97722,x97724,x97723)+E(x97721,f185(f864(x97722,a850)))+~P85(f341(f71(x97722),x97721))+P85(f341(f341(f343(x97722),f341(x97723,x97721)),x97721))+~P85(f341(f341(f343(x97722),f341(f341(x97724,f398(x97721,x97723,x97724,x97722)),f399(x97721,x97723,x97724,x97722))),f341(f341(f311(x97722),f398(x97721,x97723,x97724,x97722)),f341(f341(f311(x97722),f399(x97721,x97723,x97724,x97722)),f185(f864(x97722,a850)))))) % 19.23/19.05 [9315]~P52(x93151,x93151,x93154)+P85(f341(f341(f343(f863(x93151,x93151)),f341(f341(f250(x93151,x93151),x93152),x93153)),f309(x93151,x93154)))+P85(f341(f341(f343(f863(x93151,x93151)),f341(f341(f250(x93151,x93151),x93153),x93152)),f309(x93151,x93154)))+~P85(f341(f341(f343(f863(x93151,x93151)),f341(f341(f250(x93151,x93151),x93155),x93152)),f309(x93151,x93154)))+~P85(f341(f341(f343(f863(x93151,x93151)),f341(f341(f250(x93151,x93151),x93155),x93153)),f309(x93151,x93154))) % 19.23/19.05 [5504]E(x55041,f2(a857))+~E(f341(f50(x55042),x55045),x55041)+E(f341(f50(x55042),x55043),f341(a121,x55041))+~E(x55043,f341(f341(f311(x55042),x55044),x55045))+P85(f341(f341(f343(x55042),x55044),x55045)) % 19.23/19.05 [5626]~P60(x56262)+E(x56261,f2(x56262))+E(x56263,f2(x56262))+~E(f341(f341(f292(x56262),x56264),x56263),f341(f341(f292(x56262),x56265),x56261))+E(f341(f341(f90(x56262),x56264),x56261),f341(f341(f90(x56262),x56265),x56263)) % 19.23/19.05 [5627]~P60(x56272)+E(x56271,f2(x56272))+E(x56273,f2(x56272))+~E(f341(f341(f90(x56272),x56274),x56273),f341(f341(f90(x56272),x56275),x56271))+E(f341(f341(f292(x56272),x56274),x56271),f341(f341(f292(x56272),x56275),x56273)) % 19.23/19.05 [5700]~E(f341(f50(x57001),x57005),x57003)+~E(x57005,f185(f864(x57001,a850)))+E(f341(f50(x57001),x57002),f341(a121,x57003))+~E(x57002,f341(f341(f311(x57001),x57004),x57005))+P85(f341(f341(f343(x57001),x57004),x57005)) % 19.23/19.05 [5927]~P86(x59272)+~E(f341(x59273,x59275),f2(x59272))+E(f341(f341(f11(x59271,x59272),x59273),x59274),f2(x59272))+~P85(f341(f71(x59271),x59274))+~P85(f341(f341(f343(x59271),x59275),x59274)) % 19.23/19.05 [6310]~P101(x63103)+E(x63101,x63102)+~E(f341(f303(x63103,x63104),x63101),f341(f303(x63103,x63105),x63102))+~P85(f341(f341(f242(x63103),x63105),x63102))+~P85(f341(f341(f242(x63103),x63104),x63101)) % 19.23/19.05 [6311]~P101(x63113)+E(x63111,x63112)+~E(f341(f303(x63113,x63111),x63114),f341(f303(x63113,x63112),x63115))+~P85(f341(f341(f242(x63113),x63112),x63115))+~P85(f341(f341(f242(x63113),x63111),x63114)) % 19.23/19.05 [7416]~P101(x74161)+~P15(x74161,f341(f341(f132(x74161),x74164),x74165))+~P85(f341(f341(f343(x74161),x74163),f341(f163(x74161),x74165)))+~P85(f341(f341(f343(x74161),x74162),f341(f163(x74161),x74164)))+P85(f341(f341(f241(x74161),x74162),x74163)) % 19.23/19.05 [8514]~P100(x85141)+~P85(f341(f341(f242(f864(x85141,a850)),f304(x85141,x85145,x85142)),f304(x85141,x85144,x85143)))+~P85(f341(f341(f241(x85141),x85145),x85142))+P85(f341(f341(f242(x85141),x85142),x85143))+P85(f341(f341(f242(x85141),x85144),x85145)) % 19.23/19.05 [9816]~P18(x98162,x98165,x98163)+E(x98161,f185(f864(x98162,a850)))+~E(f341(f341(x98165,f341(x98164,f574(x98161,x98164,x98163,x98165,x98162))),f341(x98164,f575(x98161,x98164,x98163,x98165,x98162))),f341(x98164,f341(f341(x98165,f574(x98161,x98164,x98163,x98165,x98162)),f575(x98161,x98164,x98163,x98165,x98162))))+E(f341(x98163,f341(f312(x98162,x98162,x98164),x98161)),f341(x98164,f341(x98163,x98161)))+~P85(f341(f71(x98162),x98161)) % 19.23/19.05 [6307]~P19(x63072,x63075,x63073)+E(x63071,f185(f864(x63072,a850)))+~P85(f341(f71(x63072),x63071))+E(f341(x63073,f341(f341(f311(x63072),x63074),x63071)),f341(f341(x63075,x63074),f341(x63073,x63071)))+P85(f341(f341(f343(x63072),x63074),x63071)) % 19.23/19.05 [7153]~P18(x71532,x71533,x71534)+E(f341(f341(x71533,f341(x71534,x71531)),f341(x71534,x71535)),f341(x71534,x71535))+E(x71531,f185(f864(x71532,a850)))+~P85(f341(f71(x71532),x71535))+~P85(f341(f341(f241(f864(x71532,a850)),x71531),x71535)) % 19.23/19.05 [7556]~P19(x75564,x75565,x75561)+E(f341(x75561,x75562),x75563)+~P85(f341(f71(x75564),x75562))+~E(f341(f341(f3(f864(x75564,a850)),x75562),f341(f341(f311(x75564),x75563),f185(f864(x75564,a850)))),f185(f864(x75564,a850)))+~P85(f341(f341(f343(x75564),x75563),x75562)) % 19.23/19.05 [7703]E(x77031,x77032)+~E(f341(f186(f858(x77033)),x77032),f341(f186(f858(x77034)),x77035))+~E(f341(f186(f858(x77033)),x77031),f341(f186(f858(x77034)),x77035))+~E(f171(x77034,x77033,f341(f341(f172(x77034,x77033),x77035),x77031)),f171(x77034,x77033,f341(f341(f172(x77034,x77033),x77035),x77032)))+~P85(f341(f134(x77034),x77035)) % 19.23/19.05 [8438]~P71(x84381)+~P115(x84381)+~P85(f341(f71(x84382),x84385))+P85(f341(f341(f288(x84381),f341(f341(f11(x84382,x84381),x84383),x84384)),f341(f341(f11(x84382,x84381),x84383),x84385)))+~P85(f341(f341(f241(f864(x84382,a850)),x84384),x84385)) % 19.23/19.05 [8487]E(x84871,x84872)+~P9(x84873,x84874,x84875)+E(f341(f341(f111(f864(x84873,a850)),x84871),x84872),f185(f864(x84873,a850)))+~P85(f341(f341(f343(f864(x84873,a850)),x84872),f341(f341(f69(x84873),x84874),x84875)))+~P85(f341(f341(f343(f864(x84873,a850)),x84871),f341(f341(f69(x84873),x84874),x84875))) % 19.23/19.05 [9193]~P71(x91932)+~E(f341(x91933,f448(x91933,x91934,x91935,x91931,x91932)),f87(x91932))+E(f341(f341(f11(x91931,x91932),x91933),x91934),f341(f341(f11(x91931,x91932),x91933),x91935))+~P85(f341(f71(x91931),x91935))+~P85(f341(f341(f241(f864(x91931,a850)),x91934),x91935)) % 19.23/19.05 [9194]~P71(x91942)+~E(f341(x91943,f449(x91943,x91944,x91945,x91941,x91942)),f87(x91942))+E(f341(f341(f11(x91941,x91942),x91943),x91944),f341(f341(f11(x91941,x91942),x91943),x91945))+~P85(f341(f71(x91941),x91945))+~P85(f341(f341(f241(f864(x91941,a850)),x91944),x91945)) % 19.23/19.05 [9195]~P68(x91952)+~E(f341(x91953,f516(x91953,x91954,x91955,x91951,x91952)),f2(x91952))+E(f341(f341(f8(x91951,x91952),x91953),x91954),f341(f341(f8(x91951,x91952),x91953),x91955))+~P85(f341(f71(x91951),x91955))+~P85(f341(f341(f241(f864(x91951,a850)),x91954),x91955)) % 19.23/19.05 [9196]~P68(x91962)+~E(f341(x91963,f522(x91963,x91964,x91965,x91961,x91962)),f2(x91962))+E(f341(f341(f8(x91961,x91962),x91963),x91964),f341(f341(f8(x91961,x91962),x91963),x91965))+~P85(f341(f71(x91961),x91965))+~P85(f341(f341(f241(f864(x91961,a850)),x91964),x91965)) % 19.23/19.05 [9655]~P81(x96551)+~P85(f341(f71(x96552),x96555))+~P85(f341(f341(f241(x96551),f2(x96551)),f341(x96553,f508(x96553,x96554,x96555,x96552,x96551))))+P85(f341(f341(f241(x96551),f341(f341(f8(x96552,x96551),x96553),x96554)),f341(f341(f8(x96552,x96551),x96553),x96555)))+~P85(f341(f341(f241(f864(x96552,a850)),x96554),x96555)) % 19.23/19.05 [7413]E(x74131,f2(a857))+P85(f341(x74132,x74133))+~E(x74134,f341(f341(f89(a857),f341(f341(f90(a857),x74131),x74133)),x74135))+~P85(f341(f341(f242(a857),x74135),x74131))+~P85(f341(x74132,f341(f341(f51(a857),x74134),x74131))) % 19.23/19.05 [7495]E(x74951,f2(a857))+P85(f341(x74952,x74953))+~P85(f341(x74952,f60(a857,x74954,x74951)))+~E(x74954,f341(f341(f89(a857),f341(f341(f90(a857),x74951),x74955)),x74953))+~P85(f341(f341(f242(a857),x74953),x74951)) % 19.23/19.05 [7791]~P60(x77913)+E(f341(x77911,x77912),f2(x77913))+~P85(f341(f71(x77914),x77915))+E(f341(f341(f11(x77914,x77913),x77911),f341(f341(f3(f864(x77914,a850)),x77915),f341(f341(f311(x77914),x77912),f185(f864(x77914,a850))))),f341(f341(f11(x77914,x77913),x77911),x77915))+P85(f341(f341(f343(x77914),x77912),x77915)) % 19.23/19.05 [8183]~P71(x81831)+~P85(f341(f71(x81832),x81835))+~P85(f341(f71(x81832),x81834))+~E(f341(f341(f111(f864(x81832,a850)),x81834),x81835),f185(f864(x81832,a850)))+E(f341(f341(f90(x81831),f341(f341(f11(x81832,x81831),x81833),x81834)),f341(f341(f11(x81832,x81831),x81833),x81835)),f341(f341(f11(x81832,x81831),x81833),f341(f341(f110(f864(x81832,a850)),x81834),x81835))) % 19.23/19.05 [8184]~P68(x81841)+~P85(f341(f71(x81842),x81845))+~P85(f341(f71(x81842),x81844))+~E(f341(f341(f111(f864(x81842,a850)),x81844),x81845),f185(f864(x81842,a850)))+E(f341(f341(f89(x81841),f341(f341(f8(x81842,x81841),x81843),x81844)),f341(f341(f8(x81842,x81841),x81843),x81845)),f341(f341(f8(x81842,x81841),x81843),f341(f341(f110(f864(x81842,a850)),x81844),x81845))) % 19.23/19.05 [8275]~P60(x82753)+E(f341(x82751,x82752),f2(x82753))+~P85(f341(f71(x82754),x82755))+E(f341(f341(f11(x82754,x82753),x82751),f341(f341(f3(f864(x82754,a850)),x82755),f341(f341(f311(x82754),x82752),f185(f864(x82754,a850))))),f341(f341(f292(x82753),f341(f341(f11(x82754,x82753),x82751),x82755)),f341(x82751,x82752)))+~P85(f341(f341(f343(x82754),x82752),x82755)) % 19.23/19.05 [8941]~P9(x89411,x89415,x89414)+~E(f341(f341(f69(x89411),f341(f341(f311(x89411),x89412),f185(f864(x89411,a850)))),x89414),f341(f341(f69(x89411),f341(f341(f311(x89411),x89413),f185(f864(x89411,a850)))),x89414))+~P85(f341(f341(f343(x89411),x89413),x89415))+~P85(f341(f341(f343(x89411),x89412),x89415))+P85(f341(f341(f343(f863(x89411,x89411)),f341(f341(f250(x89411,x89411),x89412),x89413)),x89414)) % 19.23/19.05 [8957]~P9(x89571,x89575,x89573)+E(f341(f341(f69(x89571),f341(f341(f311(x89571),x89572),f185(f864(x89571,a850)))),x89573),f341(f341(f69(x89571),f341(f341(f311(x89571),x89574),f185(f864(x89571,a850)))),x89573))+~P85(f341(f341(f343(x89571),x89574),x89575))+~P85(f341(f341(f343(x89571),x89572),x89575))+~P85(f341(f341(f343(f863(x89571,x89571)),f341(f341(f250(x89571,x89571),x89572),x89574)),x89573)) % 19.23/19.05 [9220]~P71(x92201)+~P85(f341(f71(x92202),x92205))+~P85(f341(f71(x92202),x92204))+~E(f341(f341(f111(f864(x92202,a850)),x92204),x92205),f185(f864(x92202,a850)))+E(f341(f341(f90(x92201),f341(f341(f341(f75(x92201,x92202,f90(x92201)),x92203),f87(x92201)),x92204)),f341(f341(f341(f75(x92201,x92202,f90(x92201)),x92203),f87(x92201)),x92205)),f341(f341(f341(f75(x92201,x92202,f90(x92201)),x92203),f87(x92201)),f341(f341(f110(f864(x92202,a850)),x92204),x92205))) % 19.23/19.05 [9230]~P71(x92301)+~E(f341(x92303,f411(x92303,x92305,x92304,x92302,x92301)),f87(x92301))+~P85(f341(f71(x92302),x92304))+~P85(f341(f71(x92302),x92305))+E(f341(f341(f90(x92301),f341(f341(f11(x92302,x92301),x92303),x92304)),f341(f341(f11(x92302,x92301),x92303),x92305)),f341(f341(f11(x92302,x92301),x92303),f341(f341(f110(f864(x92302,a850)),x92304),x92305))) % 19.23/19.05 [9231]~P71(x92311)+~E(f341(x92313,f413(x92313,x92315,x92314,x92312,x92311)),f87(x92311))+~P85(f341(f71(x92312),x92314))+~P85(f341(f71(x92312),x92315))+E(f341(f341(f90(x92311),f341(f341(f11(x92312,x92311),x92313),x92314)),f341(f341(f11(x92312,x92311),x92313),x92315)),f341(f341(f11(x92312,x92311),x92313),f341(f341(f110(f864(x92312,a850)),x92314),x92315))) % 19.23/19.05 [9232]~P68(x92321)+~E(f341(x92323,f499(x92323,x92325,x92324,x92322,x92321)),f2(x92321))+~P85(f341(f71(x92322),x92324))+~P85(f341(f71(x92322),x92325))+E(f341(f341(f89(x92321),f341(f341(f8(x92322,x92321),x92323),x92324)),f341(f341(f8(x92322,x92321),x92323),x92325)),f341(f341(f8(x92322,x92321),x92323),f341(f341(f110(f864(x92322,a850)),x92324),x92325))) % 19.23/19.05 [9233]~P68(x92331)+~E(f341(x92333,f517(x92333,x92335,x92334,x92332,x92331)),f2(x92331))+~P85(f341(f71(x92332),x92334))+~P85(f341(f71(x92332),x92335))+E(f341(f341(f89(x92331),f341(f341(f8(x92332,x92331),x92333),x92334)),f341(f341(f8(x92332,x92331),x92333),x92335)),f341(f341(f8(x92332,x92331),x92333),f341(f341(f110(f864(x92332,a850)),x92334),x92335))) % 19.23/19.05 [9435]~P71(x94351)+~E(f341(x94353,f434(x94353,x94355,x94354,x94352,x94351)),f87(x94351))+~P85(f341(f71(x94352),x94354))+~P85(f341(f71(x94352),x94355))+E(f341(f341(f90(x94351),f341(f341(f341(f75(x94351,x94352,f90(x94351)),x94353),f87(x94351)),x94354)),f341(f341(f341(f75(x94351,x94352,f90(x94351)),x94353),f87(x94351)),x94355)),f341(f341(f341(f75(x94351,x94352,f90(x94351)),x94353),f87(x94351)),f341(f341(f110(f864(x94352,a850)),x94354),x94355))) % 19.23/19.05 [9540]~P71(x95402)+E(f341(f341(f11(x95401,x95402),x95403),x95404),f341(f341(f11(x95401,x95402),x95403),x95405))+~P85(f341(f71(x95401),x95405))+~P85(f341(f341(f241(f864(x95401,a850)),x95404),x95405))+P85(f341(f341(f343(x95401),f448(x95403,x95404,x95405,x95401,x95402)),f341(f341(f3(f864(x95401,a850)),x95405),x95404))) % 19.23/19.05 [9541]~P71(x95412)+E(f341(f341(f11(x95411,x95412),x95413),x95414),f341(f341(f11(x95411,x95412),x95413),x95415))+~P85(f341(f71(x95411),x95415))+~P85(f341(f341(f241(f864(x95411,a850)),x95414),x95415))+P85(f341(f341(f343(x95411),f449(x95413,x95414,x95415,x95411,x95412)),f341(f341(f3(f864(x95411,a850)),x95415),x95414))) % 19.23/19.05 [9542]~P68(x95422)+E(f341(f341(f8(x95421,x95422),x95423),x95424),f341(f341(f8(x95421,x95422),x95423),x95425))+~P85(f341(f71(x95421),x95425))+~P85(f341(f341(f241(f864(x95421,a850)),x95424),x95425))+P85(f341(f341(f343(x95421),f516(x95423,x95424,x95425,x95421,x95422)),f341(f341(f3(f864(x95421,a850)),x95425),x95424))) % 19.23/19.05 [9543]~P68(x95432)+E(f341(f341(f8(x95431,x95432),x95433),x95434),f341(f341(f8(x95431,x95432),x95433),x95435))+~P85(f341(f71(x95431),x95435))+~P85(f341(f341(f241(f864(x95431,a850)),x95434),x95435))+P85(f341(f341(f343(x95431),f522(x95433,x95434,x95435,x95431,x95432)),f341(f341(f3(f864(x95431,a850)),x95435),x95434))) % 19.23/19.05 [9558]~P71(x95581)+~P85(f341(f71(x95582),x95584))+~P85(f341(f71(x95582),x95585))+E(f341(f341(f90(x95581),f341(f341(f11(x95582,x95581),x95583),x95584)),f341(f341(f11(x95582,x95581),x95583),x95585)),f341(f341(f11(x95582,x95581),x95583),f341(f341(f110(f864(x95582,a850)),x95584),x95585)))+P85(f341(f341(f343(x95582),f411(x95583,x95585,x95584,x95582,x95581)),f341(f341(f111(f864(x95582,a850)),x95584),x95585))) % 19.23/19.05 [9559]~P71(x95591)+~P85(f341(f71(x95592),x95594))+~P85(f341(f71(x95592),x95595))+E(f341(f341(f90(x95591),f341(f341(f11(x95592,x95591),x95593),x95594)),f341(f341(f11(x95592,x95591),x95593),x95595)),f341(f341(f11(x95592,x95591),x95593),f341(f341(f110(f864(x95592,a850)),x95594),x95595)))+P85(f341(f341(f343(x95592),f413(x95593,x95595,x95594,x95592,x95591)),f341(f341(f111(f864(x95592,a850)),x95594),x95595))) % 19.23/19.05 [9560]~P68(x95601)+~P85(f341(f71(x95602),x95604))+~P85(f341(f71(x95602),x95605))+E(f341(f341(f89(x95601),f341(f341(f8(x95602,x95601),x95603),x95604)),f341(f341(f8(x95602,x95601),x95603),x95605)),f341(f341(f8(x95602,x95601),x95603),f341(f341(f110(f864(x95602,a850)),x95604),x95605)))+P85(f341(f341(f343(x95602),f499(x95603,x95605,x95604,x95602,x95601)),f341(f341(f111(f864(x95602,a850)),x95604),x95605))) % 19.23/19.05 [9561]~P68(x95611)+~P85(f341(f71(x95612),x95614))+~P85(f341(f71(x95612),x95615))+E(f341(f341(f89(x95611),f341(f341(f8(x95612,x95611),x95613),x95614)),f341(f341(f8(x95612,x95611),x95613),x95615)),f341(f341(f8(x95612,x95611),x95613),f341(f341(f110(f864(x95612,a850)),x95614),x95615)))+P85(f341(f341(f343(x95612),f517(x95613,x95615,x95614,x95612,x95611)),f341(f341(f111(f864(x95612,a850)),x95614),x95615))) % 19.23/19.05 [9574]~P81(x95745)+~P85(f341(f71(x95741),x95744))+P85(f341(f341(f241(x95745),f341(f341(f8(x95741,x95745),x95742),x95743)),f341(f341(f8(x95741,x95745),x95742),x95744)))+~P85(f341(f341(f241(f864(x95741,a850)),x95743),x95744))+P85(f341(f341(f343(x95741),f508(x95742,x95743,x95744,x95741,x95745)),f341(f341(f3(f864(x95741,a850)),x95744),x95743))) % 19.23/19.05 [9621]~P71(x96211)+~P85(f341(f71(x96212),x96214))+~P85(f341(f71(x96212),x96215))+E(f341(f341(f90(x96211),f341(f341(f341(f75(x96211,x96212,f90(x96211)),x96213),f87(x96211)),x96214)),f341(f341(f341(f75(x96211,x96212,f90(x96211)),x96213),f87(x96211)),x96215)),f341(f341(f341(f75(x96211,x96212,f90(x96211)),x96213),f87(x96211)),f341(f341(f110(f864(x96212,a850)),x96214),x96215)))+P85(f341(f341(f343(x96212),f434(x96213,x96215,x96214,x96212,x96211)),f341(f341(f111(f864(x96212,a850)),x96214),x96215))) % 19.23/19.05 [8665]~P19(x86651,x86654,x86655)+~P85(f341(f71(x86651),x86652))+E(f341(f341(f3(f864(x86651,a850)),x86652),f341(f341(f311(x86651),x86653),f185(f864(x86651,a850)))),f185(f864(x86651,a850)))+~P85(f341(f341(f343(x86651),x86653),x86652))+E(f341(f341(x86654,x86653),f341(x86655,f341(f341(f3(f864(x86651,a850)),x86652),f341(f341(f311(x86651),x86653),f185(f864(x86651,a850)))))),f341(x86655,x86652)) % 19.23/19.05 [8732]~P19(x87321,x87324,x87325)+~P85(f341(f71(x87321),x87323))+~P85(f341(f71(x87321),x87322))+E(f341(f341(f111(f864(x87321,a850)),x87322),x87323),f185(f864(x87321,a850)))+E(f341(f341(x87324,f341(x87325,f341(f341(f110(f864(x87321,a850)),x87322),x87323))),f341(x87325,f341(f341(f111(f864(x87321,a850)),x87322),x87323))),f341(f341(x87324,f341(x87325,x87322)),f341(x87325,x87323))) % 19.23/19.05 [9235]~P85(f341(f341(f241(a1),x92354),f2(a1)))+~P85(f341(f341(f242(a1),x92353),x92355))+P85(f341(f341(f241(a1),x92351),x92352))+~P85(f341(f341(f242(a1),x92353),x92354))+~P85(f341(f341(f241(a1),f341(f341(f89(a1),f341(f341(f90(a1),x92353),x92352)),x92355)),f341(f341(f89(a1),f341(f341(f90(a1),x92353),x92351)),x92354))) % 19.23/19.05 [9237]~P85(f341(f341(f241(a1),f2(a1)),x92375))+P85(f341(f341(f241(a1),x92371),x92372))+~P85(f341(f341(f242(a1),x92373),x92374))+~P85(f341(f341(f242(a1),x92375),x92374))+~P85(f341(f341(f241(a1),f341(f341(f89(a1),f341(f341(f90(a1),x92374),x92371)),x92375)),f341(f341(f89(a1),f341(f341(f90(a1),x92374),x92372)),x92373))) % 19.23/19.05 [9350]~P60(x93505)+E(f341(x93501,f412(x93501,x93502,x93503,x93504,x93505)),f2(x93505))+~P85(f341(f71(x93504),x93503))+~P85(f341(f71(x93504),x93502))+E(f341(f341(f292(x93505),f341(f341(f90(x93505),f341(f341(f11(x93504,x93505),x93501),x93503)),f341(f341(f11(x93504,x93505),x93501),x93502))),f341(f341(f11(x93504,x93505),x93501),f341(f341(f111(f864(x93504,a850)),x93503),x93502))),f341(f341(f11(x93504,x93505),x93501),f341(f341(f110(f864(x93504,a850)),x93503),x93502))) % 19.23/19.05 [9615]~P60(x96151)+~P85(f341(f71(x96152),x96154))+~P85(f341(f71(x96152),x96155))+E(f341(f341(f292(x96151),f341(f341(f90(x96151),f341(f341(f11(x96152,x96151),x96153),x96154)),f341(f341(f11(x96152,x96151),x96153),x96155))),f341(f341(f11(x96152,x96151),x96153),f341(f341(f111(f864(x96152,a850)),x96154),x96155))),f341(f341(f11(x96152,x96151),x96153),f341(f341(f110(f864(x96152,a850)),x96154),x96155)))+P85(f341(f341(f343(x96152),f412(x96153,x96155,x96154,x96152,x96151)),f341(f341(f111(f864(x96152,a850)),x96154),x96155))) % 19.23/19.05 [8977]E(f341(f341(f132(x89771),x89772),x89773),f341(f341(f132(x89771),x89774),x89775))+~E(f341(f341(f164(x89771),f341(f186(f858(x89771)),x89774)),x89772),x89774)+~E(f341(f341(f164(x89771),f341(f186(f858(x89771)),x89772)),x89774),x89772)+~E(x89775,f341(f341(f132(x89771),f341(f341(f135(x89771),f341(f186(f858(x89771)),x89774)),x89772)),x89773))+~E(f341(f341(f132(x89771),f341(f341(f135(x89771),f341(f186(f858(x89771)),x89772)),x89774)),x89775),x89773) % 19.23/19.05 [9348]~P101(x93482)+E(f341(f341(f144(x93481,x93482,x93483),x93484),f157(x93481,x93484,x93485)),x93485)+~P15(x93482,f341(f341(f149(x93481,x93482),x93483),x93485))+~P85(f341(f341(f343(x93481),x93484),f341(f163(x93481),x93485)))+~E(f341(f137(x93481),f341(f133(x93481,f341(f341(f10(x93482,a850,x93481),f341(a338,f341(x93483,x93484))),x93483)),x93485)),x93484) % 19.23/19.05 [9669]~P65(x96691)+~P85(f341(f76(x96691,x96691,f90(x96691),x96692,x96693),x96695))+~P85(f341(f341(f343(x96691),x96694),x96693))+P85(f341(f341(f343(x96691),x96692),x96693))+P85(f341(f76(x96691,x96691,f90(x96691),x96694,f341(f341(f311(x96691),x96692),f341(f341(f3(f864(x96691,a850)),x96693),f341(f341(f311(x96691),x96694),f185(f864(x96691,a850)))))),x96695)) % 19.23/19.05 [7160]E(x71601,x71602)+~P26(x71604,x71605,x71603,x71606)+~E(f341(x71603,x71601),f341(x71603,x71602))+~P85(f341(f341(f343(x71604),x71602),x71606))+~P85(f341(f341(f343(x71604),x71601),x71606)) % 19.23/19.05 [6405]~P111(x64054)+E(x64051,x64052)+~E(x64055,x64056)+E(x64053,f2(x64054))+~E(f341(f341(f89(x64054),x64055),f341(f341(f90(x64054),x64053),x64051)),f341(f341(f89(x64054),x64056),f341(f341(f90(x64054),x64053),x64052))) % 19.23/19.05 [7475]~P101(x74751)+~P6(x74751)+~P85(f341(f341(f242(x74751),x74752),f341(x74755,x74756)))+~P85(f341(f341(f343(x74753),x74756),x74754))+P85(f341(f341(f242(x74751),x74752),f341(f341(f54(x74753,x74751),x74754),x74755))) % 19.23/19.05 [9833]~P86(x98336)+~P85(f341(f71(x98331),x98335))+P85(f341(f341(f343(x98331),f637(x98332,x98333,x98334,x98335,x98331,x98336)),x98334))+P85(f341(f341(f288(x98336),f341(f341(f11(x98331,x98336),x98333),x98334)),f341(f341(f11(x98331,x98336),x98332),x98335)))+~P85(f341(f341(f241(f864(x98331,a850)),x98334),x98335)) % 19.23/19.05 [9954]~P86(x99541)+~P85(f341(f71(x99542),x99546))+~P85(f341(f341(f288(x99541),f341(x99543,f637(x99545,x99543,x99544,x99546,x99542,x99541))),f341(x99545,f637(x99545,x99543,x99544,x99546,x99542,x99541))))+P85(f341(f341(f288(x99541),f341(f341(f11(x99542,x99541),x99543),x99544)),f341(f341(f11(x99542,x99541),x99545),x99546)))+~P85(f341(f341(f241(f864(x99542,a850)),x99544),x99546)) % 19.23/19.05 [8153]~P101(x81531)+~P6(x81531)+~P85(f341(f341(f242(x81531),f341(x81534,x81536)),x81535))+~P85(f341(f341(f343(x81532),x81536),x81533))+P85(f341(f341(f242(x81531),f341(f341(f55(x81532,x81531),x81533),x81534)),x81535)) % 19.23/19.05 [8411]~P20(x84112,x84115,x84116,x84111)+~P85(f341(f71(x84112),x84114))+~P85(f341(f71(x84112),x84113))+~E(f341(f341(f111(f864(x84112,a850)),x84113),x84114),f185(f864(x84112,a850)))+E(f341(x84111,f341(f341(f110(f864(x84112,a850)),x84113),x84114)),f341(f82(x84115,x84115,x84115,f341(x84111,x84113)),f341(x84111,x84114))) % 19.23/19.05 [9066]~P115(x90661)+~P109(x90661)+~P85(f341(f341(f288(x90661),x90662),x90665))+~P85(f341(f341(f288(x90661),x90662),f341(f341(f89(x90661),x90663),x90666)))+P85(f341(f341(f288(x90661),x90662),f341(f341(f89(x90661),f341(f341(f3(x90661),x90663),f341(f341(f90(x90661),x90664),x90665))),x90666))) % 19.23/19.05 [9225]~P115(x92251)+~P109(x92251)+~P85(f341(f341(f288(x92251),x92252),x92255))+P85(f341(f341(f288(x92251),x92252),f341(f341(f89(x92251),x92253),x92254)))+~P85(f341(f341(f288(x92251),x92252),f341(f341(f89(x92251),f341(f341(f3(x92251),x92253),f341(f341(f90(x92251),x92256),x92255))),x92254))) % 19.23/19.05 [8703]E(x87031,x87032)+~P54(x87034,x87035,x87036,x87033,x87037)+~E(f341(x87033,x87031),f341(x87033,x87032))+~P85(f341(f341(f343(x87035),x87032),x87037))+~P85(f341(f341(f343(x87035),x87031),x87037)) % 19.23/19.05 [9963]~P9(x99631,x99637,x99636)+~P13(x99631,f864(x99635,a850),x99636,x99634)+P85(f341(f341(f343(x99631),f429(x99632,x99633,x99634,x99635,x99636,x99637,x99631)),x99637))+~P85(f341(f341(f343(f864(x99631,a850)),x99633),f341(f341(f69(x99631),x99637),x99636)))+P85(f341(f341(f343(f864(x99635,a850)),f341(f341(f54(x99631,f864(x99635,a850)),x99633),x99634)),x99632)) % 19.23/19.05 [10010]~P9(x100102,x100106,x100107)+~P13(x100102,f864(x100101,a850),x100107,x100104)+~P85(f341(f341(f343(f864(x100102,a850)),x100103),f341(f341(f69(x100102),x100106),x100107)))+~P85(f341(f341(f343(f864(x100101,a850)),f341(x100104,f429(x100105,x100103,x100104,x100101,x100107,x100106,x100102))),x100105))+P85(f341(f341(f343(f864(x100101,a850)),f341(f341(f54(x100102,f864(x100101,a850)),x100103),x100104)),x100105)) % 19.23/19.05 [8321]~P71(x83212)+~P26(x83211,x83215,x83218,x83214)+~E(x83213,f341(f82(x83215,x83212,x83211,x83216),x83218))+~E(x83217,f341(f312(x83211,x83215,x83218),x83214))+E(f341(f341(f11(x83211,x83212),x83213),x83214),f341(f341(f11(x83215,x83212),x83216),x83217)) % 19.23/19.05 [10013]~P71(x100132)+~P26(x100135,x100131,x100138,x100137)+~E(f341(x100136,f532(x100133,x100136,x100134,x100137,x100138,x100131,x100135,x100132)),f341(f341(f82(x100131,x100132,x100135,x100133),x100138),f532(x100133,x100136,x100134,x100137,x100138,x100131,x100135,x100132)))+~E(x100134,f341(f312(x100135,x100131,x100138),x100137))+E(f341(f341(f11(x100131,x100132),x100133),x100134),f341(f341(f11(x100135,x100132),x100136),x100137)) % 19.23/19.05 [10016]~P71(x100162)+~P26(x100161,x100165,x100168,x100164)+~E(x100167,f341(f312(x100161,x100165,x100168),x100164))+E(f341(f341(f11(x100161,x100162),x100163),x100164),f341(f341(f11(x100165,x100162),x100166),x100167))+P85(f341(f341(f343(x100161),f532(x100166,x100163,x100167,x100164,x100168,x100165,x100161,x100162)),x100164)) % 19.23/19.05 [10017]~P68(x100172)+~P26(x100171,x100175,x100178,x100174)+~E(x100177,f341(f312(x100171,x100175,x100178),x100174))+E(f341(f341(f8(x100171,x100172),x100173),x100174),f341(f341(f8(x100175,x100172),x100176),x100177))+P85(f341(f341(f343(x100171),f642(x100176,x100173,x100177,x100174,x100178,x100175,x100171,x100172)),x100174)) % 19.23/19.05 [10021]~P68(x100212)+~P26(x100215,x100211,x100218,x100217)+~E(x100214,f341(f312(x100215,x100211,x100218),x100217))+~E(f341(x100216,f642(x100213,x100216,x100214,x100217,x100218,x100211,x100215,x100212)),f341(x100213,f341(x100218,f642(x100213,x100216,x100214,x100217,x100218,x100211,x100215,x100212))))+E(f341(f341(f8(x100211,x100212),x100213),x100214),f341(f341(f8(x100215,x100212),x100216),x100217)) % 19.23/19.05 [9413]~E(f341(f186(f858(x94132)),x94135),f341(f186(f858(x94131)),x94133))+~E(f341(f186(f858(x94132)),x94134),f341(f186(f858(x94131)),x94133))+~E(f341(f341(f341(f81(x94131,f861(x94132)),f171(x94131,x94132,f341(f341(f172(x94131,x94132),x94133),x94134))),x94136),f341(f235(x94132),x94137)),f341(f341(f341(f81(x94131,f861(x94132)),f171(x94131,x94132,f341(f341(f172(x94131,x94132),x94133),x94135))),x94136),f341(f235(x94132),x94138)))+E(f171(x94131,x94132,f341(f341(f172(x94131,x94132),x94133),x94134)),f171(x94131,x94132,f341(f341(f172(x94131,x94132),x94133),x94135)))+P85(f341(f341(f343(x94131),x94136),f341(f163(x94131),x94133))) % 19.23/19.05 [9509]~P24(x95096,x95092,x95095,x95097,x95098,x95091)+~P85(f341(f71(x95092),x95094))+~P85(f341(f71(x95092),x95093))+~E(f341(f341(f111(f864(x95092,a850)),x95093),x95094),f185(f864(x95092,a850)))+E(f341(x95091,f341(f341(f110(f864(x95092,a850)),x95093),x95094)),f341(f341(x95095,f341(x95091,x95093)),f341(x95091,x95094))) % 19.23/19.05 [9908]~P24(x99088,x99082,x99085,x99087,x99086,x99081)+~E(f341(x99086,f577(x99084,x99083,x99081,x99086,x99087,x99085,x99082)),x99087)+~P85(f341(f71(x99082),x99083))+~P85(f341(f71(x99082),x99084))+E(f341(x99081,f341(f341(f110(f864(x99082,a850)),x99083),x99084)),f341(f341(x99085,f341(x99081,x99083)),f341(x99081,x99084))) % 19.23/19.05 [9969]~P24(x99698,x99692,x99695,x99697,x99696,x99691)+~P85(f341(f71(x99692),x99693))+~P85(f341(f71(x99692),x99694))+E(f341(x99691,f341(f341(f110(f864(x99692,a850)),x99693),x99694)),f341(f341(x99695,f341(x99691,x99693)),f341(x99691,x99694)))+P85(f341(f341(f343(x99692),f577(x99694,x99693,x99691,x99696,x99697,x99695,x99692)),f341(f341(f111(f864(x99692,a850)),x99693),x99694))) % 19.23/19.05 [9660]~P9(x96604,x96608,x96605)+~P9(x96601,x96609,x96603)+~P14(x96601,x96604,f864(x96602,a850),x96603,x96605,x96607)+P13(x96601,f864(x96602,a850),x96603,f341(f341(f10(f864(x96604,f864(x96602,a850)),f864(x96602,a850),x96601),f341(f54(x96604,f864(x96602,a850)),f341(f286(x96604,x96604,x96605),f341(f341(f311(x96604),x96606),f185(f864(x96604,a850)))))),x96607))+~P85(f341(f341(f343(x96604),x96606),x96608)) % 19.23/19.05 [4948]~P124(x49482)+~P129(x49482)+~P140(x49482)+~P106(x49482)+E(x49481,f2(x49482))+~E(f341(f341(f251(x49482),x49481),x49483),f2(x49482)) % 19.23/19.05 [4949]~P124(x49492)+~P129(x49492)+~P140(x49492)+~P106(x49492)+~E(x49491,f2(a857))+~E(f341(f341(f251(x49492),x49493),x49491),f2(x49492)) % 19.23/19.05 [6385]~P81(x63851)+~E(x63853,f2(x63851))+~E(x63852,f2(x63851))+E(f341(f341(f89(x63851),x63852),x63853),f2(x63851))+~P85(f341(f341(f241(x63851),f2(x63851)),x63853))+~P85(f341(f341(f241(x63851),f2(x63851)),x63852)) % 19.23/19.05 [8761]~E(f341(f249(a857,a857),x87613),f2(a857))+~E(x87611,f341(f341(f89(a857),f341(f341(f90(a857),f341(f249(a857,a857),x87613)),x87612)),f341(f259(a857,a857),x87613)))+P85(f341(f63(x87611,x87612),x87613))+~P85(f341(f341(f241(a857),f341(f259(a857,a857),x87613)),f2(a857)))+P85(f341(f341(f242(a857),f2(a857)),x87612))+~P85(f341(f341(f242(a857),x87612),f341(f259(a857,a857),x87613))) % 19.23/19.05 [8768]E(x87681,f2(a857))+~E(x87682,f341(f341(f89(a857),f341(f341(f90(a857),f341(f249(a857,a857),x87683)),x87681)),f341(f259(a857,a857),x87683)))+P85(f341(f63(x87682,x87681),x87683))+~P85(f341(f341(f242(a857),f2(a857)),x87681))+~P85(f341(f341(f241(a857),f2(a857)),f341(f259(a857,a857),x87683)))+~P85(f341(f341(f242(a857),f341(f259(a857,a857),x87683)),x87681)) % 19.23/19.05 [8782]~E(f341(f249(a857,a857),x87823),f2(a857))+~E(x87821,f341(f341(f89(a857),f341(f341(f90(a857),f341(f249(a857,a857),x87823)),x87822)),f341(f259(a857,a857),x87823)))+P85(f341(f63(x87821,x87822),x87823))+~P85(f341(f341(f242(a857),f2(a857)),x87822))+~P85(f341(f341(f241(a857),f2(a857)),f341(f259(a857,a857),x87823)))+~P85(f341(f341(f242(a857),f341(f259(a857,a857),x87823)),x87822)) % 19.23/19.05 [6783]~P95(x67832)+E(x67831,f185(f864(x67832,a850)))+E(x67833,f185(f864(x67832,a850)))+~P85(f341(f71(x67832),x67831))+~P85(f341(f71(x67832),x67833))+E(f15(x67832,f341(f341(f110(f864(x67832,a850)),x67833),x67831)),f341(f341(f110(x67832),f15(x67832,x67833)),f15(x67832,x67831))) % 19.23/19.05 [6784]~P95(x67842)+E(x67841,f185(f864(x67842,a850)))+E(x67843,f185(f864(x67842,a850)))+~P85(f341(f71(x67842),x67841))+~P85(f341(f71(x67842),x67843))+E(f12(x67842,f341(f341(f110(f864(x67842,a850)),x67843),x67841)),f341(f341(f111(x67842),f12(x67842,x67843)),f12(x67842,x67841))) % 19.23/19.05 [6785]~P101(x67852)+E(x67851,f185(f864(x67852,a850)))+E(x67853,f185(f864(x67852,a850)))+~P85(f341(f71(x67852),x67851))+~P85(f341(f71(x67852),x67853))+E(f16(x67852,f341(f341(f110(f864(x67852,a850)),x67853),x67851)),f341(f341(f240(x67852),f16(x67852,x67853)),f16(x67852,x67851))) % 19.23/19.05 [6786]~P101(x67862)+E(x67861,f185(f864(x67862,a850)))+E(x67863,f185(f864(x67862,a850)))+~P85(f341(f71(x67862),x67861))+~P85(f341(f71(x67862),x67863))+E(f17(x67862,f341(f341(f110(f864(x67862,a850)),x67863),x67861)),f341(f341(f245(x67862),f17(x67862,x67863)),f17(x67862,x67861))) % 19.23/19.05 [7447]~P92(x74472)+E(x74471,f185(f864(x74472,a850)))+E(x74473,f185(f864(x74472,a850)))+~P85(f341(f71(x74472),x74471))+~P85(f341(f71(x74472),x74473))+E(f341(f341(f90(x74472),f341(f73(x74472,f90(x74472)),x74473)),f341(f73(x74472,f90(x74472)),x74471)),f341(f73(x74472,f90(x74472)),f341(f341(f110(f864(x74472,a850)),x74473),x74471))) % 19.23/19.05 [7612]~P101(x76122)+E(x76121,f185(f864(x76122,a850)))+E(x76123,f185(f864(x76122,a850)))+~P85(f341(f71(x76122),x76121))+~P85(f341(f71(x76122),x76123))+E(f341(f341(f240(x76122),f13(x76122,f240(x76122),x76123)),f13(x76122,f240(x76122),x76121)),f13(x76122,f240(x76122),f341(f341(f110(f864(x76122,a850)),x76123),x76121))) % 19.23/19.05 [7613]~P101(x76132)+E(x76131,f185(f864(x76132,a850)))+E(x76133,f185(f864(x76132,a850)))+~P85(f341(f71(x76132),x76131))+~P85(f341(f71(x76132),x76133))+E(f341(f341(f245(x76132),f14(x76132,f245(x76132),x76133)),f14(x76132,f245(x76132),x76131)),f14(x76132,f245(x76132),f341(f341(f110(f864(x76132,a850)),x76133),x76131))) % 19.23/19.05 [8618]~P85(f341(x86181,x86183))+P85(f341(x86181,f485(x86181,x86182)))+P85(f341(x86181,f475(x86181,x86182)))+~P85(f341(f341(f242(a1),f2(a1)),x86182))+~P85(f341(f341(f343(a1),x86183),f304(a1,f87(a1),x86182)))+P85(f341(x86181,f341(f341(f3(a1),f475(x86181,x86182)),f341(f341(f90(a1),f484(x86181,x86182)),x86182)))) % 19.23/19.05 [8882]~P85(f341(x88821,x88823))+~P85(f341(x88821,f475(x88821,x88822)))+P85(f341(x88821,f485(x88821,x88822)))+~P85(f341(f341(f242(a1),f2(a1)),x88822))+~P85(f341(f341(f343(a1),x88823),f304(a1,f87(a1),x88822)))+~P85(f341(x88821,f341(f341(f3(a1),f475(x88821,x88822)),f341(f341(f90(a1),f484(x88821,x88822)),x88822)))) % 19.23/19.05 [10041]~P96(x100412)+E(x100411,f185(f864(x100412,a850)))+E(x100413,f185(f864(x100412,a850)))+~P85(f341(f71(x100412),x100411))+~P85(f341(f71(x100412),x100413))+E(f12(x100412,f341(f265(x100412),f341(f341(f10(f864(x100412,a850),a850,x100412),f96(x100412)),f341(f341(f10(f864(x100412,f864(x100412,a850)),f864(x100412,a850),x100412),f341(f10(f864(x100412,a850),a850,x100412),f96(x100412))),f341(f341(f9(x100412,f864(x100412,f864(x100412,a850)),f864(x100412,f864(x100412,a850))),f341(f341(f10(f864(x100412,f864(f864(x100412,a850),f864(x100412,a850))),f864(f864(x100412,f864(x100412,a850)),f864(x100412,f864(x100412,a850))),x100412),f20(x100412,f864(x100412,a850),f864(x100412,a850))),f341(f341(f10(f864(x100412,f864(x100412,f864(a850,a850))),f864(x100412,f864(f864(x100412,a850),f864(x100412,a850))),x100412),f341(f10(f864(x100412,f864(a850,a850)),f864(f864(x100412,a850),f864(x100412,a850)),x100412),f20(x100412,a850,a850))),f341(f341(f10(f864(x100412,f864(x100412,a850)),f864(x100412,f864(x100412,f864(a850,a850))),x100412),f341(f10(f864(x100412,a850),f864(x100412,f864(a850,a850)),x100412),f341(f10(a850,f864(a850,a850),x100412),a339))),f341(f341(f9(x100412,f864(x100412,f864(x100412,x100412)),f864(x100412,f864(x100412,a850))),f341(f341(f10(f864(f864(x100412,x100412),f864(x100412,a850)),f864(f864(x100412,f864(x100412,x100412)),f864(x100412,f864(x100412,a850))),x100412),f10(f864(x100412,x100412),f864(x100412,a850),x100412)),f341(f341(f10(f864(x100412,a850),f864(f864(x100412,x100412),f864(x100412,a850)),x100412),f10(x100412,a850,x100412)),a338))),f110(x100412)))))),f341(f341(f9(x100412,f864(x100412,a850),f864(x100412,a850)),f341(f341(f10(f864(a850,a850),f864(f864(x100412,a850),f864(x100412,a850)),x100412),f10(a850,a850,x100412)),f341(f341(f10(a850,f864(a850,a850),x100412),a339),f341(f341(f9(x100412,f864(x100412,a850),a850),f343(x100412)),x100413)))),f341(f341(f9(x100412,f864(x100412,a850),a850),f343(x100412)),x100411))))))),f341(f341(f110(x100412),f12(x100412,x100413)),f12(x100412,x100411))) % 19.23/19.05 [10042]~P96(x100422)+E(x100421,f185(f864(x100422,a850)))+E(x100423,f185(f864(x100422,a850)))+~P85(f341(f71(x100422),x100421))+~P85(f341(f71(x100422),x100423))+E(f15(x100422,f341(f265(x100422),f341(f341(f10(f864(x100422,a850),a850,x100422),f96(x100422)),f341(f341(f10(f864(x100422,f864(x100422,a850)),f864(x100422,a850),x100422),f341(f10(f864(x100422,a850),a850,x100422),f96(x100422))),f341(f341(f9(x100422,f864(x100422,f864(x100422,a850)),f864(x100422,f864(x100422,a850))),f341(f341(f10(f864(x100422,f864(f864(x100422,a850),f864(x100422,a850))),f864(f864(x100422,f864(x100422,a850)),f864(x100422,f864(x100422,a850))),x100422),f20(x100422,f864(x100422,a850),f864(x100422,a850))),f341(f341(f10(f864(x100422,f864(x100422,f864(a850,a850))),f864(x100422,f864(f864(x100422,a850),f864(x100422,a850))),x100422),f341(f10(f864(x100422,f864(a850,a850)),f864(f864(x100422,a850),f864(x100422,a850)),x100422),f20(x100422,a850,a850))),f341(f341(f10(f864(x100422,f864(x100422,a850)),f864(x100422,f864(x100422,f864(a850,a850))),x100422),f341(f10(f864(x100422,a850),f864(x100422,f864(a850,a850)),x100422),f341(f10(a850,f864(a850,a850),x100422),a339))),f341(f341(f9(x100422,f864(x100422,f864(x100422,x100422)),f864(x100422,f864(x100422,a850))),f341(f341(f10(f864(f864(x100422,x100422),f864(x100422,a850)),f864(f864(x100422,f864(x100422,x100422)),f864(x100422,f864(x100422,a850))),x100422),f10(f864(x100422,x100422),f864(x100422,a850),x100422)),f341(f341(f10(f864(x100422,a850),f864(f864(x100422,x100422),f864(x100422,a850)),x100422),f10(x100422,a850,x100422)),a338))),f111(x100422)))))),f341(f341(f9(x100422,f864(x100422,a850),f864(x100422,a850)),f341(f341(f10(f864(a850,a850),f864(f864(x100422,a850),f864(x100422,a850)),x100422),f10(a850,a850,x100422)),f341(f341(f10(a850,f864(a850,a850),x100422),a339),f341(f341(f9(x100422,f864(x100422,a850),a850),f343(x100422)),x100423)))),f341(f341(f9(x100422,f864(x100422,a850),a850),f343(x100422)),x100421))))))),f341(f341(f111(x100422),f15(x100422,x100423)),f15(x100422,x100421))) % 19.23/19.05 [10043]~P101(x100432)+E(x100431,f185(f864(x100432,a850)))+E(x100433,f185(f864(x100432,a850)))+~P85(f341(f71(x100432),x100431))+~P85(f341(f71(x100432),x100433))+E(f13(x100432,f240(x100432),f341(f265(x100432),f341(f341(f10(f864(x100432,a850),a850,x100432),f96(x100432)),f341(f341(f10(f864(x100432,f864(x100432,a850)),f864(x100432,a850),x100432),f341(f10(f864(x100432,a850),a850,x100432),f96(x100432))),f341(f341(f9(x100432,f864(x100432,f864(x100432,a850)),f864(x100432,f864(x100432,a850))),f341(f341(f10(f864(x100432,f864(f864(x100432,a850),f864(x100432,a850))),f864(f864(x100432,f864(x100432,a850)),f864(x100432,f864(x100432,a850))),x100432),f20(x100432,f864(x100432,a850),f864(x100432,a850))),f341(f341(f10(f864(x100432,f864(x100432,f864(a850,a850))),f864(x100432,f864(f864(x100432,a850),f864(x100432,a850))),x100432),f341(f10(f864(x100432,f864(a850,a850)),f864(f864(x100432,a850),f864(x100432,a850)),x100432),f20(x100432,a850,a850))),f341(f341(f10(f864(x100432,f864(x100432,a850)),f864(x100432,f864(x100432,f864(a850,a850))),x100432),f341(f10(f864(x100432,a850),f864(x100432,f864(a850,a850)),x100432),f341(f10(a850,f864(a850,a850),x100432),a339))),f341(f341(f9(x100432,f864(x100432,f864(x100432,x100432)),f864(x100432,f864(x100432,a850))),f341(f341(f10(f864(f864(x100432,x100432),f864(x100432,a850)),f864(f864(x100432,f864(x100432,x100432)),f864(x100432,f864(x100432,a850))),x100432),f10(f864(x100432,x100432),f864(x100432,a850),x100432)),f341(f341(f10(f864(x100432,a850),f864(f864(x100432,x100432),f864(x100432,a850)),x100432),f10(x100432,a850,x100432)),a338))),f245(x100432)))))),f341(f341(f9(x100432,f864(x100432,a850),f864(x100432,a850)),f341(f341(f10(f864(a850,a850),f864(f864(x100432,a850),f864(x100432,a850)),x100432),f10(a850,a850,x100432)),f341(f341(f10(a850,f864(a850,a850),x100432),a339),f341(f341(f9(x100432,f864(x100432,a850),a850),f343(x100432)),x100433)))),f341(f341(f9(x100432,f864(x100432,a850),a850),f343(x100432)),x100431))))))),f341(f341(f245(x100432),f13(x100432,f240(x100432),x100433)),f13(x100432,f240(x100432),x100431))) % 19.23/19.05 [10044]~P101(x100442)+E(x100441,f185(f864(x100442,a850)))+E(x100443,f185(f864(x100442,a850)))+~P85(f341(f71(x100442),x100441))+~P85(f341(f71(x100442),x100443))+E(f14(x100442,f245(x100442),f341(f265(x100442),f341(f341(f10(f864(x100442,a850),a850,x100442),f96(x100442)),f341(f341(f10(f864(x100442,f864(x100442,a850)),f864(x100442,a850),x100442),f341(f10(f864(x100442,a850),a850,x100442),f96(x100442))),f341(f341(f9(x100442,f864(x100442,f864(x100442,a850)),f864(x100442,f864(x100442,a850))),f341(f341(f10(f864(x100442,f864(f864(x100442,a850),f864(x100442,a850))),f864(f864(x100442,f864(x100442,a850)),f864(x100442,f864(x100442,a850))),x100442),f20(x100442,f864(x100442,a850),f864(x100442,a850))),f341(f341(f10(f864(x100442,f864(x100442,f864(a850,a850))),f864(x100442,f864(f864(x100442,a850),f864(x100442,a850))),x100442),f341(f10(f864(x100442,f864(a850,a850)),f864(f864(x100442,a850),f864(x100442,a850)),x100442),f20(x100442,a850,a850))),f341(f341(f10(f864(x100442,f864(x100442,a850)),f864(x100442,f864(x100442,f864(a850,a850))),x100442),f341(f10(f864(x100442,a850),f864(x100442,f864(a850,a850)),x100442),f341(f10(a850,f864(a850,a850),x100442),a339))),f341(f341(f9(x100442,f864(x100442,f864(x100442,x100442)),f864(x100442,f864(x100442,a850))),f341(f341(f10(f864(f864(x100442,x100442),f864(x100442,a850)),f864(f864(x100442,f864(x100442,x100442)),f864(x100442,f864(x100442,a850))),x100442),f10(f864(x100442,x100442),f864(x100442,a850),x100442)),f341(f341(f10(f864(x100442,a850),f864(f864(x100442,x100442),f864(x100442,a850)),x100442),f10(x100442,a850,x100442)),a338))),f240(x100442)))))),f341(f341(f9(x100442,f864(x100442,a850),f864(x100442,a850)),f341(f341(f10(f864(a850,a850),f864(f864(x100442,a850),f864(x100442,a850)),x100442),f10(a850,a850,x100442)),f341(f341(f10(a850,f864(a850,a850),x100442),a339),f341(f341(f9(x100442,f864(x100442,a850),a850),f343(x100442)),x100443)))),f341(f341(f9(x100442,f864(x100442,a850),a850),f343(x100442)),x100441))))))),f341(f341(f240(x100442),f14(x100442,f245(x100442),x100443)),f14(x100442,f245(x100442),x100441))) % 19.23/19.05 [7113]~P120(x71133)+E(x71131,x71132)+~E(f341(f341(f251(x71133),x71131),x71134),f341(f341(f251(x71133),x71132),x71134))+~P85(f341(f341(f241(x71133),f2(x71133)),x71132))+~P85(f341(f341(f241(x71133),f2(x71133)),x71131))+~P85(f341(f341(f242(a857),f2(a857)),x71134)) % 19.23/19.05 [7408]~P101(x74082)+E(x74081,f185(f864(x74082,a850)))+~P85(f341(f71(x74082),x74081))+~P85(f341(f341(f343(x74082),x74084),x74081))+P85(f341(f341(f242(x74082),x74083),x74084))+~P85(f341(f341(f242(x74082),x74083),f341(f73(x74082,f245(x74082)),x74081))) % 19.23/19.05 [7409]~P101(x74092)+E(x74091,f185(f864(x74092,a850)))+~P85(f341(f71(x74092),x74091))+~P85(f341(f341(f343(x74092),x74094),x74091))+P85(f341(f341(f241(x74092),x74093),x74094))+~P85(f341(f341(f241(x74092),x74093),f341(f73(x74092,f245(x74092)),x74091))) % 19.23/19.05 [7410]~P99(x74102)+E(x74101,f185(f864(x74102,a850)))+~P85(f341(f71(x74102),x74101))+~P85(f341(f341(f343(x74102),x74104),x74101))+P85(f341(f341(f241(x74102),x74103),x74104))+~P85(f341(f341(f241(x74102),x74103),f341(f73(x74102,f111(x74102)),x74101))) % 19.23/19.05 [7304]E(x73041,f2(a1))+E(f341(f341(f51(a1),x73042),x73041),x73043)+~P85(f341(f341(f241(a1),x73044),f2(a1)))+~E(x73042,f341(f341(f89(a1),f341(f341(f90(a1),x73041),x73043)),x73044))+P85(f341(f341(f242(a1),f2(a1)),x73041))+~P85(f341(f341(f242(a1),x73041),x73044)) % 19.23/19.05 [7320]E(f60(a1,x73202,x73201),x73203)+E(x73201,f2(a1))+~P85(f341(f341(f241(a1),x73203),f2(a1)))+~E(x73202,f341(f341(f89(a1),f341(f341(f90(a1),x73201),x73204)),x73203))+P85(f341(f341(f242(a1),f2(a1)),x73201))+~P85(f341(f341(f242(a1),x73201),x73203)) % 19.23/19.05 [7446]E(x74461,f2(a1))+E(f341(f341(f51(a1),x74462),x74461),x74463)+~E(x74462,f341(f341(f89(a1),f341(f341(f90(a1),x74461),x74463)),x74464))+~P85(f341(f341(f242(a1),f2(a1)),x74461))+~P85(f341(f341(f241(a1),f2(a1)),x74464))+~P85(f341(f341(f242(a1),x74464),x74461)) % 19.23/19.05 [7471]E(f60(a1,x74712,x74711),x74713)+E(x74711,f2(a1))+~E(x74712,f341(f341(f89(a1),f341(f341(f90(a1),x74711),x74714)),x74713))+~P85(f341(f341(f242(a1),f2(a1)),x74711))+~P85(f341(f341(f241(a1),f2(a1)),x74713))+~P85(f341(f341(f242(a1),x74713),x74711)) % 19.23/19.05 [7616]~P101(x76162)+E(x76161,f185(f864(x76162,a850)))+~P85(f341(f71(x76162),x76161))+~P85(f341(f341(f343(x76162),x76164),x76161))+~P85(f341(f341(f242(x76162),x76164),x76163))+P85(f341(f341(f242(x76162),f341(f73(x76162,f245(x76162)),x76161)),x76163)) % 19.23/19.05 [7617]~P101(x76172)+E(x76171,f185(f864(x76172,a850)))+~P85(f341(f71(x76172),x76171))+~P85(f341(f341(f343(x76172),x76174),x76171))+~P85(f341(f341(f241(x76172),x76174),x76173))+P85(f341(f341(f241(x76172),f341(f73(x76172,f245(x76172)),x76171)),x76173)) % 19.23/19.05 [8177]~P85(f341(f341(f241(a1),x81774),f2(a1)))+~E(x81771,f341(f341(f89(a1),f341(f341(f90(a1),x81772),x81773)),x81774))+~P85(f341(f341(f241(a1),f2(a1)),x81774))+~P85(f341(f341(f242(a1),x81774),x81772))+~P85(f341(f341(f242(a1),x81772),x81774))+P85(f341(f64(x81771,x81772),f341(f341(f250(a1,a1),x81773),x81774))) % 19.23/19.05 [8344]~P100(x83441)+P85(f341(f341(f242(f864(x83441,a850)),f304(x83441,x83442,x83443)),f304(x83441,x83444,x83445)))+~P85(f341(f341(f242(x83441),x83443),x83445))+~P85(f341(f341(f241(x83441),x83444),x83442))+~P85(f341(f341(f241(x83441),x83444),x83445))+~P85(f341(f341(f241(x83441),x83443),x83445)) % 19.23/19.05 [8345]~P100(x83451)+P85(f341(f341(f242(f864(x83451,a850)),f304(x83451,x83452,x83453)),f304(x83451,x83454,x83455)))+~P85(f341(f341(f242(x83451),x83454),x83452))+~P85(f341(f341(f241(x83451),x83453),x83455))+~P85(f341(f341(f241(x83451),x83454),x83455))+~P85(f341(f341(f241(x83451),x83454),x83452)) % 19.23/19.05 [9129]P56(x91292,x91293,x91294,x91291)+E(x91291,f185(f864(x91292,a850)))+~P85(f341(f71(x91292),x91294))+~P85(f341(f71(x91292),x91291))+~P85(f341(f341(x91293,f543(x91291,x91294,x91293,x91292)),x91295))+~P85(f341(f341(f343(x91292),x91295),x91291)) % 19.23/19.05 [9253]~E(x92533,x92535)+~P68(x92531)+~P71(x92531)+~P37(x92533)+E(f341(f341(f11(a1,x92531),x92532),x92533),f341(f341(f11(a1,x92531),x92534),x92535))+P85(f341(f341(f241(a1),f2(a1)),f524(x92532,x92534,x92533,x92535,x92531))) % 19.23/19.05 [9254]~E(x92543,x92545)+~P68(x92541)+~P71(x92541)+~P37(x92543)+E(f341(f341(f8(a1,x92541),x92542),x92543),f341(f341(f8(a1,x92541),x92544),x92545))+P85(f341(f341(f241(a1),f2(a1)),f528(x92542,x92544,x92543,x92545,x92541))) % 19.23/19.05 [9420]~E(x94205,x94203)+~P68(x94201)+~P71(x94201)+~P37(x94205)+~E(f341(x94202,f524(x94204,x94202,x94205,x94203,x94201)),f341(x94204,f524(x94204,x94202,x94205,x94203,x94201)))+E(f341(f341(f11(a1,x94201),x94202),x94203),f341(f341(f11(a1,x94201),x94204),x94205)) % 19.23/19.05 [9421]~E(x94215,x94213)+~P68(x94211)+~P71(x94211)+~P37(x94215)+~E(f341(x94212,f528(x94214,x94212,x94215,x94213,x94211)),f341(x94214,f528(x94214,x94212,x94215,x94213,x94211)))+E(f341(f341(f8(a1,x94211),x94212),x94213),f341(f341(f8(a1,x94211),x94214),x94215)) % 19.23/19.05 [9506]~P77(x95063)+E(f341(x95061,x95062),f2(x95063))+~E(f341(f341(f8(x95064,x95063),x95061),x95065),f2(x95063))+~P85(f341(f71(x95064),x95065))+P85(f341(f341(f343(x95064),f519(x95062,x95061,x95065,x95064,x95063)),x95065))+~P85(f341(f341(f343(x95064),x95062),x95065)) % 19.23/19.05 [9636]~P77(x96363)+E(f341(x96361,x96362),f2(x96363))+~E(f341(f341(f8(x96364,x96363),x96361),x96365),f2(x96363))+~P85(f341(f71(x96364),x96365))+~P85(f341(f341(f343(x96364),x96362),x96365))+~P85(f341(f341(f241(x96363),f2(x96363)),f341(x96361,f519(x96362,x96361,x96365,x96364,x96363)))) % 19.23/19.05 [8257]~P125(x82571)+~P85(f341(f341(f241(x82571),f2(x82571)),x82573))+~P85(f341(f341(f242(x82571),x82573),x82575))+~P85(f341(f341(f242(x82571),x82572),x82574))+~P85(f341(f341(f242(x82571),f2(x82571)),x82574))+P85(f341(f341(f242(x82571),f341(f341(f90(x82571),x82572),x82573)),f341(f341(f90(x82571),x82574),x82575))) % 19.23/19.05 [8258]~P125(x82581)+~P85(f341(f341(f241(x82581),f2(x82581)),x82583))+~P85(f341(f341(f241(x82581),f2(x82581)),x82582))+~P85(f341(f341(f242(x82581),x82583),x82585))+~P85(f341(f341(f242(x82581),x82582),x82584))+P85(f341(f341(f242(x82581),f341(f341(f90(x82581),x82582),x82583)),f341(f341(f90(x82581),x82584),x82585))) % 19.23/19.05 [8259]~P125(x82591)+~P85(f341(f341(f241(x82591),x82592),x82594))+~P85(f341(f341(f241(x82591),f2(x82591)),x82593))+~P85(f341(f341(f242(x82591),x82593),x82595))+~P85(f341(f341(f242(x82591),f2(x82591)),x82592))+P85(f341(f341(f242(x82591),f341(f341(f90(x82591),x82592),x82593)),f341(f341(f90(x82591),x82594),x82595))) % 19.23/19.05 [8260]~P125(x82601)+~P85(f341(f341(f241(x82601),x82603),x82605))+~P85(f341(f341(f241(x82601),f2(x82601)),x82602))+~P85(f341(f341(f242(x82601),x82602),x82604))+~P85(f341(f341(f242(x82601),f2(x82601)),x82603))+P85(f341(f341(f242(x82601),f341(f341(f90(x82601),x82602),x82603)),f341(f341(f90(x82601),x82604),x82605))) % 19.23/19.05 [8261]~P62(x82611)+~P85(f341(f341(f241(x82611),x82612),x82614))+~P85(f341(f341(f242(x82611),x82615),x82613))+~P85(f341(f341(f242(x82611),f2(x82611)),x82615))+~P85(f341(f341(f242(x82611),f2(x82611)),x82612))+P85(f341(f341(f242(x82611),f341(f341(f292(x82611),x82612),x82613)),f341(f341(f292(x82611),x82614),x82615))) % 19.23/19.05 [8262]~P62(x82621)+~P85(f341(f341(f241(x82621),x82625),x82623))+~P85(f341(f341(f241(x82621),f2(x82621)),x82622))+~P85(f341(f341(f242(x82621),x82622),x82624))+~P85(f341(f341(f242(x82621),f2(x82621)),x82625))+P85(f341(f341(f242(x82621),f341(f341(f292(x82621),x82622),x82623)),f341(f341(f292(x82621),x82624),x82625))) % 19.23/19.05 [8263]~P133(x82631)+~P85(f341(f341(f241(x82631),x82633),x82635))+~P85(f341(f341(f241(x82631),x82632),x82634))+~P85(f341(f341(f241(x82631),f2(x82631)),x82633))+~P85(f341(f341(f241(x82631),f2(x82631)),x82634))+P85(f341(f341(f241(x82631),f341(f341(f90(x82631),x82632),x82633)),f341(f341(f90(x82631),x82634),x82635))) % 19.23/19.05 [8264]~P133(x82641)+~P85(f341(f341(f241(x82641),x82643),x82645))+~P85(f341(f341(f241(x82641),x82642),x82644))+~P85(f341(f341(f241(x82641),f2(x82641)),x82643))+~P85(f341(f341(f241(x82641),f2(x82641)),x82642))+P85(f341(f341(f241(x82641),f341(f341(f90(x82641),x82642),x82643)),f341(f341(f90(x82641),x82644),x82645))) % 19.23/19.05 [8265]~P62(x82651)+~P85(f341(f341(f242(x82651),f2(x82651)),x82655))+~P85(f341(f341(f241(x82651),x82655),x82653))+~P85(f341(f341(f241(x82651),x82652),x82654))+~P85(f341(f341(f241(x82651),f2(x82651)),x82652))+P85(f341(f341(f241(x82651),f341(f341(f292(x82651),x82652),x82653)),f341(f341(f292(x82651),x82654),x82655))) % 19.23/19.05 [9544]~P68(x95445)+~P80(x95445)+E(x95441,f185(f864(x95442,a850)))+~P85(f341(f71(x95442),x95441))+P85(f341(f341(f343(x95442),f526(x95443,x95444,x95441,x95442,x95445)),x95441))+P85(f341(f341(f242(x95445),f341(f341(f8(x95442,x95445),x95444),x95441)),f341(f341(f8(x95442,x95445),x95443),x95441))) % 19.23/19.05 [9656]~P68(x96561)+~P78(x96561)+~P85(f341(f71(x96562),x96565))+~P85(f341(f341(f241(x96561),f2(x96561)),f341(x96563,f520(x96563,x96564,x96565,x96562,x96561))))+P85(f341(f341(f241(x96561),f341(f341(f8(x96562,x96561),x96563),x96564)),f341(f341(f8(x96562,x96561),x96563),x96565)))+~P85(f341(f341(f241(f864(x96562,a850)),x96564),x96565)) % 19.23/19.05 [9821]~P68(x98213)+~P80(x98213)+E(x98211,f185(f864(x98212,a850)))+~P85(f341(f71(x98212),x98211))+~P85(f341(f341(f242(x98213),f341(x98214,f526(x98215,x98214,x98211,x98212,x98213))),f341(x98215,f526(x98215,x98214,x98211,x98212,x98213))))+P85(f341(f341(f242(x98213),f341(f341(f8(x98212,x98213),x98214),x98211)),f341(f341(f8(x98212,x98213),x98215),x98211))) % 19.23/19.05 [6974]~P18(x69742,x69745,x69744)+E(x69741,f185(f864(x69742,a850)))+E(x69743,f185(f864(x69742,a850)))+~P85(f341(f71(x69742),x69741))+~P85(f341(f71(x69742),x69743))+E(f341(x69744,f341(f341(f110(f864(x69742,a850)),x69743),x69741)),f341(f341(x69745,f341(x69744,x69743)),f341(x69744,x69741))) % 19.23/19.05 [7581]~P143(x75811,x75813,x75814)+P85(f341(x75811,x75812))+~P85(f341(f341(f242(a1),x75814),f2(a1)))+~P85(f341(f341(f241(a1),x75815),f2(a1)))+~E(x75813,f341(f341(f89(a1),f341(f341(f90(a1),x75814),x75812)),x75815))+~P85(f341(f341(f242(a1),x75814),x75815)) % 19.23/19.05 [7582]~P142(x75821,x75823,x75824)+P85(f341(x75821,x75822))+~P85(f341(f341(f242(a1),x75824),f2(a1)))+~P85(f341(f341(f241(a1),x75822),f2(a1)))+~E(x75823,f341(f341(f89(a1),f341(f341(f90(a1),x75824),x75825)),x75822))+~P85(f341(f341(f242(a1),x75824),x75822)) % 19.23/19.05 [7625]~P143(x76251,x76253,x76254)+P85(f341(x76251,x76252))+~E(x76253,f341(f341(f89(a1),f341(f341(f90(a1),x76254),x76252)),x76255))+~P85(f341(f341(f242(a1),f2(a1)),x76254))+~P85(f341(f341(f241(a1),f2(a1)),x76255))+~P85(f341(f341(f242(a1),x76255),x76254)) % 19.23/19.05 [7626]~P142(x76261,x76263,x76264)+P85(f341(x76261,x76262))+~E(x76263,f341(f341(f89(a1),f341(f341(f90(a1),x76264),x76265)),x76262))+~P85(f341(f341(f242(a1),f2(a1)),x76264))+~P85(f341(f341(f241(a1),f2(a1)),x76262))+~P85(f341(f341(f242(a1),x76262),x76264)) % 19.23/19.05 [8547]P85(f341(f341(x85471,x85472),x85473))+~P85(f341(f341(x85471,f341(f341(f51(a1),x85474),x85475)),f60(a1,x85474,x85475)))+~P85(f341(f341(f242(a1),x85475),f2(a1)))+~P85(f341(f341(f241(a1),x85473),f2(a1)))+~E(x85474,f341(f341(f89(a1),f341(f341(f90(a1),x85475),x85472)),x85473))+~P85(f341(f341(f242(a1),x85475),x85473)) % 19.23/19.05 [8554]P85(f341(f341(x85541,x85542),x85543))+~P85(f341(f341(x85541,f341(f341(f51(a1),x85544),x85545)),f60(a1,x85544,x85545)))+~E(x85544,f341(f341(f89(a1),f341(f341(f90(a1),x85545),x85542)),x85543))+~P85(f341(f341(f242(a1),f2(a1)),x85545))+~P85(f341(f341(f241(a1),f2(a1)),x85543))+~P85(f341(f341(f242(a1),x85543),x85545)) % 19.23/19.05 [8774]E(x87741,x87742)+~P53(x87743,x87745,x87744)+~P85(f341(f341(f343(x87743),x87742),x87745))+~P85(f341(f341(f343(x87743),x87741),x87745))+P85(f341(f341(f343(f863(x87743,x87743)),f341(f341(f250(x87743,x87743),x87741),x87742)),x87744))+P85(f341(f341(f343(f863(x87743,x87743)),f341(f341(f250(x87743,x87743),x87742),x87741)),x87744)) % 19.23/19.05 [9575]~P68(x95755)+~P78(x95755)+~P85(f341(f71(x95751),x95754))+P85(f341(f341(f241(x95755),f341(f341(f8(x95751,x95755),x95752),x95753)),f341(f341(f8(x95751,x95755),x95752),x95754)))+~P85(f341(f341(f241(f864(x95751,a850)),x95753),x95754))+P85(f341(f341(f343(x95751),f520(x95752,x95753,x95754,x95751,x95755)),f341(f341(f3(f864(x95751,a850)),x95754),x95753))) % 19.23/19.05 [9663]E(x96631,f185(f864(x96632,a850)))+~P85(f341(f71(x96632),x96633))+~P85(f341(f71(x96632),x96631))+P85(f341(f341(f343(f863(f864(x96632,a850),f864(x96632,a850))),f341(f341(f250(f864(x96632,a850),f864(x96632,a850)),x96633),x96631)),f334(x96632,x96634)))+~P85(f341(f341(f343(x96632),x96635),x96631))+~P85(f341(f341(f343(f863(x96632,x96632)),f341(f341(f250(x96632,x96632),f545(x96634,x96631,x96633,x96632)),x96635)),x96634)) % 19.23/19.05 [9664]E(x96641,f185(f864(x96642,a850)))+~P85(f341(f71(x96642),x96643))+~P85(f341(f71(x96642),x96641))+P85(f341(f341(f343(f863(f864(x96642,a850),f864(x96642,a850))),f341(f341(f250(f864(x96642,a850),f864(x96642,a850)),x96643),x96641)),f334(x96642,x96644)))+~P85(f341(f341(f343(x96642),x96645),x96641))+~P85(f341(f341(f343(f863(x96642,x96642)),f341(f341(f250(x96642,x96642),f632(x96644,x96641,x96643,x96642)),x96645)),x96644)) % 19.23/19.05 [9824]~P77(x98241)+~E(f341(f341(f8(x98245,x98241),x98242),x98246),x98244)+~P85(f341(f71(x98245),x98246))+P85(f341(f341(f343(x98245),f521(x98243,x98244,x98242,x98246,x98245,x98241)),x98246))+P85(f341(f341(f241(x98241),f341(x98242,x98243)),x98244))+~P85(f341(f341(f343(x98245),x98243),x98246)) % 19.23/19.05 [9880]~P77(x98801)+~E(f341(f341(f8(x98805,x98801),x98802),x98806),x98804)+~P85(f341(f71(x98805),x98806))+~P85(f341(f341(f343(x98805),x98803),x98806))+~P85(f341(f341(f241(x98801),f2(x98801)),f341(x98802,f521(x98803,x98804,x98802,x98806,x98805,x98801))))+P85(f341(f341(f241(x98801),f341(x98802,x98803)),x98804)) % 19.23/19.05 [9997]~E(x99975,x99978)+~E(x99974,x99977)+~P68(x99972)+~P103(x99971)+E(f341(f341(f8(x99971,x99972),x99973),f341(f303(x99971,x99974),x99975)),f341(f341(f8(x99971,x99972),x99976),f341(f303(x99971,x99977),x99978)))+P85(f341(f341(f241(x99971),x99974),f641(x99973,x99976,x99975,x99978,x99974,x99977,x99971,x99972))) % 19.23/19.05 [10012]~E(x100127,x100124)+~E(x100128,x100125)+~P68(x100122)+~P103(x100121)+~E(f341(x100123,f641(x100126,x100123,x100128,x100125,x100127,x100124,x100121,x100122)),f341(x100126,f641(x100126,x100123,x100128,x100125,x100127,x100124,x100121,x100122)))+E(f341(f341(f8(x100121,x100122),x100123),f341(f303(x100121,x100124),x100125)),f341(f341(f8(x100121,x100122),x100126),f341(f303(x100121,x100127),x100128))) % 19.23/19.05 [10015]~E(x100154,x100157)+~E(x100155,x100158)+~P68(x100152)+~P103(x100151)+E(f341(f341(f8(x100151,x100152),x100153),f341(f303(x100151,x100154),x100155)),f341(f341(f8(x100151,x100152),x100156),f341(f303(x100151,x100157),x100158)))+P85(f341(f341(f242(x100151),f641(x100153,x100156,x100155,x100158,x100154,x100157,x100151,x100152)),x100155)) % 19.23/19.05 [9668]~P9(x96685,x96689,x96686)+~P9(x96681,x966810,x96683)+~P14(x96681,x96685,f864(x96682,a850),x96683,x96686,x96688)+~P85(f341(f341(f343(x96685),x96687),x96689))+~P85(f341(f341(f343(x96681),x96684),x966810))+E(f341(f341(f54(x96681,f864(x96682,a850)),f341(f286(x96681,x96681,x96683),f341(f341(f311(x96681),x96684),f185(f864(x96681,a850))))),f341(f341(f10(f864(x96685,f864(x96682,a850)),f864(x96682,a850),x96681),f341(f54(x96685,f864(x96682,a850)),f341(f286(x96685,x96685,x96686),f341(f341(f311(x96685),x96687),f185(f864(x96685,a850)))))),x96688)),f341(f341(x96688,x96684),x96687)) % 19.23/19.05 [5476]~P101(x54763)+~P15(x54763,x54762)+~P15(x54763,x54761)+E(x54761,x54762)+~E(f341(f163(x54763),x54761),f341(f163(x54763),x54762))+~P85(f341(f134(x54763),x54762))+~P85(f341(f134(x54763),x54761)) % 19.23/19.05 [4832]~P124(x48322)+~P129(x48322)+~P140(x48322)+~P106(x48322)+~E(x48323,f2(x48322))+E(x48321,f2(a857))+E(f341(f341(f251(x48322),x48323),x48321),f2(x48322)) % 19.23/19.05 [9013]E(x90131,f2(a857))+~E(x90132,f341(f341(f89(a857),f341(f341(f90(a857),f341(f249(a857,a857),x90133)),x90131)),f341(f259(a857,a857),x90133)))+P85(f341(f63(x90132,x90131),x90133))+~P85(f341(f341(f241(a857),f341(f259(a857,a857),x90133)),f2(a857)))+~P85(f341(f341(f241(a857),f2(a857)),f341(f259(a857,a857),x90133)))+~P85(f341(f341(f242(a857),x90131),f341(f259(a857,a857),x90133)))+~P85(f341(f341(f242(a857),f341(f259(a857,a857),x90133)),x90131)) % 19.23/19.05 [9022]~E(f341(f249(a857,a857),x90223),f2(a857))+~E(x90221,f341(f341(f89(a857),f341(f341(f90(a857),f341(f249(a857,a857),x90223)),x90222)),f341(f259(a857,a857),x90223)))+P85(f341(f63(x90221,x90222),x90223))+~P85(f341(f341(f241(a857),f341(f259(a857,a857),x90223)),f2(a857)))+~P85(f341(f341(f241(a857),f2(a857)),f341(f259(a857,a857),x90223)))+~P85(f341(f341(f242(a857),x90222),f341(f259(a857,a857),x90223)))+~P85(f341(f341(f242(a857),f341(f259(a857,a857),x90223)),x90222)) % 19.23/19.05 [7940]~P65(x79402)+E(x79401,f185(f864(x79402,a850)))+E(x79403,f185(f864(x79402,a850)))+~P85(f341(f71(x79402),x79401))+~P85(f341(f71(x79402),x79403))+~E(f341(f341(f111(f864(x79402,a850)),x79403),x79401),f185(f864(x79402,a850)))+E(f341(f341(f90(x79402),f341(f73(x79402,f90(x79402)),x79403)),f341(f73(x79402,f90(x79402)),x79401)),f341(f73(x79402,f90(x79402)),f341(f341(f110(f864(x79402,a850)),x79403),x79401))) % 19.23/19.05 [7719]E(x77191,f2(a1))+E(f341(f341(f51(a1),x77192),x77191),x77193)+~P85(f341(f341(f241(a1),x77194),f2(a1)))+~E(x77192,f341(f341(f89(a1),f341(f341(f90(a1),x77191),x77193)),x77194))+~P85(f341(f341(f241(a1),f2(a1)),x77194))+~P85(f341(f341(f242(a1),x77194),x77191))+~P85(f341(f341(f242(a1),x77191),x77194)) % 19.23/19.05 [7725]E(f60(a1,x77252,x77251),x77253)+E(x77251,f2(a1))+~P85(f341(f341(f241(a1),x77253),f2(a1)))+~E(x77252,f341(f341(f89(a1),f341(f341(f90(a1),x77251),x77254)),x77253))+~P85(f341(f341(f241(a1),f2(a1)),x77253))+~P85(f341(f341(f242(a1),x77253),x77251))+~P85(f341(f341(f242(a1),x77251),x77253)) % 19.23/19.05 [6749]~P4(x67492)+E(x67491,f2(x67492))+E(x67493,f2(x67492))+~E(f341(f341(f51(x67492),x67494),x67493),f341(f341(f51(x67492),x67495),x67491))+E(f341(f341(f90(x67492),x67494),x67491),f341(f341(f90(x67492),x67493),x67495))+~P85(f341(f341(f288(x67492),x67491),x67495))+~P85(f341(f341(f288(x67492),x67493),x67494)) % 19.23/19.05 [6750]~P4(x67502)+E(x67501,f2(x67502))+E(x67503,f2(x67502))+~E(f341(f341(f90(x67502),x67504),x67503),f341(f341(f90(x67502),x67501),x67505))+E(f341(f341(f51(x67502),x67504),x67501),f341(f341(f51(x67502),x67505),x67503))+~P85(f341(f341(f288(x67502),x67501),x67504))+~P85(f341(f341(f288(x67502),x67503),x67505)) % 19.23/19.05 [7634]~P19(x76342,x76345,x76344)+E(x76341,f185(f864(x76342,a850)))+E(x76343,f185(f864(x76342,a850)))+~P85(f341(f71(x76342),x76341))+~P85(f341(f71(x76342),x76343))+~E(f341(f341(f111(f864(x76342,a850)),x76343),x76341),f185(f864(x76342,a850)))+E(f341(x76344,f341(f341(f110(f864(x76342,a850)),x76343),x76341)),f341(f341(x76345,f341(x76344,x76343)),f341(x76344,x76341))) % 19.23/19.05 [9226]~P26(x92263,x92261,x92265,x92264)+~P26(x92261,x92263,x92266,x92262)+E(f341(f50(x92261),x92262),f341(f50(x92263),x92264))+~P85(f341(f71(x92263),x92264))+~P85(f341(f71(x92261),x92262))+~P85(f341(f341(f241(f864(x92263,a850)),f341(f312(x92261,x92263,x92266),x92262)),x92264))+~P85(f341(f341(f241(f864(x92261,a850)),f341(f312(x92263,x92261,x92265),x92264)),x92262)) % 19.23/19.05 [9175]~P85(f341(f341(f242(a1),f341(f341(f89(a1),f341(f341(f90(a1),x91755),x91751)),x91756)),f2(a1)))+~E(f341(f341(f89(a1),f341(f341(f90(a1),x91753),x91752)),x91754),f341(f341(f89(a1),f341(f341(f90(a1),x91755),x91751)),x91756))+~P85(f341(f341(f242(a1),f2(a1)),x91755))+~P85(f341(f341(f241(a1),f2(a1)),x91756))+~P85(f341(f341(f242(a1),x91754),x91753))+~P85(f341(f341(f241(a1),x91755),x91753))+P85(f341(f341(f241(a1),x91751),x91752)) % 19.23/19.05 [8964]~E(f341(f341(f89(a1),f341(f341(f90(a1),x89643),x89641)),x89644),f341(f341(f89(a1),f341(f341(f90(a1),x89645),x89642)),x89646))+~P85(f341(f341(f242(a1),f2(a1)),x89645))+~P85(f341(f341(f241(a1),f2(a1)),x89644))+~P85(f341(f341(f242(a1),x89646),x89645))+~P85(f341(f341(f241(a1),x89645),x89643))+P85(f341(f341(f241(a1),x89641),x89642))+~P85(f341(f341(f241(a1),f2(a1)),f341(f341(f89(a1),f341(f341(f90(a1),x89645),x89642)),x89646))) % 19.23/19.05 [9131]~P126(x91311)+~E(f341(f341(f89(x91311),x91312),x91314),f87(x91311))+~P85(f341(f341(f241(x91311),f2(x91311)),x91314))+~P85(f341(f341(f241(x91311),f2(x91311)),x91312))+~P85(f341(f341(f242(x91311),x91315),x91316))+~P85(f341(f341(f242(x91311),x91313),x91316))+P85(f341(f341(f242(x91311),f341(f341(f89(x91311),f341(f341(f90(x91311),x91312),x91313)),f341(f341(f90(x91311),x91314),x91315))),x91316)) % 19.23/19.05 [9132]~P128(x91321)+~E(f341(f341(f89(x91321),x91322),x91324),f87(x91321))+~P85(f341(f341(f241(x91321),x91325),x91326))+~P85(f341(f341(f241(x91321),x91323),x91326))+~P85(f341(f341(f241(x91321),f2(x91321)),x91324))+~P85(f341(f341(f241(x91321),f2(x91321)),x91322))+P85(f341(f341(f241(x91321),f341(f341(f89(x91321),f341(f341(f90(x91321),x91322),x91323)),f341(f341(f90(x91321),x91324),x91325))),x91326)) % 19.23/19.05 [9920]~P9(x99207,x99206,x99205)+E(x99201,x99202)+~P13(x99207,f864(x99204,a850),x99205,x99203)+E(f341(x99203,f428(x99201,x99202,x99203,x99204,x99205,x99206,x99207)),f341(x99203,f426(x99201,x99202,x99203,x99204,x99205,x99206,x99207)))+~E(f341(f341(f54(x99207,f864(x99204,a850)),x99201),x99203),f341(f341(f54(x99207,f864(x99204,a850)),x99202),x99203))+~P85(f341(f341(f343(f864(x99207,a850)),x99202),f341(f341(f69(x99207),x99206),x99205)))+~P85(f341(f341(f343(f864(x99207,a850)),x99201),f341(f341(f69(x99207),x99206),x99205))) % 19.23/19.05 [9961]~P9(x99613,x99617,x99616)+E(x99611,x99612)+~P13(x99613,f864(x99615,a850),x99616,x99614)+~E(f341(f341(f54(x99613,f864(x99615,a850)),x99611),x99614),f341(f341(f54(x99613,f864(x99615,a850)),x99612),x99614))+P85(f341(f341(f343(x99613),f426(x99611,x99612,x99614,x99615,x99616,x99617,x99613)),x99617))+~P85(f341(f341(f343(f864(x99613,a850)),x99612),f341(f341(f69(x99613),x99617),x99616)))+~P85(f341(f341(f343(f864(x99613,a850)),x99611),f341(f341(f69(x99613),x99617),x99616))) % 19.23/19.05 [9962]~P9(x99623,x99627,x99626)+E(x99621,x99622)+~P13(x99623,f864(x99625,a850),x99626,x99624)+~E(f341(f341(f54(x99623,f864(x99625,a850)),x99621),x99624),f341(f341(f54(x99623,f864(x99625,a850)),x99622),x99624))+P85(f341(f341(f343(x99623),f428(x99621,x99622,x99624,x99625,x99626,x99627,x99623)),x99627))+~P85(f341(f341(f343(f864(x99623,a850)),x99622),f341(f341(f69(x99623),x99627),x99626)))+~P85(f341(f341(f343(f864(x99623,a850)),x99621),f341(f341(f69(x99623),x99627),x99626))) % 19.23/19.05 [10028]E(x100281,x100282)+~P9(x100283,x100286,x100287)+~P13(x100283,f864(x100284,a850),x100287,x100285)+~E(f341(f341(f54(x100283,f864(x100284,a850)),x100281),x100285),f341(f341(f54(x100283,f864(x100284,a850)),x100282),x100285))+~P85(f341(f341(f343(f863(x100283,x100283)),f341(f341(f250(x100283,x100283),f426(x100281,x100282,x100285,x100284,x100287,x100286,x100283)),f428(x100281,x100282,x100285,x100284,x100287,x100286,x100283))),x100287))+~P85(f341(f341(f343(f864(x100283,a850)),x100282),f341(f341(f69(x100283),x100286),x100287)))+~P85(f341(f341(f343(f864(x100283,a850)),x100281),f341(f341(f69(x100283),x100286),x100287))) % 19.23/19.05 [8963]~P9(x89631,x89637,x89634)+~E(x89635,x89636)+~P85(f341(f341(f343(x89631),x89633),x89636))+~P85(f341(f341(f343(x89631),x89632),x89635))+~P85(f341(f341(f343(f864(x89631,a850)),x89636),f341(f341(f69(x89631),x89637),x89634)))+~P85(f341(f341(f343(f864(x89631,a850)),x89635),f341(f341(f69(x89631),x89637),x89634)))+P85(f341(f341(f343(f863(x89631,x89631)),f341(f341(f250(x89631,x89631),x89632),x89633)),x89634)) % 19.23/19.05 [9097]E(x90971,x90972)+~P9(x90973,x90974,x90975)+~P85(f341(f341(f343(x90973),x90976),x90972))+~P85(f341(f341(f343(x90973),x90977),x90971))+~P85(f341(f341(f343(f864(x90973,a850)),x90972),f341(f341(f69(x90973),x90974),x90975)))+~P85(f341(f341(f343(f864(x90973,a850)),x90971),f341(f341(f69(x90973),x90974),x90975)))+~P85(f341(f341(f343(f863(x90973,x90973)),f341(f341(f250(x90973,x90973),x90977),x90976)),x90975)) % 19.23/19.05 [10046]~P9(x100469,x100468,x100467)+~P9(x100461,x1004611,x1004610)+~P14(x100461,x100469,f864(x100466,a850),x1004610,x100467,x100465)+P85(f341(f341(f343(x100461),f430(x100462,x100463,x100464,x100465,x100466,x100467,x100468,x100469,x1004610,x1004611,x100461)),x1004611))+~P85(f341(f341(f343(f864(x100469,a850)),x100463),f341(f341(f69(x100469),x100468),x100467)))+~P85(f341(f341(f343(f864(x100461,a850)),x100464),f341(f341(f69(x100461),x1004611),x1004610)))+P85(f341(f341(f343(f864(x100466,a850)),f341(f341(f54(x100461,f864(x100466,a850)),x100464),f341(f341(f10(f864(x100469,f864(x100466,a850)),f864(x100466,a850),x100461),f341(f54(x100469,f864(x100466,a850)),x100463)),x100465))),x100462)) % 19.23/19.05 [10047]~P9(x1004711,x1004710,x100479)+~P9(x100471,x100478,x100477)+~P14(x1004711,x100471,f864(x100476,a850),x100479,x100477,x100475)+P85(f341(f341(f343(x100471),f431(x100472,x100473,x100474,x100475,x100476,x100477,x100478,x100471,x100479,x1004710,x1004711)),x100478))+~P85(f341(f341(f343(f864(x1004711,a850)),x100474),f341(f341(f69(x1004711),x1004710),x100479)))+~P85(f341(f341(f343(f864(x100471,a850)),x100473),f341(f341(f69(x100471),x100478),x100477)))+P85(f341(f341(f343(f864(x100476,a850)),f341(f341(f54(x1004711,f864(x100476,a850)),x100474),f341(f341(f10(f864(x100471,f864(x100476,a850)),f864(x100476,a850),x1004711),f341(f54(x100471,f864(x100476,a850)),x100473)),x100475))),x100472)) % 19.23/19.05 [10048]~P9(x100482,x100488,x100489)+~P9(x100484,x1004810,x1004811)+~P14(x100482,x100484,f864(x100481,a850),x100489,x1004811,x100486)+~P85(f341(f341(f343(f864(x100482,a850)),x100483),f341(f341(f69(x100482),x100488),x100489)))+~P85(f341(f341(f343(f864(x100484,a850)),x100485),f341(f341(f69(x100484),x1004810),x1004811)))+~P85(f341(f341(f343(f864(x100481,a850)),f341(f341(x100486,f430(x100487,x100485,x100483,x100486,x100481,x1004811,x1004810,x100484,x100489,x100488,x100482)),f431(x100487,x100485,x100483,x100486,x100481,x1004811,x1004810,x100484,x100489,x100488,x100482))),x100487))+P85(f341(f341(f343(f864(x100481,a850)),f341(f341(f54(x100482,f864(x100481,a850)),x100483),f341(f341(f10(f864(x100484,f864(x100481,a850)),f864(x100481,a850),x100482),f341(f54(x100484,f864(x100481,a850)),x100485)),x100486))),x100487)) % 19.23/19.05 [9006]E(x90061,x90062)+~P101(x90064)+~P26(x90063,x90064,x90065,f341(f341(f110(f864(x90063,a850)),f341(f163(x90063),x90061)),f341(f163(x90063),x90062)))+~E(f341(f163(x90063),x90061),f341(f163(x90063),x90062))+~P15(x90064,f341(f341(f149(x90063,x90064),x90065),x90062))+~P15(x90064,f341(f341(f149(x90063,x90064),x90065),x90061))+~P85(f341(f134(x90064),f341(f341(f149(x90063,x90064),x90065),x90062)))+~P85(f341(f134(x90064),f341(f341(f149(x90063,x90064),x90065),x90061))) % 19.23/19.05 %EqnAxiom % 19.23/19.05 [1]E(x11,x11) % 19.23/19.05 [2]E(x22,x21)+~E(x21,x22) % 19.23/19.05 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 19.23/19.05 [4]~E(x41,x42)+E(f2(x41),f2(x42)) % 19.23/19.05 [5]~E(x51,x52)+E(f3(x51),f3(x52)) % 19.23/19.05 [6]~E(x61,x62)+E(f109(x61),f109(x62)) % 19.23/19.05 [7]~E(x71,x72)+E(f36(x71),f36(x72)) % 19.23/19.05 [8]~E(x81,x82)+E(f341(x81,x83),f341(x82,x83)) % 19.23/19.05 [9]~E(x91,x92)+E(f341(x93,x91),f341(x93,x92)) % 19.23/19.05 [10]~E(x101,x102)+E(f93(x101),f93(x102)) % 19.23/19.05 [11]~E(x111,x112)+E(f9(x111,x113,x114),f9(x112,x113,x114)) % 19.23/19.05 [12]~E(x121,x122)+E(f9(x123,x121,x124),f9(x123,x122,x124)) % 19.23/19.05 [13]~E(x131,x132)+E(f9(x133,x134,x131),f9(x133,x134,x132)) % 19.23/19.05 [14]~E(x141,x142)+E(f250(x141,x143),f250(x142,x143)) % 19.23/19.05 [15]~E(x151,x152)+E(f250(x153,x151),f250(x153,x152)) % 19.23/19.05 [16]~E(x161,x162)+E(f8(x161,x163),f8(x162,x163)) % 19.23/19.05 [17]~E(x171,x172)+E(f8(x173,x171),f8(x173,x172)) % 19.23/19.05 [18]~E(x181,x182)+E(f185(x181),f185(x182)) % 19.23/19.05 [19]~E(x191,x192)+E(f431(x191,x193,x194,x195,x196,x197,x198,x199,x1910,x1911,x1912),f431(x192,x193,x194,x195,x196,x197,x198,x199,x1910,x1911,x1912)) % 19.23/19.05 [20]~E(x201,x202)+E(f431(x203,x201,x204,x205,x206,x207,x208,x209,x2010,x2011,x2012),f431(x203,x202,x204,x205,x206,x207,x208,x209,x2010,x2011,x2012)) % 19.23/19.05 [21]~E(x211,x212)+E(f431(x213,x214,x211,x215,x216,x217,x218,x219,x2110,x2111,x2112),f431(x213,x214,x212,x215,x216,x217,x218,x219,x2110,x2111,x2112)) % 19.23/19.05 [22]~E(x221,x222)+E(f431(x223,x224,x225,x221,x226,x227,x228,x229,x2210,x2211,x2212),f431(x223,x224,x225,x222,x226,x227,x228,x229,x2210,x2211,x2212)) % 19.23/19.05 [23]~E(x231,x232)+E(f431(x233,x234,x235,x236,x231,x237,x238,x239,x2310,x2311,x2312),f431(x233,x234,x235,x236,x232,x237,x238,x239,x2310,x2311,x2312)) % 19.23/19.05 [24]~E(x241,x242)+E(f431(x243,x244,x245,x246,x247,x241,x248,x249,x2410,x2411,x2412),f431(x243,x244,x245,x246,x247,x242,x248,x249,x2410,x2411,x2412)) % 19.23/19.05 [25]~E(x251,x252)+E(f431(x253,x254,x255,x256,x257,x258,x251,x259,x2510,x2511,x2512),f431(x253,x254,x255,x256,x257,x258,x252,x259,x2510,x2511,x2512)) % 19.23/19.05 [26]~E(x261,x262)+E(f431(x263,x264,x265,x266,x267,x268,x269,x261,x2610,x2611,x2612),f431(x263,x264,x265,x266,x267,x268,x269,x262,x2610,x2611,x2612)) % 19.23/19.05 [27]~E(x271,x272)+E(f431(x273,x274,x275,x276,x277,x278,x279,x2710,x271,x2711,x2712),f431(x273,x274,x275,x276,x277,x278,x279,x2710,x272,x2711,x2712)) % 19.23/19.05 [28]~E(x281,x282)+E(f431(x283,x284,x285,x286,x287,x288,x289,x2810,x2811,x281,x2812),f431(x283,x284,x285,x286,x287,x288,x289,x2810,x2811,x282,x2812)) % 19.23/19.05 [29]~E(x291,x292)+E(f431(x293,x294,x295,x296,x297,x298,x299,x2910,x2911,x2912,x291),f431(x293,x294,x295,x296,x297,x298,x299,x2910,x2911,x2912,x292)) % 19.23/19.05 [30]~E(x301,x302)+E(f240(x301),f240(x302)) % 19.23/19.05 [31]~E(x311,x312)+E(f110(x311),f110(x312)) % 19.23/19.05 [32]~E(x321,x322)+E(f245(x321),f245(x322)) % 19.23/19.05 [33]~E(x331,x332)+E(f111(x331),f111(x332)) % 19.23/19.05 [34]~E(x341,x342)+E(f112(x341),f112(x342)) % 19.23/19.05 [35]~E(x351,x352)+E(f41(x351),f41(x352)) % 19.23/19.05 [36]~E(x361,x362)+E(f10(x361,x363,x364),f10(x362,x363,x364)) % 19.23/19.05 [37]~E(x371,x372)+E(f10(x373,x371,x374),f10(x373,x372,x374)) % 19.23/19.05 [38]~E(x381,x382)+E(f10(x383,x384,x381),f10(x383,x384,x382)) % 19.23/19.05 [39]~E(x391,x392)+E(f87(x391),f87(x392)) % 19.23/19.05 [40]~E(x401,x402)+E(f430(x401,x403,x404,x405,x406,x407,x408,x409,x4010,x4011,x4012),f430(x402,x403,x404,x405,x406,x407,x408,x409,x4010,x4011,x4012)) % 19.23/19.05 [41]~E(x411,x412)+E(f430(x413,x411,x414,x415,x416,x417,x418,x419,x4110,x4111,x4112),f430(x413,x412,x414,x415,x416,x417,x418,x419,x4110,x4111,x4112)) % 19.23/19.05 [42]~E(x421,x422)+E(f430(x423,x424,x421,x425,x426,x427,x428,x429,x4210,x4211,x4212),f430(x423,x424,x422,x425,x426,x427,x428,x429,x4210,x4211,x4212)) % 19.23/19.05 [43]~E(x431,x432)+E(f430(x433,x434,x435,x431,x436,x437,x438,x439,x4310,x4311,x4312),f430(x433,x434,x435,x432,x436,x437,x438,x439,x4310,x4311,x4312)) % 19.23/19.05 [44]~E(x441,x442)+E(f430(x443,x444,x445,x446,x441,x447,x448,x449,x4410,x4411,x4412),f430(x443,x444,x445,x446,x442,x447,x448,x449,x4410,x4411,x4412)) % 19.23/19.05 [45]~E(x451,x452)+E(f430(x453,x454,x455,x456,x457,x451,x458,x459,x4510,x4511,x4512),f430(x453,x454,x455,x456,x457,x452,x458,x459,x4510,x4511,x4512)) % 19.23/19.05 [46]~E(x461,x462)+E(f430(x463,x464,x465,x466,x467,x468,x461,x469,x4610,x4611,x4612),f430(x463,x464,x465,x466,x467,x468,x462,x469,x4610,x4611,x4612)) % 19.23/19.05 [47]~E(x471,x472)+E(f430(x473,x474,x475,x476,x477,x478,x479,x471,x4710,x4711,x4712),f430(x473,x474,x475,x476,x477,x478,x479,x472,x4710,x4711,x4712)) % 19.23/19.05 [48]~E(x481,x482)+E(f430(x483,x484,x485,x486,x487,x488,x489,x4810,x481,x4811,x4812),f430(x483,x484,x485,x486,x487,x488,x489,x4810,x482,x4811,x4812)) % 19.23/19.05 [49]~E(x491,x492)+E(f430(x493,x494,x495,x496,x497,x498,x499,x4910,x4911,x491,x4912),f430(x493,x494,x495,x496,x497,x498,x499,x4910,x4911,x492,x4912)) % 19.23/19.05 [50]~E(x501,x502)+E(f430(x503,x504,x505,x506,x507,x508,x509,x5010,x5011,x5012,x501),f430(x503,x504,x505,x506,x507,x508,x509,x5010,x5011,x5012,x502)) % 19.23/19.05 [51]~E(x511,x512)+E(f120(x511),f120(x512)) % 19.23/19.05 [52]~E(x521,x522)+E(f343(x521),f343(x522)) % 19.23/19.05 [53]~E(x531,x532)+E(f864(x531,x533),f864(x532,x533)) % 19.23/19.05 [54]~E(x541,x542)+E(f864(x543,x541),f864(x543,x542)) % 19.23/19.05 [55]~E(x551,x552)+E(f6(x551),f6(x552)) % 19.23/19.05 [56]~E(x561,x562)+E(f248(x561),f248(x562)) % 19.23/19.05 [57]~E(x571,x572)+E(f42(x571),f42(x572)) % 19.23/19.05 [58]~E(x581,x582)+E(f44(x581),f44(x582)) % 19.23/19.05 [59]~E(x591,x592)+E(f71(x591),f71(x592)) % 19.23/19.05 [60]~E(x601,x602)+E(f43(x601),f43(x602)) % 19.23/19.05 [61]~E(x611,x612)+E(f241(x611),f241(x612)) % 19.23/19.05 [62]~E(x621,x622)+E(f858(x621),f858(x622)) % 19.23/19.05 [63]~E(x631,x632)+E(f88(x631),f88(x632)) % 19.23/19.05 [64]~E(x641,x642)+E(f20(x641,x643,x644),f20(x642,x643,x644)) % 19.23/19.05 [65]~E(x651,x652)+E(f20(x653,x651,x654),f20(x653,x652,x654)) % 19.23/19.05 [66]~E(x661,x662)+E(f20(x663,x664,x661),f20(x663,x664,x662)) % 19.23/19.05 [67]~E(x671,x672)+E(f186(x671),f186(x672)) % 19.23/19.05 [68]~E(x681,x682)+E(f89(x681),f89(x682)) % 19.23/19.05 [69]~E(x691,x692)+E(f113(x691),f113(x692)) % 19.23/19.05 [70]~E(x701,x702)+E(f50(x701),f50(x702)) % 19.23/19.05 [71]~E(x711,x712)+E(f69(x711),f69(x712)) % 19.23/19.05 [72]~E(x721,x722)+E(f612(x721,x723,x724),f612(x722,x723,x724)) % 19.23/19.05 [73]~E(x731,x732)+E(f612(x733,x731,x734),f612(x733,x732,x734)) % 19.23/19.05 [74]~E(x741,x742)+E(f612(x743,x744,x741),f612(x743,x744,x742)) % 19.23/19.05 [75]~E(x751,x752)+E(f330(x751,x753),f330(x752,x753)) % 19.23/19.05 [76]~E(x761,x762)+E(f330(x763,x761),f330(x763,x762)) % 19.23/19.05 [77]~E(x771,x772)+E(f242(x771),f242(x772)) % 19.23/19.05 [78]~E(x781,x782)+E(f163(x781),f163(x782)) % 19.23/19.05 [79]~E(x791,x792)+E(f158(x791),f158(x792)) % 19.23/19.05 [80]~E(x801,x802)+E(f288(x801),f288(x802)) % 19.23/19.05 [81]~E(x811,x812)+E(f259(x811,x813),f259(x812,x813)) % 19.23/19.05 [82]~E(x821,x822)+E(f259(x823,x821),f259(x823,x822)) % 19.23/19.05 [83]~E(x831,x832)+E(f55(x831,x833),f55(x832,x833)) % 19.23/19.05 [84]~E(x841,x842)+E(f55(x843,x841),f55(x843,x842)) % 19.23/19.05 [85]~E(x851,x852)+E(f292(x851),f292(x852)) % 19.23/19.05 [86]~E(x861,x862)+E(f13(x861,x863,x864),f13(x862,x863,x864)) % 19.23/19.05 [87]~E(x871,x872)+E(f13(x873,x871,x874),f13(x873,x872,x874)) % 19.23/19.05 [88]~E(x881,x882)+E(f13(x883,x884,x881),f13(x883,x884,x882)) % 19.23/19.05 [89]~E(x891,x892)+E(f312(x891,x893,x894),f312(x892,x893,x894)) % 19.23/19.05 [90]~E(x901,x902)+E(f312(x903,x901,x904),f312(x903,x902,x904)) % 19.23/19.05 [91]~E(x911,x912)+E(f312(x913,x914,x911),f312(x913,x914,x912)) % 19.23/19.05 [92]~E(x921,x922)+E(f91(x921,x923),f91(x922,x923)) % 19.23/19.05 [93]~E(x931,x932)+E(f91(x933,x931),f91(x933,x932)) % 19.23/19.05 [94]~E(x941,x942)+E(f735(x941,x943,x944),f735(x942,x943,x944)) % 19.23/19.05 [95]~E(x951,x952)+E(f735(x953,x951,x954),f735(x953,x952,x954)) % 19.23/19.05 [96]~E(x961,x962)+E(f735(x963,x964,x961),f735(x963,x964,x962)) % 19.23/19.05 [97]~E(x971,x972)+E(f122(x971),f122(x972)) % 19.23/19.05 [98]~E(x981,x982)+E(f100(x981),f100(x982)) % 19.23/19.05 [99]~E(x991,x992)+E(f134(x991),f134(x992)) % 19.23/19.05 [100]~E(x1001,x1002)+E(f11(x1001,x1003),f11(x1002,x1003)) % 19.23/19.05 [101]~E(x1011,x1012)+E(f11(x1013,x1011),f11(x1013,x1012)) % 19.23/19.05 [102]~E(x1021,x1022)+E(f90(x1021),f90(x1022)) % 19.23/19.05 [103]~E(x1031,x1032)+E(f265(x1031),f265(x1032)) % 19.23/19.05 [104]~E(x1041,x1042)+E(f35(x1041,x1043,x1044),f35(x1042,x1043,x1044)) % 19.23/19.05 [105]~E(x1051,x1052)+E(f35(x1053,x1051,x1054),f35(x1053,x1052,x1054)) % 19.23/19.05 [106]~E(x1061,x1062)+E(f35(x1063,x1064,x1061),f35(x1063,x1064,x1062)) % 19.23/19.05 [107]~E(x1071,x1072)+E(f84(x1071),f84(x1072)) % 19.23/19.05 [108]~E(x1081,x1082)+E(f157(x1081,x1083,x1084),f157(x1082,x1083,x1084)) % 19.23/19.05 [109]~E(x1091,x1092)+E(f157(x1093,x1091,x1094),f157(x1093,x1092,x1094)) % 19.23/19.05 [110]~E(x1101,x1102)+E(f157(x1103,x1104,x1101),f157(x1103,x1104,x1102)) % 19.23/19.05 [111]~E(x1111,x1112)+E(f249(x1111,x1113),f249(x1112,x1113)) % 19.23/19.05 [112]~E(x1121,x1122)+E(f249(x1123,x1121),f249(x1123,x1122)) % 19.23/19.05 [113]~E(x1131,x1132)+E(f863(x1131,x1133),f863(x1132,x1133)) % 19.23/19.05 [114]~E(x1141,x1142)+E(f863(x1143,x1141),f863(x1143,x1142)) % 19.23/19.05 [115]~E(x1151,x1152)+E(f51(x1151),f51(x1152)) % 19.23/19.05 [116]~E(x1161,x1162)+E(f14(x1161,x1163,x1164),f14(x1162,x1163,x1164)) % 19.23/19.05 [117]~E(x1171,x1172)+E(f14(x1173,x1171,x1174),f14(x1173,x1172,x1174)) % 19.23/19.05 [118]~E(x1181,x1182)+E(f14(x1183,x1184,x1181),f14(x1183,x1184,x1182)) % 19.23/19.05 [119]~E(x1191,x1192)+E(f188(x1191),f188(x1192)) % 19.23/19.05 [120]~E(x1201,x1202)+E(f235(x1201),f235(x1202)) % 19.23/19.05 [121]~E(x1211,x1212)+E(f140(x1211,x1213),f140(x1212,x1213)) % 19.23/19.05 [122]~E(x1221,x1222)+E(f140(x1223,x1221),f140(x1223,x1222)) % 19.23/19.05 [123]~E(x1231,x1232)+E(f266(x1231),f266(x1232)) % 19.23/19.05 [124]~E(x1241,x1242)+E(f132(x1241),f132(x1242)) % 19.23/19.05 [125]~E(x1251,x1252)+E(f146(x1251),f146(x1252)) % 19.23/19.05 [126]~E(x1261,x1262)+E(f52(x1261,x1263),f52(x1262,x1263)) % 19.23/19.05 [127]~E(x1271,x1272)+E(f52(x1273,x1271),f52(x1273,x1272)) % 19.23/19.05 [128]~E(x1281,x1282)+E(f82(x1281,x1283,x1284,x1285),f82(x1282,x1283,x1284,x1285)) % 19.23/19.05 [129]~E(x1291,x1292)+E(f82(x1293,x1291,x1294,x1295),f82(x1293,x1292,x1294,x1295)) % 19.23/19.05 [130]~E(x1301,x1302)+E(f82(x1303,x1304,x1301,x1305),f82(x1303,x1304,x1302,x1305)) % 19.23/19.05 [131]~E(x1311,x1312)+E(f82(x1313,x1314,x1315,x1311),f82(x1313,x1314,x1315,x1312)) % 19.23/19.05 [132]~E(x1321,x1322)+E(f311(x1321),f311(x1322)) % 19.23/19.05 [133]~E(x1331,x1332)+E(f820(x1331,x1333,x1334),f820(x1332,x1333,x1334)) % 19.23/19.05 [134]~E(x1341,x1342)+E(f820(x1343,x1341,x1344),f820(x1343,x1342,x1344)) % 19.23/19.05 [135]~E(x1351,x1352)+E(f820(x1353,x1354,x1351),f820(x1353,x1354,x1352)) % 19.23/19.05 [136]~E(x1361,x1362)+E(f789(x1361,x1363,x1364),f789(x1362,x1363,x1364)) % 19.23/19.05 [137]~E(x1371,x1372)+E(f789(x1373,x1371,x1374),f789(x1373,x1372,x1374)) % 19.23/19.05 [138]~E(x1381,x1382)+E(f789(x1383,x1384,x1381),f789(x1383,x1384,x1382)) % 19.23/19.05 [139]~E(x1391,x1392)+E(f17(x1391,x1393),f17(x1392,x1393)) % 19.23/19.05 [140]~E(x1401,x1402)+E(f17(x1403,x1401),f17(x1403,x1402)) % 19.23/19.05 [141]~E(x1411,x1412)+E(f115(x1411),f115(x1412)) % 19.23/19.05 [142]~E(x1421,x1422)+E(f116(x1421),f116(x1422)) % 19.23/19.05 [143]~E(x1431,x1432)+E(f342(x1431),f342(x1432)) % 19.23/19.05 [144]~E(x1441,x1442)+E(f18(x1441,x1443),f18(x1442,x1443)) % 19.23/19.05 [145]~E(x1451,x1452)+E(f18(x1453,x1451),f18(x1453,x1452)) % 19.23/19.05 [146]~E(x1461,x1462)+E(f309(x1461,x1463),f309(x1462,x1463)) % 19.23/19.05 [147]~E(x1471,x1472)+E(f309(x1473,x1471),f309(x1473,x1472)) % 19.23/19.05 [148]~E(x1481,x1482)+E(f247(x1481,x1483),f247(x1482,x1483)) % 19.23/19.05 [149]~E(x1491,x1492)+E(f247(x1493,x1491),f247(x1493,x1492)) % 19.23/19.05 [150]~E(x1501,x1502)+E(f643(x1501,x1503,x1504,x1505,x1506),f643(x1502,x1503,x1504,x1505,x1506)) % 19.23/19.05 [151]~E(x1511,x1512)+E(f643(x1513,x1511,x1514,x1515,x1516),f643(x1513,x1512,x1514,x1515,x1516)) % 19.23/19.05 [152]~E(x1521,x1522)+E(f643(x1523,x1524,x1521,x1525,x1526),f643(x1523,x1524,x1522,x1525,x1526)) % 19.23/19.05 [153]~E(x1531,x1532)+E(f643(x1533,x1534,x1535,x1531,x1536),f643(x1533,x1534,x1535,x1532,x1536)) % 19.23/19.05 [154]~E(x1541,x1542)+E(f643(x1543,x1544,x1545,x1546,x1541),f643(x1543,x1544,x1545,x1546,x1542)) % 19.23/19.05 [155]~E(x1551,x1552)+E(f175(x1551,x1553,x1554,x1555),f175(x1552,x1553,x1554,x1555)) % 19.23/19.05 [156]~E(x1561,x1562)+E(f175(x1563,x1561,x1564,x1565),f175(x1563,x1562,x1564,x1565)) % 19.23/19.05 [157]~E(x1571,x1572)+E(f175(x1573,x1574,x1571,x1575),f175(x1573,x1574,x1572,x1575)) % 19.23/19.05 [158]~E(x1581,x1582)+E(f175(x1583,x1584,x1585,x1581),f175(x1583,x1584,x1585,x1582)) % 19.23/19.05 [159]~E(x1591,x1592)+E(f795(x1591,x1593,x1594),f795(x1592,x1593,x1594)) % 19.23/19.05 [160]~E(x1601,x1602)+E(f795(x1603,x1601,x1604),f795(x1603,x1602,x1604)) % 19.23/19.05 [161]~E(x1611,x1612)+E(f795(x1613,x1614,x1611),f795(x1613,x1614,x1612)) % 19.23/19.05 [162]~E(x1621,x1622)+E(f251(x1621),f251(x1622)) % 19.23/19.05 [163]~E(x1631,x1632)+E(f438(x1631,x1633,x1634),f438(x1632,x1633,x1634)) % 19.23/19.05 [164]~E(x1641,x1642)+E(f438(x1643,x1641,x1644),f438(x1643,x1642,x1644)) % 19.23/19.05 [165]~E(x1651,x1652)+E(f438(x1653,x1654,x1651),f438(x1653,x1654,x1652)) % 19.23/19.05 [166]~E(x1661,x1662)+E(f7(x1661),f7(x1662)) % 19.23/19.05 [167]~E(x1671,x1672)+E(f715(x1671,x1673,x1674,x1675,x1676,x1677),f715(x1672,x1673,x1674,x1675,x1676,x1677)) % 19.23/19.05 [168]~E(x1681,x1682)+E(f715(x1683,x1681,x1684,x1685,x1686,x1687),f715(x1683,x1682,x1684,x1685,x1686,x1687)) % 19.23/19.05 [169]~E(x1691,x1692)+E(f715(x1693,x1694,x1691,x1695,x1696,x1697),f715(x1693,x1694,x1692,x1695,x1696,x1697)) % 19.23/19.05 [170]~E(x1701,x1702)+E(f715(x1703,x1704,x1705,x1701,x1706,x1707),f715(x1703,x1704,x1705,x1702,x1706,x1707)) % 19.23/19.05 [171]~E(x1711,x1712)+E(f715(x1713,x1714,x1715,x1716,x1711,x1717),f715(x1713,x1714,x1715,x1716,x1712,x1717)) % 19.23/19.05 [172]~E(x1721,x1722)+E(f715(x1723,x1724,x1725,x1726,x1727,x1721),f715(x1723,x1724,x1725,x1726,x1727,x1722)) % 19.23/19.05 [173]~E(x1731,x1732)+E(f286(x1731,x1733,x1734),f286(x1732,x1733,x1734)) % 19.23/19.05 [174]~E(x1741,x1742)+E(f286(x1743,x1741,x1744),f286(x1743,x1742,x1744)) % 19.23/19.05 [175]~E(x1751,x1752)+E(f286(x1753,x1754,x1751),f286(x1753,x1754,x1752)) % 19.23/19.05 [176]~E(x1761,x1762)+E(f823(x1761,x1763,x1764),f823(x1762,x1763,x1764)) % 19.23/19.05 [177]~E(x1771,x1772)+E(f823(x1773,x1771,x1774),f823(x1773,x1772,x1774)) % 19.23/19.05 [178]~E(x1781,x1782)+E(f823(x1783,x1784,x1781),f823(x1783,x1784,x1782)) % 19.23/19.05 [179]~E(x1791,x1792)+E(f64(x1791,x1793),f64(x1792,x1793)) % 19.23/19.05 [180]~E(x1801,x1802)+E(f64(x1803,x1801),f64(x1803,x1802)) % 19.23/19.05 [181]~E(x1811,x1812)+E(f630(x1811,x1813,x1814),f630(x1812,x1813,x1814)) % 19.23/19.05 [182]~E(x1821,x1822)+E(f630(x1823,x1821,x1824),f630(x1823,x1822,x1824)) % 19.23/19.05 [183]~E(x1831,x1832)+E(f630(x1833,x1834,x1831),f630(x1833,x1834,x1832)) % 19.23/19.05 [184]~E(x1841,x1842)+E(f595(x1841,x1843),f595(x1842,x1843)) % 19.23/19.05 [185]~E(x1851,x1852)+E(f595(x1853,x1851),f595(x1853,x1852)) % 19.23/19.05 [186]~E(x1861,x1862)+E(f137(x1861),f137(x1862)) % 19.23/19.05 [187]~E(x1871,x1872)+E(f842(x1871,x1873,x1874),f842(x1872,x1873,x1874)) % 19.23/19.05 [188]~E(x1881,x1882)+E(f842(x1883,x1881,x1884),f842(x1883,x1882,x1884)) % 19.23/19.05 [189]~E(x1891,x1892)+E(f842(x1893,x1894,x1891),f842(x1893,x1894,x1892)) % 19.23/19.05 [190]~E(x1901,x1902)+E(f148(x1901),f148(x1902)) % 19.23/19.05 [191]~E(x1911,x1912)+E(f706(x1911,x1913,x1914),f706(x1912,x1913,x1914)) % 19.23/19.05 [192]~E(x1921,x1922)+E(f706(x1923,x1921,x1924),f706(x1923,x1922,x1924)) % 19.23/19.05 [193]~E(x1931,x1932)+E(f706(x1933,x1934,x1931),f706(x1933,x1934,x1932)) % 19.23/19.05 [194]~E(x1941,x1942)+E(f33(x1941,x1943,x1944),f33(x1942,x1943,x1944)) % 19.23/19.05 [195]~E(x1951,x1952)+E(f33(x1953,x1951,x1954),f33(x1953,x1952,x1954)) % 19.23/19.05 [196]~E(x1961,x1962)+E(f33(x1963,x1964,x1961),f33(x1963,x1964,x1962)) % 19.23/19.05 [197]~E(x1971,x1972)+E(f304(x1971,x1973,x1974),f304(x1972,x1973,x1974)) % 19.23/19.05 [198]~E(x1981,x1982)+E(f304(x1983,x1981,x1984),f304(x1983,x1982,x1984)) % 19.23/19.05 [199]~E(x1991,x1992)+E(f304(x1993,x1994,x1991),f304(x1993,x1994,x1992)) % 19.23/19.05 [200]~E(x2001,x2002)+E(f177(x2001,x2003,x2004,x2005,x2006),f177(x2002,x2003,x2004,x2005,x2006)) % 19.23/19.05 [201]~E(x2011,x2012)+E(f177(x2013,x2011,x2014,x2015,x2016),f177(x2013,x2012,x2014,x2015,x2016)) % 19.23/19.05 [202]~E(x2021,x2022)+E(f177(x2023,x2024,x2021,x2025,x2026),f177(x2023,x2024,x2022,x2025,x2026)) % 19.23/19.05 [203]~E(x2031,x2032)+E(f177(x2033,x2034,x2035,x2031,x2036),f177(x2033,x2034,x2035,x2032,x2036)) % 19.23/19.05 [204]~E(x2041,x2042)+E(f177(x2043,x2044,x2045,x2046,x2041),f177(x2043,x2044,x2045,x2046,x2042)) % 19.23/19.05 [205]~E(x2051,x2052)+E(f181(x2051,x2053,x2054,x2055),f181(x2052,x2053,x2054,x2055)) % 19.23/19.05 [206]~E(x2061,x2062)+E(f181(x2063,x2061,x2064,x2065),f181(x2063,x2062,x2064,x2065)) % 19.23/19.05 [207]~E(x2071,x2072)+E(f181(x2073,x2074,x2071,x2075),f181(x2073,x2074,x2072,x2075)) % 19.23/19.05 [208]~E(x2081,x2082)+E(f181(x2083,x2084,x2085,x2081),f181(x2083,x2084,x2085,x2082)) % 19.23/19.05 [209]~E(x2091,x2092)+E(f306(x2091,x2093,x2094),f306(x2092,x2093,x2094)) % 19.23/19.05 [210]~E(x2101,x2102)+E(f306(x2103,x2101,x2104),f306(x2103,x2102,x2104)) % 19.23/19.05 [211]~E(x2111,x2112)+E(f306(x2113,x2114,x2111),f306(x2113,x2114,x2112)) % 19.23/19.05 [212]~E(x2121,x2122)+E(f147(x2121),f147(x2122)) % 19.23/19.05 [213]~E(x2131,x2132)+E(f54(x2131,x2133),f54(x2132,x2133)) % 19.23/19.05 [214]~E(x2141,x2142)+E(f54(x2143,x2141),f54(x2143,x2142)) % 19.23/19.05 [215]~E(x2151,x2152)+E(f290(x2151,x2153,x2154),f290(x2152,x2153,x2154)) % 19.23/19.05 [216]~E(x2161,x2162)+E(f290(x2163,x2161,x2164),f290(x2163,x2162,x2164)) % 19.23/19.05 [217]~E(x2171,x2172)+E(f290(x2173,x2174,x2171),f290(x2173,x2174,x2172)) % 19.23/19.05 [218]~E(x2181,x2182)+E(f465(x2181,x2183,x2184,x2185),f465(x2182,x2183,x2184,x2185)) % 19.23/19.05 [219]~E(x2191,x2192)+E(f465(x2193,x2191,x2194,x2195),f465(x2193,x2192,x2194,x2195)) % 19.23/19.05 [220]~E(x2201,x2202)+E(f465(x2203,x2204,x2201,x2205),f465(x2203,x2204,x2202,x2205)) % 19.23/19.05 [221]~E(x2211,x2212)+E(f465(x2213,x2214,x2215,x2211),f465(x2213,x2214,x2215,x2212)) % 19.23/19.05 [222]~E(x2221,x2222)+E(f192(x2221),f192(x2222)) % 19.23/19.05 [223]~E(x2231,x2232)+E(f149(x2231,x2233),f149(x2232,x2233)) % 19.23/19.05 [224]~E(x2241,x2242)+E(f149(x2243,x2241),f149(x2243,x2242)) % 19.23/19.05 [225]~E(x2251,x2252)+E(f60(x2251,x2253,x2254),f60(x2252,x2253,x2254)) % 19.23/19.05 [226]~E(x2261,x2262)+E(f60(x2263,x2261,x2264),f60(x2263,x2262,x2264)) % 19.23/19.05 [227]~E(x2271,x2272)+E(f60(x2273,x2274,x2271),f60(x2273,x2274,x2272)) % 19.23/19.05 [228]~E(x2281,x2282)+E(f261(x2281,x2283,x2284,x2285,x2286,x2287),f261(x2282,x2283,x2284,x2285,x2286,x2287)) % 19.23/19.05 [229]~E(x2291,x2292)+E(f261(x2293,x2291,x2294,x2295,x2296,x2297),f261(x2293,x2292,x2294,x2295,x2296,x2297)) % 19.23/19.05 [230]~E(x2301,x2302)+E(f261(x2303,x2304,x2301,x2305,x2306,x2307),f261(x2303,x2304,x2302,x2305,x2306,x2307)) % 19.23/19.05 [231]~E(x2311,x2312)+E(f261(x2313,x2314,x2315,x2311,x2316,x2317),f261(x2313,x2314,x2315,x2312,x2316,x2317)) % 19.23/19.05 [232]~E(x2321,x2322)+E(f261(x2323,x2324,x2325,x2326,x2321,x2327),f261(x2323,x2324,x2325,x2326,x2322,x2327)) % 19.23/19.05 [233]~E(x2331,x2332)+E(f261(x2333,x2334,x2335,x2336,x2337,x2331),f261(x2333,x2334,x2335,x2336,x2337,x2332)) % 19.23/19.05 [234]~E(x2341,x2342)+E(f105(x2341),f105(x2342)) % 19.23/19.05 [235]~E(x2351,x2352)+E(f792(x2351,x2353,x2354),f792(x2352,x2353,x2354)) % 19.23/19.05 [236]~E(x2361,x2362)+E(f792(x2363,x2361,x2364),f792(x2363,x2362,x2364)) % 19.23/19.05 [237]~E(x2371,x2372)+E(f792(x2373,x2374,x2371),f792(x2373,x2374,x2372)) % 19.23/19.05 [238]~E(x2381,x2382)+E(f262(x2381,x2383,x2384,x2385),f262(x2382,x2383,x2384,x2385)) % 19.23/19.05 [239]~E(x2391,x2392)+E(f262(x2393,x2391,x2394,x2395),f262(x2393,x2392,x2394,x2395)) % 19.23/19.05 [240]~E(x2401,x2402)+E(f262(x2403,x2404,x2401,x2405),f262(x2403,x2404,x2402,x2405)) % 19.23/19.05 [241]~E(x2411,x2412)+E(f262(x2413,x2414,x2415,x2411),f262(x2413,x2414,x2415,x2412)) % 19.23/19.05 [242]~E(x2421,x2422)+E(f294(x2421,x2423),f294(x2422,x2423)) % 19.23/19.05 [243]~E(x2431,x2432)+E(f294(x2433,x2431),f294(x2433,x2432)) % 19.23/19.05 [244]~E(x2441,x2442)+E(f152(x2441,x2443),f152(x2442,x2443)) % 19.23/19.05 [245]~E(x2451,x2452)+E(f152(x2453,x2451),f152(x2453,x2452)) % 19.23/19.05 [246]~E(x2461,x2462)+E(f653(x2461,x2463,x2464,x2465,x2466),f653(x2462,x2463,x2464,x2465,x2466)) % 19.23/19.05 [247]~E(x2471,x2472)+E(f653(x2473,x2471,x2474,x2475,x2476),f653(x2473,x2472,x2474,x2475,x2476)) % 19.23/19.05 [248]~E(x2481,x2482)+E(f653(x2483,x2484,x2481,x2485,x2486),f653(x2483,x2484,x2482,x2485,x2486)) % 19.23/19.05 [249]~E(x2491,x2492)+E(f653(x2493,x2494,x2495,x2491,x2496),f653(x2493,x2494,x2495,x2492,x2496)) % 19.23/19.05 [250]~E(x2501,x2502)+E(f653(x2503,x2504,x2505,x2506,x2501),f653(x2503,x2504,x2505,x2506,x2502)) % 19.23/19.05 [251]~E(x2511,x2512)+E(f717(x2511,x2513,x2514,x2515,x2516,x2517),f717(x2512,x2513,x2514,x2515,x2516,x2517)) % 19.23/19.05 [252]~E(x2521,x2522)+E(f717(x2523,x2521,x2524,x2525,x2526,x2527),f717(x2523,x2522,x2524,x2525,x2526,x2527)) % 19.23/19.05 [253]~E(x2531,x2532)+E(f717(x2533,x2534,x2531,x2535,x2536,x2537),f717(x2533,x2534,x2532,x2535,x2536,x2537)) % 19.23/19.05 [254]~E(x2541,x2542)+E(f717(x2543,x2544,x2545,x2541,x2546,x2547),f717(x2543,x2544,x2545,x2542,x2546,x2547)) % 19.23/19.05 [255]~E(x2551,x2552)+E(f717(x2553,x2554,x2555,x2556,x2551,x2557),f717(x2553,x2554,x2555,x2556,x2552,x2557)) % 19.23/19.05 [256]~E(x2561,x2562)+E(f717(x2563,x2564,x2565,x2566,x2567,x2561),f717(x2563,x2564,x2565,x2566,x2567,x2562)) % 19.23/19.05 [257]~E(x2571,x2572)+E(f129(x2571),f129(x2572)) % 19.23/19.05 [258]~E(x2581,x2582)+E(f289(x2581,x2583),f289(x2582,x2583)) % 19.23/19.05 [259]~E(x2591,x2592)+E(f289(x2593,x2591),f289(x2593,x2592)) % 19.23/19.05 [260]~E(x2601,x2602)+E(f718(x2601,x2603,x2604,x2605,x2606,x2607),f718(x2602,x2603,x2604,x2605,x2606,x2607)) % 19.23/19.05 [261]~E(x2611,x2612)+E(f718(x2613,x2611,x2614,x2615,x2616,x2617),f718(x2613,x2612,x2614,x2615,x2616,x2617)) % 19.23/19.05 [262]~E(x2621,x2622)+E(f718(x2623,x2624,x2621,x2625,x2626,x2627),f718(x2623,x2624,x2622,x2625,x2626,x2627)) % 19.23/19.05 [263]~E(x2631,x2632)+E(f718(x2633,x2634,x2635,x2631,x2636,x2637),f718(x2633,x2634,x2635,x2632,x2636,x2637)) % 19.23/19.05 [264]~E(x2641,x2642)+E(f718(x2643,x2644,x2645,x2646,x2641,x2647),f718(x2643,x2644,x2645,x2646,x2642,x2647)) % 19.23/19.05 [265]~E(x2651,x2652)+E(f718(x2653,x2654,x2655,x2656,x2657,x2651),f718(x2653,x2654,x2655,x2656,x2657,x2652)) % 19.23/19.05 [266]~E(x2661,x2662)+E(f622(x2661),f622(x2662)) % 19.23/19.05 [267]~E(x2671,x2672)+E(f861(x2671),f861(x2672)) % 19.23/19.05 [268]~E(x2681,x2682)+E(f314(x2681,x2683,x2684),f314(x2682,x2683,x2684)) % 19.23/19.05 [269]~E(x2691,x2692)+E(f314(x2693,x2691,x2694),f314(x2693,x2692,x2694)) % 19.23/19.05 [270]~E(x2701,x2702)+E(f314(x2703,x2704,x2701),f314(x2703,x2704,x2702)) % 19.23/19.05 [271]~E(x2711,x2712)+E(f123(x2711,x2713),f123(x2712,x2713)) % 19.23/19.05 [272]~E(x2721,x2722)+E(f123(x2723,x2721),f123(x2723,x2722)) % 19.23/19.05 [273]~E(x2731,x2732)+E(f260(x2731,x2733,x2734),f260(x2732,x2733,x2734)) % 19.23/19.05 [274]~E(x2741,x2742)+E(f260(x2743,x2741,x2744),f260(x2743,x2742,x2744)) % 19.23/19.05 [275]~E(x2751,x2752)+E(f260(x2753,x2754,x2751),f260(x2753,x2754,x2752)) % 19.23/19.05 [276]~E(x2761,x2762)+E(f189(x2761),f189(x2762)) % 19.23/19.05 [277]~E(x2771,x2772)+E(f53(x2771,x2773),f53(x2772,x2773)) % 19.23/19.05 [278]~E(x2781,x2782)+E(f53(x2783,x2781),f53(x2783,x2782)) % 19.23/19.05 [279]~E(x2791,x2792)+E(f124(x2791),f124(x2792)) % 19.23/19.05 [280]~E(x2801,x2802)+E(f101(x2801,x2803,x2804),f101(x2802,x2803,x2804)) % 19.23/19.05 [281]~E(x2811,x2812)+E(f101(x2813,x2811,x2814),f101(x2813,x2812,x2814)) % 19.23/19.05 [282]~E(x2821,x2822)+E(f101(x2823,x2824,x2821),f101(x2823,x2824,x2822)) % 19.23/19.05 [283]~E(x2831,x2832)+E(f37(x2831,x2833),f37(x2832,x2833)) % 19.23/19.05 [284]~E(x2841,x2842)+E(f37(x2843,x2841),f37(x2843,x2842)) % 19.23/19.05 [285]~E(x2851,x2852)+E(f179(x2851,x2853),f179(x2852,x2853)) % 19.23/19.05 [286]~E(x2861,x2862)+E(f179(x2863,x2861),f179(x2863,x2862)) % 19.23/19.05 [287]~E(x2871,x2872)+E(f214(x2871,x2873,x2874,x2875,x2876,x2877,x2878),f214(x2872,x2873,x2874,x2875,x2876,x2877,x2878)) % 19.23/19.05 [288]~E(x2881,x2882)+E(f214(x2883,x2881,x2884,x2885,x2886,x2887,x2888),f214(x2883,x2882,x2884,x2885,x2886,x2887,x2888)) % 19.23/19.05 [289]~E(x2891,x2892)+E(f214(x2893,x2894,x2891,x2895,x2896,x2897,x2898),f214(x2893,x2894,x2892,x2895,x2896,x2897,x2898)) % 19.23/19.05 [290]~E(x2901,x2902)+E(f214(x2903,x2904,x2905,x2901,x2906,x2907,x2908),f214(x2903,x2904,x2905,x2902,x2906,x2907,x2908)) % 19.23/19.05 [291]~E(x2911,x2912)+E(f214(x2913,x2914,x2915,x2916,x2911,x2917,x2918),f214(x2913,x2914,x2915,x2916,x2912,x2917,x2918)) % 19.23/19.05 [292]~E(x2921,x2922)+E(f214(x2923,x2924,x2925,x2926,x2927,x2921,x2928),f214(x2923,x2924,x2925,x2926,x2927,x2922,x2928)) % 19.23/19.05 [293]~E(x2931,x2932)+E(f214(x2933,x2934,x2935,x2936,x2937,x2938,x2931),f214(x2933,x2934,x2935,x2936,x2937,x2938,x2932)) % 19.23/19.05 [294]~E(x2941,x2942)+E(f162(x2941),f162(x2942)) % 19.23/19.05 [295]~E(x2951,x2952)+E(f204(x2951,x2953),f204(x2952,x2953)) % 19.23/19.05 [296]~E(x2961,x2962)+E(f204(x2963,x2961),f204(x2963,x2962)) % 19.23/19.05 [297]~E(x2971,x2972)+E(f257(x2971,x2973),f257(x2972,x2973)) % 19.23/19.05 [298]~E(x2981,x2982)+E(f257(x2983,x2981),f257(x2983,x2982)) % 19.23/19.05 [299]~E(x2991,x2992)+E(f404(x2991,x2993,x2994,x2995),f404(x2992,x2993,x2994,x2995)) % 19.23/19.05 [300]~E(x3001,x3002)+E(f404(x3003,x3001,x3004,x3005),f404(x3003,x3002,x3004,x3005)) % 19.23/19.05 [301]~E(x3011,x3012)+E(f404(x3013,x3014,x3011,x3015),f404(x3013,x3014,x3012,x3015)) % 19.23/19.05 [302]~E(x3021,x3022)+E(f404(x3023,x3024,x3025,x3021),f404(x3023,x3024,x3025,x3022)) % 19.23/19.05 [303]~E(x3031,x3032)+E(f138(x3031,x3033,x3034,x3035),f138(x3032,x3033,x3034,x3035)) % 19.23/19.05 [304]~E(x3041,x3042)+E(f138(x3043,x3041,x3044,x3045),f138(x3043,x3042,x3044,x3045)) % 19.23/19.05 [305]~E(x3051,x3052)+E(f138(x3053,x3054,x3051,x3055),f138(x3053,x3054,x3052,x3055)) % 19.23/19.05 [306]~E(x3061,x3062)+E(f138(x3063,x3064,x3065,x3061),f138(x3063,x3064,x3065,x3062)) % 19.23/19.05 [307]~E(x3071,x3072)+E(f623(x3071,x3073),f623(x3072,x3073)) % 19.23/19.05 [308]~E(x3081,x3082)+E(f623(x3083,x3081),f623(x3083,x3082)) % 19.23/19.05 [309]~E(x3091,x3092)+E(f96(x3091),f96(x3092)) % 19.23/19.05 [310]~E(x3101,x3102)+E(f136(x3101,x3103),f136(x3102,x3103)) % 19.23/19.05 [311]~E(x3111,x3112)+E(f136(x3113,x3111),f136(x3113,x3112)) % 19.23/19.05 [312]~E(x3121,x3122)+E(f174(x3121,x3123,x3124),f174(x3122,x3123,x3124)) % 19.23/19.05 [313]~E(x3131,x3132)+E(f174(x3133,x3131,x3134),f174(x3133,x3132,x3134)) % 19.23/19.05 [314]~E(x3141,x3142)+E(f174(x3143,x3144,x3141),f174(x3143,x3144,x3142)) % 19.23/19.05 [315]~E(x3151,x3152)+E(f287(x3151,x3153),f287(x3152,x3153)) % 19.23/19.05 [316]~E(x3161,x3162)+E(f287(x3163,x3161),f287(x3163,x3162)) % 19.23/19.05 [317]~E(x3171,x3172)+E(f171(x3171,x3173,x3174),f171(x3172,x3173,x3174)) % 19.23/19.05 [318]~E(x3181,x3182)+E(f171(x3183,x3181,x3184),f171(x3183,x3182,x3184)) % 19.23/19.05 [319]~E(x3191,x3192)+E(f171(x3193,x3194,x3191),f171(x3193,x3194,x3192)) % 19.23/19.05 [320]~E(x3201,x3202)+E(f711(x3201,x3203,x3204,x3205,x3206,x3207),f711(x3202,x3203,x3204,x3205,x3206,x3207)) % 19.23/19.05 [321]~E(x3211,x3212)+E(f711(x3213,x3211,x3214,x3215,x3216,x3217),f711(x3213,x3212,x3214,x3215,x3216,x3217)) % 19.23/19.05 [322]~E(x3221,x3222)+E(f711(x3223,x3224,x3221,x3225,x3226,x3227),f711(x3223,x3224,x3222,x3225,x3226,x3227)) % 19.23/19.05 [323]~E(x3231,x3232)+E(f711(x3233,x3234,x3235,x3231,x3236,x3237),f711(x3233,x3234,x3235,x3232,x3236,x3237)) % 19.23/19.05 [324]~E(x3241,x3242)+E(f711(x3243,x3244,x3245,x3246,x3241,x3247),f711(x3243,x3244,x3245,x3246,x3242,x3247)) % 19.23/19.05 [325]~E(x3251,x3252)+E(f711(x3253,x3254,x3255,x3256,x3257,x3251),f711(x3253,x3254,x3255,x3256,x3257,x3252)) % 19.23/19.05 [326]~E(x3261,x3262)+E(f511(x3261,x3263,x3264,x3265),f511(x3262,x3263,x3264,x3265)) % 19.23/19.05 [327]~E(x3271,x3272)+E(f511(x3273,x3271,x3274,x3275),f511(x3273,x3272,x3274,x3275)) % 19.23/19.05 [328]~E(x3281,x3282)+E(f511(x3283,x3284,x3281,x3285),f511(x3283,x3284,x3282,x3285)) % 19.23/19.05 [329]~E(x3291,x3292)+E(f511(x3293,x3294,x3295,x3291),f511(x3293,x3294,x3295,x3292)) % 19.23/19.05 [330]~E(x3301,x3302)+E(f74(x3301,x3303,x3304),f74(x3302,x3303,x3304)) % 19.23/19.05 [331]~E(x3311,x3312)+E(f74(x3313,x3311,x3314),f74(x3313,x3312,x3314)) % 19.23/19.05 [332]~E(x3321,x3322)+E(f74(x3323,x3324,x3321),f74(x3323,x3324,x3322)) % 19.23/19.05 [333]~E(x3331,x3332)+E(f730(x3331,x3333,x3334,x3335,x3336),f730(x3332,x3333,x3334,x3335,x3336)) % 19.23/19.05 [334]~E(x3341,x3342)+E(f730(x3343,x3341,x3344,x3345,x3346),f730(x3343,x3342,x3344,x3345,x3346)) % 19.23/19.05 [335]~E(x3351,x3352)+E(f730(x3353,x3354,x3351,x3355,x3356),f730(x3353,x3354,x3352,x3355,x3356)) % 19.23/19.05 [336]~E(x3361,x3362)+E(f730(x3363,x3364,x3365,x3361,x3366),f730(x3363,x3364,x3365,x3362,x3366)) % 19.23/19.05 [337]~E(x3371,x3372)+E(f730(x3373,x3374,x3375,x3376,x3371),f730(x3373,x3374,x3375,x3376,x3372)) % 19.23/19.05 [338]~E(x3381,x3382)+E(f151(x3381,x3383,x3384,x3385),f151(x3382,x3383,x3384,x3385)) % 19.23/19.05 [339]~E(x3391,x3392)+E(f151(x3393,x3391,x3394,x3395),f151(x3393,x3392,x3394,x3395)) % 19.23/19.05 [340]~E(x3401,x3402)+E(f151(x3403,x3404,x3401,x3405),f151(x3403,x3404,x3402,x3405)) % 19.23/19.05 [341]~E(x3411,x3412)+E(f151(x3413,x3414,x3415,x3411),f151(x3413,x3414,x3415,x3412)) % 19.23/19.05 [342]~E(x3421,x3422)+E(f223(x3421,x3423,x3424,x3425),f223(x3422,x3423,x3424,x3425)) % 19.23/19.05 [343]~E(x3431,x3432)+E(f223(x3433,x3431,x3434,x3435),f223(x3433,x3432,x3434,x3435)) % 19.23/19.05 [344]~E(x3441,x3442)+E(f223(x3443,x3444,x3441,x3445),f223(x3443,x3444,x3442,x3445)) % 19.23/19.05 [345]~E(x3451,x3452)+E(f223(x3453,x3454,x3455,x3451),f223(x3453,x3454,x3455,x3452)) % 19.23/19.05 [346]~E(x3461,x3462)+E(f172(x3461,x3463),f172(x3462,x3463)) % 19.23/19.05 [347]~E(x3471,x3472)+E(f172(x3473,x3471),f172(x3473,x3472)) % 19.23/19.05 [348]~E(x3481,x3482)+E(f403(x3481,x3483,x3484,x3485),f403(x3482,x3483,x3484,x3485)) % 19.23/19.05 [349]~E(x3491,x3492)+E(f403(x3493,x3491,x3494,x3495),f403(x3493,x3492,x3494,x3495)) % 19.23/19.05 [350]~E(x3501,x3502)+E(f403(x3503,x3504,x3501,x3505),f403(x3503,x3504,x3502,x3505)) % 19.23/19.05 [351]~E(x3511,x3512)+E(f403(x3513,x3514,x3515,x3511),f403(x3513,x3514,x3515,x3512)) % 19.23/19.05 [352]~E(x3521,x3522)+E(f606(x3521),f606(x3522)) % 19.23/19.05 [353]~E(x3531,x3532)+E(f215(x3531),f215(x3532)) % 19.23/19.05 [354]~E(x3541,x3542)+E(f276(x3541,x3543),f276(x3542,x3543)) % 19.23/19.05 [355]~E(x3551,x3552)+E(f276(x3553,x3551),f276(x3553,x3552)) % 19.23/19.05 [356]~E(x3561,x3562)+E(f307(x3561,x3563,x3564),f307(x3562,x3563,x3564)) % 19.23/19.05 [357]~E(x3571,x3572)+E(f307(x3573,x3571,x3574),f307(x3573,x3572,x3574)) % 19.23/19.05 [358]~E(x3581,x3582)+E(f307(x3583,x3584,x3581),f307(x3583,x3584,x3582)) % 19.23/19.05 [359]~E(x3591,x3592)+E(f636(x3591,x3593,x3594),f636(x3592,x3593,x3594)) % 19.23/19.05 [360]~E(x3601,x3602)+E(f636(x3603,x3601,x3604),f636(x3603,x3602,x3604)) % 19.23/19.05 [361]~E(x3611,x3612)+E(f636(x3613,x3614,x3611),f636(x3613,x3614,x3612)) % 19.23/19.05 [362]~E(x3621,x3622)+E(f313(x3621,x3623),f313(x3622,x3623)) % 19.23/19.05 [363]~E(x3631,x3632)+E(f313(x3633,x3631),f313(x3633,x3632)) % 19.23/19.05 [364]~E(x3641,x3642)+E(f30(x3641,x3643),f30(x3642,x3643)) % 19.23/19.05 [365]~E(x3651,x3652)+E(f30(x3653,x3651),f30(x3653,x3652)) % 19.23/19.05 [366]~E(x3661,x3662)+E(f143(x3661,x3663),f143(x3662,x3663)) % 19.23/19.05 [367]~E(x3671,x3672)+E(f143(x3673,x3671),f143(x3673,x3672)) % 19.23/19.05 [368]~E(x3681,x3682)+E(f745(x3681,x3683,x3684,x3685,x3686),f745(x3682,x3683,x3684,x3685,x3686)) % 19.23/19.05 [369]~E(x3691,x3692)+E(f745(x3693,x3691,x3694,x3695,x3696),f745(x3693,x3692,x3694,x3695,x3696)) % 19.23/19.05 [370]~E(x3701,x3702)+E(f745(x3703,x3704,x3701,x3705,x3706),f745(x3703,x3704,x3702,x3705,x3706)) % 19.23/19.05 [371]~E(x3711,x3712)+E(f745(x3713,x3714,x3715,x3711,x3716),f745(x3713,x3714,x3715,x3712,x3716)) % 19.23/19.05 [372]~E(x3721,x3722)+E(f745(x3723,x3724,x3725,x3726,x3721),f745(x3723,x3724,x3725,x3726,x3722)) % 19.23/19.05 [373]~E(x3731,x3732)+E(f16(x3731,x3733),f16(x3732,x3733)) % 19.23/19.05 [374]~E(x3741,x3742)+E(f16(x3743,x3741),f16(x3743,x3742)) % 19.23/19.05 [375]~E(x3751,x3752)+E(f333(x3751,x3753),f333(x3752,x3753)) % 19.23/19.05 [376]~E(x3761,x3762)+E(f333(x3763,x3761),f333(x3763,x3762)) % 19.23/19.05 [377]~E(x3771,x3772)+E(f81(x3771,x3773),f81(x3772,x3773)) % 19.23/19.05 [378]~E(x3781,x3782)+E(f81(x3783,x3781),f81(x3783,x3782)) % 19.23/19.05 [379]~E(x3791,x3792)+E(f334(x3791,x3793),f334(x3792,x3793)) % 19.23/19.05 [380]~E(x3801,x3802)+E(f334(x3803,x3801),f334(x3803,x3802)) % 19.23/19.05 [381]~E(x3811,x3812)+E(f625(x3811,x3813),f625(x3812,x3813)) % 19.23/19.05 [382]~E(x3821,x3822)+E(f625(x3823,x3821),f625(x3823,x3822)) % 19.23/19.05 [383]~E(x3831,x3832)+E(f164(x3831),f164(x3832)) % 19.23/19.05 [384]~E(x3841,x3842)+E(f97(x3841),f97(x3842)) % 19.23/19.05 [385]~E(x3851,x3852)+E(f565(x3851,x3853,x3854,x3855,x3856,x3857,x3858,x3859),f565(x3852,x3853,x3854,x3855,x3856,x3857,x3858,x3859)) % 19.23/19.05 [386]~E(x3861,x3862)+E(f565(x3863,x3861,x3864,x3865,x3866,x3867,x3868,x3869),f565(x3863,x3862,x3864,x3865,x3866,x3867,x3868,x3869)) % 19.23/19.05 [387]~E(x3871,x3872)+E(f565(x3873,x3874,x3871,x3875,x3876,x3877,x3878,x3879),f565(x3873,x3874,x3872,x3875,x3876,x3877,x3878,x3879)) % 19.23/19.05 [388]~E(x3881,x3882)+E(f565(x3883,x3884,x3885,x3881,x3886,x3887,x3888,x3889),f565(x3883,x3884,x3885,x3882,x3886,x3887,x3888,x3889)) % 19.23/19.05 [389]~E(x3891,x3892)+E(f565(x3893,x3894,x3895,x3896,x3891,x3897,x3898,x3899),f565(x3893,x3894,x3895,x3896,x3892,x3897,x3898,x3899)) % 19.23/19.05 [390]~E(x3901,x3902)+E(f565(x3903,x3904,x3905,x3906,x3907,x3901,x3908,x3909),f565(x3903,x3904,x3905,x3906,x3907,x3902,x3908,x3909)) % 19.23/19.05 [391]~E(x3911,x3912)+E(f565(x3913,x3914,x3915,x3916,x3917,x3918,x3911,x3919),f565(x3913,x3914,x3915,x3916,x3917,x3918,x3912,x3919)) % 19.23/19.05 [392]~E(x3921,x3922)+E(f565(x3923,x3924,x3925,x3926,x3927,x3928,x3929,x3921),f565(x3923,x3924,x3925,x3926,x3927,x3928,x3929,x3922)) % 19.23/19.05 [393]~E(x3931,x3932)+E(f303(x3931,x3933),f303(x3932,x3933)) % 19.23/19.05 [394]~E(x3941,x3942)+E(f303(x3943,x3941),f303(x3943,x3942)) % 19.23/19.05 [395]~E(x3951,x3952)+E(f144(x3951,x3953,x3954),f144(x3952,x3953,x3954)) % 19.23/19.05 [396]~E(x3961,x3962)+E(f144(x3963,x3961,x3964),f144(x3963,x3962,x3964)) % 19.23/19.05 [397]~E(x3971,x3972)+E(f144(x3973,x3974,x3971),f144(x3973,x3974,x3972)) % 19.23/19.05 [398]~E(x3981,x3982)+E(f310(x3981),f310(x3982)) % 19.23/19.05 [399]~E(x3991,x3992)+E(f39(x3991,x3993,x3994,x3995,x3996,x3997,x3998,x3999,x39910,x39911),f39(x3992,x3993,x3994,x3995,x3996,x3997,x3998,x3999,x39910,x39911)) % 19.23/19.05 [400]~E(x4001,x4002)+E(f39(x4003,x4001,x4004,x4005,x4006,x4007,x4008,x4009,x40010,x40011),f39(x4003,x4002,x4004,x4005,x4006,x4007,x4008,x4009,x40010,x40011)) % 19.23/19.05 [401]~E(x4011,x4012)+E(f39(x4013,x4014,x4011,x4015,x4016,x4017,x4018,x4019,x40110,x40111),f39(x4013,x4014,x4012,x4015,x4016,x4017,x4018,x4019,x40110,x40111)) % 19.23/19.05 [402]~E(x4021,x4022)+E(f39(x4023,x4024,x4025,x4021,x4026,x4027,x4028,x4029,x40210,x40211),f39(x4023,x4024,x4025,x4022,x4026,x4027,x4028,x4029,x40210,x40211)) % 19.23/19.05 [403]~E(x4031,x4032)+E(f39(x4033,x4034,x4035,x4036,x4031,x4037,x4038,x4039,x40310,x40311),f39(x4033,x4034,x4035,x4036,x4032,x4037,x4038,x4039,x40310,x40311)) % 19.23/19.05 [404]~E(x4041,x4042)+E(f39(x4043,x4044,x4045,x4046,x4047,x4041,x4048,x4049,x40410,x40411),f39(x4043,x4044,x4045,x4046,x4047,x4042,x4048,x4049,x40410,x40411)) % 19.23/19.05 [405]~E(x4051,x4052)+E(f39(x4053,x4054,x4055,x4056,x4057,x4058,x4051,x4059,x40510,x40511),f39(x4053,x4054,x4055,x4056,x4057,x4058,x4052,x4059,x40510,x40511)) % 19.23/19.05 [406]~E(x4061,x4062)+E(f39(x4063,x4064,x4065,x4066,x4067,x4068,x4069,x4061,x40610,x40611),f39(x4063,x4064,x4065,x4066,x4067,x4068,x4069,x4062,x40610,x40611)) % 19.23/19.05 [407]~E(x4071,x4072)+E(f39(x4073,x4074,x4075,x4076,x4077,x4078,x4079,x40710,x4071,x40711),f39(x4073,x4074,x4075,x4076,x4077,x4078,x4079,x40710,x4072,x40711)) % 19.23/19.05 [408]~E(x4081,x4082)+E(f39(x4083,x4084,x4085,x4086,x4087,x4088,x4089,x40810,x40811,x4081),f39(x4083,x4084,x4085,x4086,x4087,x4088,x4089,x40810,x40811,x4082)) % 19.23/19.05 [409]~E(x4091,x4092)+E(f762(x4091,x4093,x4094,x4095),f762(x4092,x4093,x4094,x4095)) % 19.23/19.05 [410]~E(x4101,x4102)+E(f762(x4103,x4101,x4104,x4105),f762(x4103,x4102,x4104,x4105)) % 19.23/19.05 [411]~E(x4111,x4112)+E(f762(x4113,x4114,x4111,x4115),f762(x4113,x4114,x4112,x4115)) % 19.23/19.05 [412]~E(x4121,x4122)+E(f762(x4123,x4124,x4125,x4121),f762(x4123,x4124,x4125,x4122)) % 19.23/19.05 [413]~E(x4131,x4132)+E(f201(x4131,x4133,x4134,x4135),f201(x4132,x4133,x4134,x4135)) % 19.23/19.05 [414]~E(x4141,x4142)+E(f201(x4143,x4141,x4144,x4145),f201(x4143,x4142,x4144,x4145)) % 19.23/19.05 [415]~E(x4151,x4152)+E(f201(x4153,x4154,x4151,x4155),f201(x4153,x4154,x4152,x4155)) % 19.23/19.05 [416]~E(x4161,x4162)+E(f201(x4163,x4164,x4165,x4161),f201(x4163,x4164,x4165,x4162)) % 19.23/19.05 [417]~E(x4171,x4172)+E(f593(x4171,x4173,x4174,x4175),f593(x4172,x4173,x4174,x4175)) % 19.23/19.05 [418]~E(x4181,x4182)+E(f593(x4183,x4181,x4184,x4185),f593(x4183,x4182,x4184,x4185)) % 19.23/19.05 [419]~E(x4191,x4192)+E(f593(x4193,x4194,x4191,x4195),f593(x4193,x4194,x4192,x4195)) % 19.23/19.05 [420]~E(x4201,x4202)+E(f593(x4203,x4204,x4205,x4201),f593(x4203,x4204,x4205,x4202)) % 19.23/19.05 [421]~E(x4211,x4212)+E(f161(x4211,x4213,x4214),f161(x4212,x4213,x4214)) % 19.23/19.05 [422]~E(x4221,x4222)+E(f161(x4223,x4221,x4224),f161(x4223,x4222,x4224)) % 19.23/19.05 [423]~E(x4231,x4232)+E(f161(x4233,x4234,x4231),f161(x4233,x4234,x4232)) % 19.23/19.05 [424]~E(x4241,x4242)+E(f856(x4241),f856(x4242)) % 19.23/19.05 [425]~E(x4251,x4252)+E(f12(x4251,x4253),f12(x4252,x4253)) % 19.23/19.05 [426]~E(x4261,x4262)+E(f12(x4263,x4261),f12(x4263,x4262)) % 19.23/19.05 [427]~E(x4271,x4272)+E(f199(x4271,x4273,x4274,x4275),f199(x4272,x4273,x4274,x4275)) % 19.23/19.05 [428]~E(x4281,x4282)+E(f199(x4283,x4281,x4284,x4285),f199(x4283,x4282,x4284,x4285)) % 19.23/19.05 [429]~E(x4291,x4292)+E(f199(x4293,x4294,x4291,x4295),f199(x4293,x4294,x4292,x4295)) % 19.23/19.05 [430]~E(x4301,x4302)+E(f199(x4303,x4304,x4305,x4301),f199(x4303,x4304,x4305,x4302)) % 19.23/19.05 [431]~E(x4311,x4312)+E(f300(x4311,x4313,x4314,x4315),f300(x4312,x4313,x4314,x4315)) % 19.23/19.05 [432]~E(x4321,x4322)+E(f300(x4323,x4321,x4324,x4325),f300(x4323,x4322,x4324,x4325)) % 19.23/19.05 [433]~E(x4331,x4332)+E(f300(x4333,x4334,x4331,x4335),f300(x4333,x4334,x4332,x4335)) % 19.23/19.05 [434]~E(x4341,x4342)+E(f300(x4343,x4344,x4345,x4341),f300(x4343,x4344,x4345,x4342)) % 19.23/19.05 [435]~E(x4351,x4352)+E(f94(x4351,x4353),f94(x4352,x4353)) % 19.23/19.05 [436]~E(x4361,x4362)+E(f94(x4363,x4361),f94(x4363,x4362)) % 19.23/19.05 [437]~E(x4371,x4372)+E(f358(x4371,x4373,x4374,x4375),f358(x4372,x4373,x4374,x4375)) % 19.23/19.05 [438]~E(x4381,x4382)+E(f358(x4383,x4381,x4384,x4385),f358(x4383,x4382,x4384,x4385)) % 19.23/19.05 [439]~E(x4391,x4392)+E(f358(x4393,x4394,x4391,x4395),f358(x4393,x4394,x4392,x4395)) % 19.23/19.05 [440]~E(x4401,x4402)+E(f358(x4403,x4404,x4405,x4401),f358(x4403,x4404,x4405,x4402)) % 19.23/19.05 [441]~E(x4411,x4412)+E(f99(x4411,x4413),f99(x4412,x4413)) % 19.23/19.05 [442]~E(x4421,x4422)+E(f99(x4423,x4421),f99(x4423,x4422)) % 19.23/19.05 [443]~E(x4431,x4432)+E(f168(x4431,x4433),f168(x4432,x4433)) % 19.23/19.05 [444]~E(x4441,x4442)+E(f168(x4443,x4441),f168(x4443,x4442)) % 19.23/19.05 [445]~E(x4451,x4452)+E(f484(x4451,x4453),f484(x4452,x4453)) % 19.23/19.05 [446]~E(x4461,x4462)+E(f484(x4463,x4461),f484(x4463,x4462)) % 19.23/19.05 [447]~E(x4471,x4472)+E(f160(x4471),f160(x4472)) % 19.23/19.05 [448]~E(x4481,x4482)+E(f370(x4481),f370(x4482)) % 19.23/19.05 [449]~E(x4491,x4492)+E(f68(x4491,x4493),f68(x4492,x4493)) % 19.23/19.05 [450]~E(x4501,x4502)+E(f68(x4503,x4501),f68(x4503,x4502)) % 19.23/19.05 [451]~E(x4511,x4512)+E(f552(x4511,x4513),f552(x4512,x4513)) % 19.23/19.05 [452]~E(x4521,x4522)+E(f552(x4523,x4521),f552(x4523,x4522)) % 19.23/19.05 [453]~E(x4531,x4532)+E(f305(x4531),f305(x4532)) % 19.23/19.05 [454]~E(x4541,x4542)+E(f442(x4541,x4543,x4544,x4545,x4546),f442(x4542,x4543,x4544,x4545,x4546)) % 19.23/19.05 [455]~E(x4551,x4552)+E(f442(x4553,x4551,x4554,x4555,x4556),f442(x4553,x4552,x4554,x4555,x4556)) % 19.23/19.05 [456]~E(x4561,x4562)+E(f442(x4563,x4564,x4561,x4565,x4566),f442(x4563,x4564,x4562,x4565,x4566)) % 19.23/19.05 [457]~E(x4571,x4572)+E(f442(x4573,x4574,x4575,x4571,x4576),f442(x4573,x4574,x4575,x4572,x4576)) % 19.23/19.05 [458]~E(x4581,x4582)+E(f442(x4583,x4584,x4585,x4586,x4581),f442(x4583,x4584,x4585,x4586,x4582)) % 19.23/19.05 [459]~E(x4591,x4592)+E(f182(x4591),f182(x4592)) % 19.23/19.05 [460]~E(x4601,x4602)+E(f699(x4601,x4603,x4604,x4605),f699(x4602,x4603,x4604,x4605)) % 19.23/19.05 [461]~E(x4611,x4612)+E(f699(x4613,x4611,x4614,x4615),f699(x4613,x4612,x4614,x4615)) % 19.23/19.05 [462]~E(x4621,x4622)+E(f699(x4623,x4624,x4621,x4625),f699(x4623,x4624,x4622,x4625)) % 19.23/19.05 [463]~E(x4631,x4632)+E(f699(x4633,x4634,x4635,x4631),f699(x4633,x4634,x4635,x4632)) % 19.23/19.05 [464]~E(x4641,x4642)+E(f167(x4641,x4643,x4644),f167(x4642,x4643,x4644)) % 19.23/19.05 [465]~E(x4651,x4652)+E(f167(x4653,x4651,x4654),f167(x4653,x4652,x4654)) % 19.23/19.05 [466]~E(x4661,x4662)+E(f167(x4663,x4664,x4661),f167(x4663,x4664,x4662)) % 19.23/19.05 [467]~E(x4671,x4672)+E(f291(x4671,x4673,x4674,x4675),f291(x4672,x4673,x4674,x4675)) % 19.23/19.05 [468]~E(x4681,x4682)+E(f291(x4683,x4681,x4684,x4685),f291(x4683,x4682,x4684,x4685)) % 19.23/19.05 [469]~E(x4691,x4692)+E(f291(x4693,x4694,x4691,x4695),f291(x4693,x4694,x4692,x4695)) % 19.23/19.05 [470]~E(x4701,x4702)+E(f291(x4703,x4704,x4705,x4701),f291(x4703,x4704,x4705,x4702)) % 19.23/19.05 [471]~E(x4711,x4712)+E(f219(x4711,x4713),f219(x4712,x4713)) % 19.23/19.05 [472]~E(x4721,x4722)+E(f219(x4723,x4721),f219(x4723,x4722)) % 19.23/19.05 [473]~E(x4731,x4732)+E(f740(x4731,x4733,x4734),f740(x4732,x4733,x4734)) % 19.23/19.05 [474]~E(x4741,x4742)+E(f740(x4743,x4741,x4744),f740(x4743,x4742,x4744)) % 19.23/19.05 [475]~E(x4751,x4752)+E(f740(x4753,x4754,x4751),f740(x4753,x4754,x4752)) % 19.23/19.05 [476]~E(x4761,x4762)+E(f532(x4761,x4763,x4764,x4765,x4766,x4767,x4768,x4769),f532(x4762,x4763,x4764,x4765,x4766,x4767,x4768,x4769)) % 19.23/19.05 [477]~E(x4771,x4772)+E(f532(x4773,x4771,x4774,x4775,x4776,x4777,x4778,x4779),f532(x4773,x4772,x4774,x4775,x4776,x4777,x4778,x4779)) % 19.23/19.05 [478]~E(x4781,x4782)+E(f532(x4783,x4784,x4781,x4785,x4786,x4787,x4788,x4789),f532(x4783,x4784,x4782,x4785,x4786,x4787,x4788,x4789)) % 19.23/19.05 [479]~E(x4791,x4792)+E(f532(x4793,x4794,x4795,x4791,x4796,x4797,x4798,x4799),f532(x4793,x4794,x4795,x4792,x4796,x4797,x4798,x4799)) % 19.23/19.05 [480]~E(x4801,x4802)+E(f532(x4803,x4804,x4805,x4806,x4801,x4807,x4808,x4809),f532(x4803,x4804,x4805,x4806,x4802,x4807,x4808,x4809)) % 19.23/19.05 [481]~E(x4811,x4812)+E(f532(x4813,x4814,x4815,x4816,x4817,x4811,x4818,x4819),f532(x4813,x4814,x4815,x4816,x4817,x4812,x4818,x4819)) % 19.23/19.05 [482]~E(x4821,x4822)+E(f532(x4823,x4824,x4825,x4826,x4827,x4828,x4821,x4829),f532(x4823,x4824,x4825,x4826,x4827,x4828,x4822,x4829)) % 19.23/19.05 [483]~E(x4831,x4832)+E(f532(x4833,x4834,x4835,x4836,x4837,x4838,x4839,x4831),f532(x4833,x4834,x4835,x4836,x4837,x4838,x4839,x4832)) % 19.23/19.05 [484]~E(x4841,x4842)+E(f135(x4841),f135(x4842)) % 19.23/19.05 [485]~E(x4851,x4852)+E(f555(x4851,x4853,x4854,x4855,x4856,x4857),f555(x4852,x4853,x4854,x4855,x4856,x4857)) % 19.23/19.05 [486]~E(x4861,x4862)+E(f555(x4863,x4861,x4864,x4865,x4866,x4867),f555(x4863,x4862,x4864,x4865,x4866,x4867)) % 19.23/19.05 [487]~E(x4871,x4872)+E(f555(x4873,x4874,x4871,x4875,x4876,x4877),f555(x4873,x4874,x4872,x4875,x4876,x4877)) % 19.23/19.05 [488]~E(x4881,x4882)+E(f555(x4883,x4884,x4885,x4881,x4886,x4887),f555(x4883,x4884,x4885,x4882,x4886,x4887)) % 19.23/19.05 [489]~E(x4891,x4892)+E(f555(x4893,x4894,x4895,x4896,x4891,x4897),f555(x4893,x4894,x4895,x4896,x4892,x4897)) % 19.23/19.05 [490]~E(x4901,x4902)+E(f555(x4903,x4904,x4905,x4906,x4907,x4901),f555(x4903,x4904,x4905,x4906,x4907,x4902)) % 19.23/19.05 [491]~E(x4911,x4912)+E(f34(x4911,x4913,x4914),f34(x4912,x4913,x4914)) % 19.23/19.05 [492]~E(x4921,x4922)+E(f34(x4923,x4921,x4924),f34(x4923,x4922,x4924)) % 19.23/19.05 [493]~E(x4931,x4932)+E(f34(x4933,x4934,x4931),f34(x4933,x4934,x4932)) % 19.23/19.05 [494]~E(x4941,x4942)+E(f529(x4941,x4943,x4944,x4945,x4946),f529(x4942,x4943,x4944,x4945,x4946)) % 19.23/19.05 [495]~E(x4951,x4952)+E(f529(x4953,x4951,x4954,x4955,x4956),f529(x4953,x4952,x4954,x4955,x4956)) % 19.23/19.05 [496]~E(x4961,x4962)+E(f529(x4963,x4964,x4961,x4965,x4966),f529(x4963,x4964,x4962,x4965,x4966)) % 19.23/19.05 [497]~E(x4971,x4972)+E(f529(x4973,x4974,x4975,x4971,x4976),f529(x4973,x4974,x4975,x4972,x4976)) % 19.23/19.05 [498]~E(x4981,x4982)+E(f529(x4983,x4984,x4985,x4986,x4981),f529(x4983,x4984,x4985,x4986,x4982)) % 19.23/19.05 [499]~E(x4991,x4992)+E(f770(x4991,x4993,x4994),f770(x4992,x4993,x4994)) % 19.23/19.05 [500]~E(x5001,x5002)+E(f770(x5003,x5001,x5004),f770(x5003,x5002,x5004)) % 19.23/19.05 [501]~E(x5011,x5012)+E(f770(x5013,x5014,x5011),f770(x5013,x5014,x5012)) % 19.23/19.05 [502]~E(x5021,x5022)+E(f169(x5021,x5023),f169(x5022,x5023)) % 19.23/19.05 [503]~E(x5031,x5032)+E(f169(x5033,x5031),f169(x5033,x5032)) % 19.23/19.05 [504]~E(x5041,x5042)+E(f797(x5041,x5043,x5044),f797(x5042,x5043,x5044)) % 19.23/19.05 [505]~E(x5051,x5052)+E(f797(x5053,x5051,x5054),f797(x5053,x5052,x5054)) % 19.23/19.05 [506]~E(x5061,x5062)+E(f797(x5063,x5064,x5061),f797(x5063,x5064,x5062)) % 19.23/19.05 [507]~E(x5071,x5072)+E(f133(x5071,x5073),f133(x5072,x5073)) % 19.23/19.05 [508]~E(x5081,x5082)+E(f133(x5083,x5081),f133(x5083,x5082)) % 19.23/19.05 [509]~E(x5091,x5092)+E(f859(x5091),f859(x5092)) % 19.23/19.05 [510]~E(x5101,x5102)+E(f271(x5101,x5103,x5104),f271(x5102,x5103,x5104)) % 19.23/19.05 [511]~E(x5111,x5112)+E(f271(x5113,x5111,x5114),f271(x5113,x5112,x5114)) % 19.23/19.05 [512]~E(x5121,x5122)+E(f271(x5123,x5124,x5121),f271(x5123,x5124,x5122)) % 19.23/19.05 [513]~E(x5131,x5132)+E(f128(x5131,x5133,x5134,x5135),f128(x5132,x5133,x5134,x5135)) % 19.23/19.05 [514]~E(x5141,x5142)+E(f128(x5143,x5141,x5144,x5145),f128(x5143,x5142,x5144,x5145)) % 19.23/19.05 [515]~E(x5151,x5152)+E(f128(x5153,x5154,x5151,x5155),f128(x5153,x5154,x5152,x5155)) % 19.23/19.05 [516]~E(x5161,x5162)+E(f128(x5163,x5164,x5165,x5161),f128(x5163,x5164,x5165,x5162)) % 19.23/19.05 [517]~E(x5171,x5172)+E(f777(x5171,x5173,x5174),f777(x5172,x5173,x5174)) % 19.23/19.05 [518]~E(x5181,x5182)+E(f777(x5183,x5181,x5184),f777(x5183,x5182,x5184)) % 19.23/19.05 [519]~E(x5191,x5192)+E(f777(x5193,x5194,x5191),f777(x5193,x5194,x5192)) % 19.23/19.05 [520]~E(x5201,x5202)+E(f672(x5201,x5203,x5204,x5205,x5206),f672(x5202,x5203,x5204,x5205,x5206)) % 19.23/19.05 [521]~E(x5211,x5212)+E(f672(x5213,x5211,x5214,x5215,x5216),f672(x5213,x5212,x5214,x5215,x5216)) % 19.23/19.05 [522]~E(x5221,x5222)+E(f672(x5223,x5224,x5221,x5225,x5226),f672(x5223,x5224,x5222,x5225,x5226)) % 19.23/19.05 [523]~E(x5231,x5232)+E(f672(x5233,x5234,x5235,x5231,x5236),f672(x5233,x5234,x5235,x5232,x5236)) % 19.23/19.05 [524]~E(x5241,x5242)+E(f672(x5243,x5244,x5245,x5246,x5241),f672(x5243,x5244,x5245,x5246,x5242)) % 19.23/19.05 [525]~E(x5251,x5252)+E(f15(x5251,x5253),f15(x5252,x5253)) % 19.23/19.05 [526]~E(x5261,x5262)+E(f15(x5263,x5261),f15(x5263,x5262)) % 19.23/19.05 [527]~E(x5271,x5272)+E(f178(x5271,x5273,x5274,x5275),f178(x5272,x5273,x5274,x5275)) % 19.23/19.05 [528]~E(x5281,x5282)+E(f178(x5283,x5281,x5284,x5285),f178(x5283,x5282,x5284,x5285)) % 19.23/19.05 [529]~E(x5291,x5292)+E(f178(x5293,x5294,x5291,x5295),f178(x5293,x5294,x5292,x5295)) % 19.23/19.05 [530]~E(x5301,x5302)+E(f178(x5303,x5304,x5305,x5301),f178(x5303,x5304,x5305,x5302)) % 19.23/19.05 [531]~E(x5311,x5312)+E(f308(x5311),f308(x5312)) % 19.23/19.05 [532]~E(x5321,x5322)+E(f500(x5321,x5323,x5324,x5325,x5326),f500(x5322,x5323,x5324,x5325,x5326)) % 19.23/19.05 [533]~E(x5331,x5332)+E(f500(x5333,x5331,x5334,x5335,x5336),f500(x5333,x5332,x5334,x5335,x5336)) % 19.23/19.05 [534]~E(x5341,x5342)+E(f500(x5343,x5344,x5341,x5345,x5346),f500(x5343,x5344,x5342,x5345,x5346)) % 19.23/19.05 [535]~E(x5351,x5352)+E(f500(x5353,x5354,x5355,x5351,x5356),f500(x5353,x5354,x5355,x5352,x5356)) % 19.23/19.05 [536]~E(x5361,x5362)+E(f500(x5363,x5364,x5365,x5366,x5361),f500(x5363,x5364,x5365,x5366,x5362)) % 19.23/19.05 [537]~E(x5371,x5372)+E(f75(x5371,x5373,x5374),f75(x5372,x5373,x5374)) % 19.23/19.05 [538]~E(x5381,x5382)+E(f75(x5383,x5381,x5384),f75(x5383,x5382,x5384)) % 19.23/19.05 [539]~E(x5391,x5392)+E(f75(x5393,x5394,x5391),f75(x5393,x5394,x5392)) % 19.23/19.05 [540]~E(x5401,x5402)+E(f829(x5401,x5403,x5404,x5405),f829(x5402,x5403,x5404,x5405)) % 19.23/19.05 [541]~E(x5411,x5412)+E(f829(x5413,x5411,x5414,x5415),f829(x5413,x5412,x5414,x5415)) % 19.23/19.05 [542]~E(x5421,x5422)+E(f829(x5423,x5424,x5421,x5425),f829(x5423,x5424,x5422,x5425)) % 19.23/19.05 [543]~E(x5431,x5432)+E(f829(x5433,x5434,x5435,x5431),f829(x5433,x5434,x5435,x5432)) % 19.23/19.05 [544]~E(x5441,x5442)+E(f455(x5441,x5443),f455(x5442,x5443)) % 19.23/19.05 [545]~E(x5451,x5452)+E(f455(x5453,x5451),f455(x5453,x5452)) % 19.23/19.05 [546]~E(x5461,x5462)+E(f153(x5461,x5463),f153(x5462,x5463)) % 19.23/19.05 [547]~E(x5471,x5472)+E(f153(x5473,x5471),f153(x5473,x5472)) % 19.23/19.05 [548]~E(x5481,x5482)+E(f865(x5481,x5483),f865(x5482,x5483)) % 19.23/19.05 [549]~E(x5491,x5492)+E(f865(x5493,x5491),f865(x5493,x5492)) % 19.23/19.05 [550]~E(x5501,x5502)+E(f176(x5501,x5503,x5504),f176(x5502,x5503,x5504)) % 19.23/19.05 [551]~E(x5511,x5512)+E(f176(x5513,x5511,x5514),f176(x5513,x5512,x5514)) % 19.23/19.05 [552]~E(x5521,x5522)+E(f176(x5523,x5524,x5521),f176(x5523,x5524,x5522)) % 19.23/19.05 [553]~E(x5531,x5532)+E(f237(x5531,x5533,x5534,x5535),f237(x5532,x5533,x5534,x5535)) % 19.23/19.05 [554]~E(x5541,x5542)+E(f237(x5543,x5541,x5544,x5545),f237(x5543,x5542,x5544,x5545)) % 19.23/19.05 [555]~E(x5551,x5552)+E(f237(x5553,x5554,x5551,x5555),f237(x5553,x5554,x5552,x5555)) % 19.23/19.05 [556]~E(x5561,x5562)+E(f237(x5563,x5564,x5565,x5561),f237(x5563,x5564,x5565,x5562)) % 19.23/19.05 [557]~E(x5571,x5572)+E(f38(x5571,x5573),f38(x5572,x5573)) % 19.23/19.05 [558]~E(x5581,x5582)+E(f38(x5583,x5581),f38(x5583,x5582)) % 19.23/19.05 [559]~E(x5591,x5592)+E(f847(x5591,x5593,x5594,x5595,x5596,x5597,x5598),f847(x5592,x5593,x5594,x5595,x5596,x5597,x5598)) % 19.23/19.05 [560]~E(x5601,x5602)+E(f847(x5603,x5601,x5604,x5605,x5606,x5607,x5608),f847(x5603,x5602,x5604,x5605,x5606,x5607,x5608)) % 19.23/19.05 [561]~E(x5611,x5612)+E(f847(x5613,x5614,x5611,x5615,x5616,x5617,x5618),f847(x5613,x5614,x5612,x5615,x5616,x5617,x5618)) % 19.23/19.05 [562]~E(x5621,x5622)+E(f847(x5623,x5624,x5625,x5621,x5626,x5627,x5628),f847(x5623,x5624,x5625,x5622,x5626,x5627,x5628)) % 19.23/19.05 [563]~E(x5631,x5632)+E(f847(x5633,x5634,x5635,x5636,x5631,x5637,x5638),f847(x5633,x5634,x5635,x5636,x5632,x5637,x5638)) % 19.23/19.05 [564]~E(x5641,x5642)+E(f847(x5643,x5644,x5645,x5646,x5647,x5641,x5648),f847(x5643,x5644,x5645,x5646,x5647,x5642,x5648)) % 19.23/19.05 [565]~E(x5651,x5652)+E(f847(x5653,x5654,x5655,x5656,x5657,x5658,x5651),f847(x5653,x5654,x5655,x5656,x5657,x5658,x5652)) % 19.23/19.05 [566]~E(x5661,x5662)+E(f406(x5661,x5663,x5664),f406(x5662,x5663,x5664)) % 19.23/19.05 [567]~E(x5671,x5672)+E(f406(x5673,x5671,x5674),f406(x5673,x5672,x5674)) % 19.23/19.05 [568]~E(x5681,x5682)+E(f406(x5683,x5684,x5681),f406(x5683,x5684,x5682)) % 19.23/19.05 [569]~E(x5691,x5692)+E(f267(x5691),f267(x5692)) % 19.23/19.05 [570]~E(x5701,x5702)+E(f466(x5701,x5703,x5704,x5705),f466(x5702,x5703,x5704,x5705)) % 19.23/19.05 [571]~E(x5711,x5712)+E(f466(x5713,x5711,x5714,x5715),f466(x5713,x5712,x5714,x5715)) % 19.23/19.05 [572]~E(x5721,x5722)+E(f466(x5723,x5724,x5721,x5725),f466(x5723,x5724,x5722,x5725)) % 19.23/19.05 [573]~E(x5731,x5732)+E(f466(x5733,x5734,x5735,x5731),f466(x5733,x5734,x5735,x5732)) % 19.23/19.05 [574]~E(x5741,x5742)+E(f345(x5741,x5743,x5744,x5745),f345(x5742,x5743,x5744,x5745)) % 19.23/19.05 [575]~E(x5751,x5752)+E(f345(x5753,x5751,x5754,x5755),f345(x5753,x5752,x5754,x5755)) % 19.23/19.05 [576]~E(x5761,x5762)+E(f345(x5763,x5764,x5761,x5765),f345(x5763,x5764,x5762,x5765)) % 19.23/19.05 [577]~E(x5771,x5772)+E(f345(x5773,x5774,x5775,x5771),f345(x5773,x5774,x5775,x5772)) % 19.23/19.05 [578]~E(x5781,x5782)+E(f472(x5781,x5783,x5784,x5785,x5786),f472(x5782,x5783,x5784,x5785,x5786)) % 19.23/19.05 [579]~E(x5791,x5792)+E(f472(x5793,x5791,x5794,x5795,x5796),f472(x5793,x5792,x5794,x5795,x5796)) % 19.23/19.05 [580]~E(x5801,x5802)+E(f472(x5803,x5804,x5801,x5805,x5806),f472(x5803,x5804,x5802,x5805,x5806)) % 19.23/19.05 [581]~E(x5811,x5812)+E(f472(x5813,x5814,x5815,x5811,x5816),f472(x5813,x5814,x5815,x5812,x5816)) % 19.23/19.05 [582]~E(x5821,x5822)+E(f472(x5823,x5824,x5825,x5826,x5821),f472(x5823,x5824,x5825,x5826,x5822)) % 19.23/19.05 [583]~E(x5831,x5832)+E(f772(x5831),f772(x5832)) % 19.23/19.05 [584]~E(x5841,x5842)+E(f475(x5841,x5843),f475(x5842,x5843)) % 19.23/19.05 [585]~E(x5851,x5852)+E(f475(x5853,x5851),f475(x5853,x5852)) % 19.23/19.05 [586]~E(x5861,x5862)+E(f544(x5861,x5863,x5864,x5865,x5866),f544(x5862,x5863,x5864,x5865,x5866)) % 19.23/19.05 [587]~E(x5871,x5872)+E(f544(x5873,x5871,x5874,x5875,x5876),f544(x5873,x5872,x5874,x5875,x5876)) % 19.23/19.05 [588]~E(x5881,x5882)+E(f544(x5883,x5884,x5881,x5885,x5886),f544(x5883,x5884,x5882,x5885,x5886)) % 19.23/19.05 [589]~E(x5891,x5892)+E(f544(x5893,x5894,x5895,x5891,x5896),f544(x5893,x5894,x5895,x5892,x5896)) % 19.23/19.05 [590]~E(x5901,x5902)+E(f544(x5903,x5904,x5905,x5906,x5901),f544(x5903,x5904,x5905,x5906,x5902)) % 19.23/19.05 [591]~E(x5911,x5912)+E(f783(x5911,x5913),f783(x5912,x5913)) % 19.23/19.05 [592]~E(x5921,x5922)+E(f783(x5923,x5921),f783(x5923,x5922)) % 19.23/19.05 [593]~E(x5931,x5932)+E(f297(x5931,x5933,x5934),f297(x5932,x5933,x5934)) % 19.23/19.05 [594]~E(x5941,x5942)+E(f297(x5943,x5941,x5944),f297(x5943,x5942,x5944)) % 19.23/19.05 [595]~E(x5951,x5952)+E(f297(x5953,x5954,x5951),f297(x5953,x5954,x5952)) % 19.23/19.05 [596]~E(x5961,x5962)+E(f561(x5961,x5963,x5964),f561(x5962,x5963,x5964)) % 19.23/19.05 [597]~E(x5971,x5972)+E(f561(x5973,x5971,x5974),f561(x5973,x5972,x5974)) % 19.23/19.05 [598]~E(x5981,x5982)+E(f561(x5983,x5984,x5981),f561(x5983,x5984,x5982)) % 19.23/19.05 [599]~E(x5991,x5992)+E(f537(x5991,x5993,x5994,x5995),f537(x5992,x5993,x5994,x5995)) % 19.23/19.05 [600]~E(x6001,x6002)+E(f537(x6003,x6001,x6004,x6005),f537(x6003,x6002,x6004,x6005)) % 19.23/19.05 [601]~E(x6011,x6012)+E(f537(x6013,x6014,x6011,x6015),f537(x6013,x6014,x6012,x6015)) % 19.23/19.05 [602]~E(x6021,x6022)+E(f537(x6023,x6024,x6025,x6021),f537(x6023,x6024,x6025,x6022)) % 19.23/19.05 [603]~E(x6031,x6032)+E(f119(x6031),f119(x6032)) % 19.23/19.05 [604]~E(x6041,x6042)+E(f453(x6041,x6043,x6044,x6045),f453(x6042,x6043,x6044,x6045)) % 19.23/19.05 [605]~E(x6051,x6052)+E(f453(x6053,x6051,x6054,x6055),f453(x6053,x6052,x6054,x6055)) % 19.23/19.05 [606]~E(x6061,x6062)+E(f453(x6063,x6064,x6061,x6065),f453(x6063,x6064,x6062,x6065)) % 19.23/19.05 [607]~E(x6071,x6072)+E(f453(x6073,x6074,x6075,x6071),f453(x6073,x6074,x6075,x6072)) % 19.23/19.05 [608]~E(x6081,x6082)+E(f563(x6081,x6083,x6084,x6085,x6086),f563(x6082,x6083,x6084,x6085,x6086)) % 19.23/19.05 [609]~E(x6091,x6092)+E(f563(x6093,x6091,x6094,x6095,x6096),f563(x6093,x6092,x6094,x6095,x6096)) % 19.23/19.05 [610]~E(x6101,x6102)+E(f563(x6103,x6104,x6101,x6105,x6106),f563(x6103,x6104,x6102,x6105,x6106)) % 19.23/19.05 [611]~E(x6111,x6112)+E(f563(x6113,x6114,x6115,x6111,x6116),f563(x6113,x6114,x6115,x6112,x6116)) % 19.23/19.05 [612]~E(x6121,x6122)+E(f563(x6123,x6124,x6125,x6126,x6121),f563(x6123,x6124,x6125,x6126,x6122)) % 19.23/19.05 [613]~E(x6131,x6132)+E(f61(x6131,x6133),f61(x6132,x6133)) % 19.23/19.05 [614]~E(x6141,x6142)+E(f61(x6143,x6141),f61(x6143,x6142)) % 19.23/19.05 [615]~E(x6151,x6152)+E(f640(x6151,x6153,x6154),f640(x6152,x6153,x6154)) % 19.23/19.05 [616]~E(x6161,x6162)+E(f640(x6163,x6161,x6164),f640(x6163,x6162,x6164)) % 19.23/19.05 [617]~E(x6171,x6172)+E(f640(x6173,x6174,x6171),f640(x6173,x6174,x6172)) % 19.23/19.05 [618]~E(x6181,x6182)+E(f335(x6181,x6183,x6184,x6185),f335(x6182,x6183,x6184,x6185)) % 19.23/19.05 [619]~E(x6191,x6192)+E(f335(x6193,x6191,x6194,x6195),f335(x6193,x6192,x6194,x6195)) % 19.23/19.05 [620]~E(x6201,x6202)+E(f335(x6203,x6204,x6201,x6205),f335(x6203,x6204,x6202,x6205)) % 19.23/19.05 [621]~E(x6211,x6212)+E(f335(x6213,x6214,x6215,x6211),f335(x6213,x6214,x6215,x6212)) % 19.23/19.05 [622]~E(x6221,x6222)+E(f835(x6221,x6223,x6224),f835(x6222,x6223,x6224)) % 19.23/19.05 [623]~E(x6231,x6232)+E(f835(x6233,x6231,x6234),f835(x6233,x6232,x6234)) % 19.23/19.05 [624]~E(x6241,x6242)+E(f835(x6243,x6244,x6241),f835(x6243,x6244,x6242)) % 19.23/19.05 [625]~E(x6251,x6252)+E(f788(x6251,x6253,x6254),f788(x6252,x6253,x6254)) % 19.23/19.05 [626]~E(x6261,x6262)+E(f788(x6263,x6261,x6264),f788(x6263,x6262,x6264)) % 19.23/19.05 [627]~E(x6271,x6272)+E(f788(x6273,x6274,x6271),f788(x6273,x6274,x6272)) % 19.23/19.05 [628]~E(x6281,x6282)+E(f234(x6281,x6283),f234(x6282,x6283)) % 19.23/19.05 [629]~E(x6291,x6292)+E(f234(x6293,x6291),f234(x6293,x6292)) % 19.23/19.05 [630]~E(x6301,x6302)+E(f73(x6301,x6303),f73(x6302,x6303)) % 19.23/19.05 [631]~E(x6311,x6312)+E(f73(x6313,x6311),f73(x6313,x6312)) % 19.23/19.05 [632]~E(x6321,x6322)+E(f796(x6321,x6323,x6324),f796(x6322,x6323,x6324)) % 19.23/19.05 [633]~E(x6331,x6332)+E(f796(x6333,x6331,x6334),f796(x6333,x6332,x6334)) % 19.23/19.05 [634]~E(x6341,x6342)+E(f796(x6343,x6344,x6341),f796(x6343,x6344,x6342)) % 19.23/19.05 [635]~E(x6351,x6352)+E(f678(x6351,x6353,x6354,x6355,x6356),f678(x6352,x6353,x6354,x6355,x6356)) % 19.23/19.05 [636]~E(x6361,x6362)+E(f678(x6363,x6361,x6364,x6365,x6366),f678(x6363,x6362,x6364,x6365,x6366)) % 19.23/19.05 [637]~E(x6371,x6372)+E(f678(x6373,x6374,x6371,x6375,x6376),f678(x6373,x6374,x6372,x6375,x6376)) % 19.23/19.05 [638]~E(x6381,x6382)+E(f678(x6383,x6384,x6385,x6381,x6386),f678(x6383,x6384,x6385,x6382,x6386)) % 19.23/19.05 [639]~E(x6391,x6392)+E(f678(x6393,x6394,x6395,x6396,x6391),f678(x6393,x6394,x6395,x6396,x6392)) % 19.23/19.05 [640]~E(x6401,x6402)+E(f648(x6401,x6403,x6404),f648(x6402,x6403,x6404)) % 19.23/19.05 [641]~E(x6411,x6412)+E(f648(x6413,x6411,x6414),f648(x6413,x6412,x6414)) % 19.23/19.05 [642]~E(x6421,x6422)+E(f648(x6423,x6424,x6421),f648(x6423,x6424,x6422)) % 19.23/19.05 [643]~E(x6431,x6432)+E(f239(x6431),f239(x6432)) % 19.23/19.05 [644]~E(x6441,x6442)+E(f275(x6441,x6443),f275(x6442,x6443)) % 19.23/19.05 [645]~E(x6451,x6452)+E(f275(x6453,x6451),f275(x6453,x6452)) % 19.23/19.05 [646]~E(x6461,x6462)+E(f616(x6461,x6463,x6464),f616(x6462,x6463,x6464)) % 19.23/19.05 [647]~E(x6471,x6472)+E(f616(x6473,x6471,x6474),f616(x6473,x6472,x6474)) % 19.23/19.05 [648]~E(x6481,x6482)+E(f616(x6483,x6484,x6481),f616(x6483,x6484,x6482)) % 19.23/19.05 [649]~E(x6491,x6492)+E(f644(x6491,x6493,x6494),f644(x6492,x6493,x6494)) % 19.23/19.05 [650]~E(x6501,x6502)+E(f644(x6503,x6501,x6504),f644(x6503,x6502,x6504)) % 19.23/19.05 [651]~E(x6511,x6512)+E(f644(x6513,x6514,x6511),f644(x6513,x6514,x6512)) % 19.23/19.05 [652]~E(x6521,x6522)+E(f794(x6521,x6523,x6524),f794(x6522,x6523,x6524)) % 19.23/19.05 [653]~E(x6531,x6532)+E(f794(x6533,x6531,x6534),f794(x6533,x6532,x6534)) % 19.23/19.05 [654]~E(x6541,x6542)+E(f794(x6543,x6544,x6541),f794(x6543,x6544,x6542)) % 19.23/19.05 [655]~E(x6551,x6552)+E(f390(x6551,x6553),f390(x6552,x6553)) % 19.23/19.05 [656]~E(x6561,x6562)+E(f390(x6563,x6561),f390(x6563,x6562)) % 19.23/19.05 [657]~E(x6571,x6572)+E(f694(x6571,x6573,x6574,x6575),f694(x6572,x6573,x6574,x6575)) % 19.23/19.05 [658]~E(x6581,x6582)+E(f694(x6583,x6581,x6584,x6585),f694(x6583,x6582,x6584,x6585)) % 19.23/19.05 [659]~E(x6591,x6592)+E(f694(x6593,x6594,x6591,x6595),f694(x6593,x6594,x6592,x6595)) % 19.23/19.05 [660]~E(x6601,x6602)+E(f694(x6603,x6604,x6605,x6601),f694(x6603,x6604,x6605,x6602)) % 19.23/19.05 [661]~E(x6611,x6612)+E(f467(x6611,x6613,x6614,x6615),f467(x6612,x6613,x6614,x6615)) % 19.23/19.05 [662]~E(x6621,x6622)+E(f467(x6623,x6621,x6624,x6625),f467(x6623,x6622,x6624,x6625)) % 19.23/19.05 [663]~E(x6631,x6632)+E(f467(x6633,x6634,x6631,x6635),f467(x6633,x6634,x6632,x6635)) % 19.23/19.05 [664]~E(x6641,x6642)+E(f467(x6643,x6644,x6645,x6641),f467(x6643,x6644,x6645,x6642)) % 19.23/19.05 [665]~E(x6651,x6652)+E(f436(x6651,x6653,x6654,x6655),f436(x6652,x6653,x6654,x6655)) % 19.23/19.05 [666]~E(x6661,x6662)+E(f436(x6663,x6661,x6664,x6665),f436(x6663,x6662,x6664,x6665)) % 19.23/19.05 [667]~E(x6671,x6672)+E(f436(x6673,x6674,x6671,x6675),f436(x6673,x6674,x6672,x6675)) % 19.23/19.05 [668]~E(x6681,x6682)+E(f436(x6683,x6684,x6685,x6681),f436(x6683,x6684,x6685,x6682)) % 19.23/19.05 [669]~E(x6691,x6692)+E(f367(x6691,x6693,x6694,x6695),f367(x6692,x6693,x6694,x6695)) % 19.23/19.05 [670]~E(x6701,x6702)+E(f367(x6703,x6701,x6704,x6705),f367(x6703,x6702,x6704,x6705)) % 19.23/19.05 [671]~E(x6711,x6712)+E(f367(x6713,x6714,x6711,x6715),f367(x6713,x6714,x6712,x6715)) % 19.23/19.05 [672]~E(x6721,x6722)+E(f367(x6723,x6724,x6725,x6721),f367(x6723,x6724,x6725,x6722)) % 19.23/19.05 [673]~E(x6731,x6732)+E(f243(x6731,x6733),f243(x6732,x6733)) % 19.23/19.05 [674]~E(x6741,x6742)+E(f243(x6743,x6741),f243(x6743,x6742)) % 19.23/19.05 [675]~E(x6751,x6752)+E(f258(x6751,x6753,x6754,x6755),f258(x6752,x6753,x6754,x6755)) % 19.23/19.05 [676]~E(x6761,x6762)+E(f258(x6763,x6761,x6764,x6765),f258(x6763,x6762,x6764,x6765)) % 19.23/19.05 [677]~E(x6771,x6772)+E(f258(x6773,x6774,x6771,x6775),f258(x6773,x6774,x6772,x6775)) % 19.23/19.05 [678]~E(x6781,x6782)+E(f258(x6783,x6784,x6785,x6781),f258(x6783,x6784,x6785,x6782)) % 19.23/19.05 [679]~E(x6791,x6792)+E(f776(x6791,x6793),f776(x6792,x6793)) % 19.23/19.05 [680]~E(x6801,x6802)+E(f776(x6803,x6801),f776(x6803,x6802)) % 19.23/19.05 [681]~E(x6811,x6812)+E(f170(x6811),f170(x6812)) % 19.23/19.05 [682]~E(x6821,x6822)+E(f364(x6821,x6823,x6824,x6825),f364(x6822,x6823,x6824,x6825)) % 19.23/19.05 [683]~E(x6831,x6832)+E(f364(x6833,x6831,x6834,x6835),f364(x6833,x6832,x6834,x6835)) % 19.23/19.05 [684]~E(x6841,x6842)+E(f364(x6843,x6844,x6841,x6845),f364(x6843,x6844,x6842,x6845)) % 19.23/19.05 [685]~E(x6851,x6852)+E(f364(x6853,x6854,x6855,x6851),f364(x6853,x6854,x6855,x6852)) % 19.23/19.05 [686]~E(x6861,x6862)+E(f270(x6861,x6863),f270(x6862,x6863)) % 19.23/19.05 [687]~E(x6871,x6872)+E(f270(x6873,x6871),f270(x6873,x6872)) % 19.23/19.05 [688]~E(x6881,x6882)+E(f256(x6881,x6883,x6884),f256(x6882,x6883,x6884)) % 19.23/19.05 [689]~E(x6891,x6892)+E(f256(x6893,x6891,x6894),f256(x6893,x6892,x6894)) % 19.23/19.05 [690]~E(x6901,x6902)+E(f256(x6903,x6904,x6901),f256(x6903,x6904,x6902)) % 19.23/19.05 [691]~E(x6911,x6912)+E(f221(x6911,x6913),f221(x6912,x6913)) % 19.23/19.05 [692]~E(x6921,x6922)+E(f221(x6923,x6921),f221(x6923,x6922)) % 19.23/19.05 [693]~E(x6931,x6932)+E(f209(x6931,x6933,x6934,x6935),f209(x6932,x6933,x6934,x6935)) % 19.23/19.05 [694]~E(x6941,x6942)+E(f209(x6943,x6941,x6944,x6945),f209(x6943,x6942,x6944,x6945)) % 19.23/19.05 [695]~E(x6951,x6952)+E(f209(x6953,x6954,x6951,x6955),f209(x6953,x6954,x6952,x6955)) % 19.23/19.05 [696]~E(x6961,x6962)+E(f209(x6963,x6964,x6965,x6961),f209(x6963,x6964,x6965,x6962)) % 19.23/19.05 [697]~E(x6971,x6972)+E(f691(x6971,x6973,x6974),f691(x6972,x6973,x6974)) % 19.23/19.05 [698]~E(x6981,x6982)+E(f691(x6983,x6981,x6984),f691(x6983,x6982,x6984)) % 19.23/19.05 [699]~E(x6991,x6992)+E(f691(x6993,x6994,x6991),f691(x6993,x6994,x6992)) % 19.23/19.05 [700]~E(x7001,x7002)+E(f525(x7001,x7003,x7004,x7005,x7006),f525(x7002,x7003,x7004,x7005,x7006)) % 19.23/19.05 [701]~E(x7011,x7012)+E(f525(x7013,x7011,x7014,x7015,x7016),f525(x7013,x7012,x7014,x7015,x7016)) % 19.23/19.05 [702]~E(x7021,x7022)+E(f525(x7023,x7024,x7021,x7025,x7026),f525(x7023,x7024,x7022,x7025,x7026)) % 19.23/19.05 [703]~E(x7031,x7032)+E(f525(x7033,x7034,x7035,x7031,x7036),f525(x7033,x7034,x7035,x7032,x7036)) % 19.23/19.05 [704]~E(x7041,x7042)+E(f525(x7043,x7044,x7045,x7046,x7041),f525(x7043,x7044,x7045,x7046,x7042)) % 19.23/19.05 [705]~E(x7051,x7052)+E(f590(x7051,x7053,x7054),f590(x7052,x7053,x7054)) % 19.23/19.05 [706]~E(x7061,x7062)+E(f590(x7063,x7061,x7064),f590(x7063,x7062,x7064)) % 19.23/19.05 [707]~E(x7071,x7072)+E(f590(x7073,x7074,x7071),f590(x7073,x7074,x7072)) % 19.23/19.05 [708]~E(x7081,x7082)+E(f103(x7081,x7083,x7084,x7085),f103(x7082,x7083,x7084,x7085)) % 19.23/19.05 [709]~E(x7091,x7092)+E(f103(x7093,x7091,x7094,x7095),f103(x7093,x7092,x7094,x7095)) % 19.23/19.05 [710]~E(x7101,x7102)+E(f103(x7103,x7104,x7101,x7105),f103(x7103,x7104,x7102,x7105)) % 19.23/19.05 [711]~E(x7111,x7112)+E(f103(x7113,x7114,x7115,x7111),f103(x7113,x7114,x7115,x7112)) % 19.23/19.05 [712]~E(x7121,x7122)+E(f531(x7121,x7123,x7124,x7125,x7126,x7127),f531(x7122,x7123,x7124,x7125,x7126,x7127)) % 19.23/19.05 [713]~E(x7131,x7132)+E(f531(x7133,x7131,x7134,x7135,x7136,x7137),f531(x7133,x7132,x7134,x7135,x7136,x7137)) % 19.23/19.05 [714]~E(x7141,x7142)+E(f531(x7143,x7144,x7141,x7145,x7146,x7147),f531(x7143,x7144,x7142,x7145,x7146,x7147)) % 19.23/19.05 [715]~E(x7151,x7152)+E(f531(x7153,x7154,x7155,x7151,x7156,x7157),f531(x7153,x7154,x7155,x7152,x7156,x7157)) % 19.23/19.05 [716]~E(x7161,x7162)+E(f531(x7163,x7164,x7165,x7166,x7161,x7167),f531(x7163,x7164,x7165,x7166,x7162,x7167)) % 19.23/19.05 [717]~E(x7171,x7172)+E(f531(x7173,x7174,x7175,x7176,x7177,x7171),f531(x7173,x7174,x7175,x7176,x7177,x7172)) % 19.23/19.05 [718]~E(x7181,x7182)+E(f159(x7181,x7183,x7184,x7185),f159(x7182,x7183,x7184,x7185)) % 19.23/19.05 [719]~E(x7191,x7192)+E(f159(x7193,x7191,x7194,x7195),f159(x7193,x7192,x7194,x7195)) % 19.23/19.05 [720]~E(x7201,x7202)+E(f159(x7203,x7204,x7201,x7205),f159(x7203,x7204,x7202,x7205)) % 19.23/19.05 [721]~E(x7211,x7212)+E(f159(x7213,x7214,x7215,x7211),f159(x7213,x7214,x7215,x7212)) % 19.23/19.05 [722]~E(x7221,x7222)+E(f458(x7221,x7223),f458(x7222,x7223)) % 19.23/19.05 [723]~E(x7231,x7232)+E(f458(x7233,x7231),f458(x7233,x7232)) % 19.23/19.05 [724]~E(x7241,x7242)+E(f154(x7241,x7243),f154(x7242,x7243)) % 19.23/19.05 [725]~E(x7251,x7252)+E(f154(x7253,x7251),f154(x7253,x7252)) % 19.23/19.05 [726]~E(x7261,x7262)+E(f302(x7261),f302(x7262)) % 19.23/19.05 [727]~E(x7271,x7272)+E(f727(x7271,x7273,x7274,x7275,x7276),f727(x7272,x7273,x7274,x7275,x7276)) % 19.23/19.05 [728]~E(x7281,x7282)+E(f727(x7283,x7281,x7284,x7285,x7286),f727(x7283,x7282,x7284,x7285,x7286)) % 19.23/19.05 [729]~E(x7291,x7292)+E(f727(x7293,x7294,x7291,x7295,x7296),f727(x7293,x7294,x7292,x7295,x7296)) % 19.23/19.05 [730]~E(x7301,x7302)+E(f727(x7303,x7304,x7305,x7301,x7306),f727(x7303,x7304,x7305,x7302,x7306)) % 19.23/19.05 [731]~E(x7311,x7312)+E(f727(x7313,x7314,x7315,x7316,x7311),f727(x7313,x7314,x7315,x7316,x7312)) % 19.23/19.05 [732]~E(x7321,x7322)+E(f155(x7321,x7323),f155(x7322,x7323)) % 19.23/19.05 [733]~E(x7331,x7332)+E(f155(x7333,x7331),f155(x7333,x7332)) % 19.23/19.05 [734]~E(x7341,x7342)+E(f63(x7341,x7343),f63(x7342,x7343)) % 19.23/19.05 [735]~E(x7351,x7352)+E(f63(x7353,x7351),f63(x7353,x7352)) % 19.23/19.05 [736]~E(x7361,x7362)+E(f298(x7361,x7363,x7364,x7365,x7366),f298(x7362,x7363,x7364,x7365,x7366)) % 19.23/19.05 [737]~E(x7371,x7372)+E(f298(x7373,x7371,x7374,x7375,x7376),f298(x7373,x7372,x7374,x7375,x7376)) % 19.23/19.05 [738]~E(x7381,x7382)+E(f298(x7383,x7384,x7381,x7385,x7386),f298(x7383,x7384,x7382,x7385,x7386)) % 19.23/19.05 [739]~E(x7391,x7392)+E(f298(x7393,x7394,x7395,x7391,x7396),f298(x7393,x7394,x7395,x7392,x7396)) % 19.23/19.05 [740]~E(x7401,x7402)+E(f298(x7403,x7404,x7405,x7406,x7401),f298(x7403,x7404,x7405,x7406,x7402)) % 19.23/19.05 [741]~E(x7411,x7412)+E(f346(x7411),f346(x7412)) % 19.23/19.05 [742]~E(x7421,x7422)+E(f649(x7421,x7423,x7424),f649(x7422,x7423,x7424)) % 19.23/19.05 [743]~E(x7431,x7432)+E(f649(x7433,x7431,x7434),f649(x7433,x7432,x7434)) % 19.23/19.05 [744]~E(x7441,x7442)+E(f649(x7443,x7444,x7441),f649(x7443,x7444,x7442)) % 19.23/19.05 [745]~E(x7451,x7452)+E(f441(x7451,x7453,x7454),f441(x7452,x7453,x7454)) % 19.23/19.05 [746]~E(x7461,x7462)+E(f441(x7463,x7461,x7464),f441(x7463,x7462,x7464)) % 19.23/19.05 [747]~E(x7471,x7472)+E(f441(x7473,x7474,x7471),f441(x7473,x7474,x7472)) % 19.23/19.05 [748]~E(x7481,x7482)+E(f656(x7481,x7483,x7484,x7485,x7486),f656(x7482,x7483,x7484,x7485,x7486)) % 19.23/19.05 [749]~E(x7491,x7492)+E(f656(x7493,x7491,x7494,x7495,x7496),f656(x7493,x7492,x7494,x7495,x7496)) % 19.23/19.05 [750]~E(x7501,x7502)+E(f656(x7503,x7504,x7501,x7505,x7506),f656(x7503,x7504,x7502,x7505,x7506)) % 19.23/19.05 [751]~E(x7511,x7512)+E(f656(x7513,x7514,x7515,x7511,x7516),f656(x7513,x7514,x7515,x7512,x7516)) % 19.23/19.05 [752]~E(x7521,x7522)+E(f656(x7523,x7524,x7525,x7526,x7521),f656(x7523,x7524,x7525,x7526,x7522)) % 19.23/19.05 [753]~E(x7531,x7532)+E(f331(x7531,x7533),f331(x7532,x7533)) % 19.23/19.05 [754]~E(x7541,x7542)+E(f331(x7543,x7541),f331(x7543,x7542)) % 19.23/19.05 [755]~E(x7551,x7552)+E(f845(x7551,x7553,x7554,x7555,x7556),f845(x7552,x7553,x7554,x7555,x7556)) % 19.23/19.05 [756]~E(x7561,x7562)+E(f845(x7563,x7561,x7564,x7565,x7566),f845(x7563,x7562,x7564,x7565,x7566)) % 19.23/19.05 [757]~E(x7571,x7572)+E(f845(x7573,x7574,x7571,x7575,x7576),f845(x7573,x7574,x7572,x7575,x7576)) % 19.23/19.05 [758]~E(x7581,x7582)+E(f845(x7583,x7584,x7585,x7581,x7586),f845(x7583,x7584,x7585,x7582,x7586)) % 19.23/19.05 [759]~E(x7591,x7592)+E(f845(x7593,x7594,x7595,x7596,x7591),f845(x7593,x7594,x7595,x7596,x7592)) % 19.23/19.05 [760]~E(x7601,x7602)+E(f141(x7601,x7603),f141(x7602,x7603)) % 19.23/19.05 [761]~E(x7611,x7612)+E(f141(x7613,x7611),f141(x7613,x7612)) % 19.23/19.05 [762]~E(x7621,x7622)+E(f538(x7621),f538(x7622)) % 19.23/19.05 [763]~E(x7631,x7632)+E(f564(x7631,x7633,x7634,x7635,x7636),f564(x7632,x7633,x7634,x7635,x7636)) % 19.23/19.05 [764]~E(x7641,x7642)+E(f564(x7643,x7641,x7644,x7645,x7646),f564(x7643,x7642,x7644,x7645,x7646)) % 19.23/19.05 [765]~E(x7651,x7652)+E(f564(x7653,x7654,x7651,x7655,x7656),f564(x7653,x7654,x7652,x7655,x7656)) % 19.23/19.05 [766]~E(x7661,x7662)+E(f564(x7663,x7664,x7665,x7661,x7666),f564(x7663,x7664,x7665,x7662,x7666)) % 19.23/19.05 [767]~E(x7671,x7672)+E(f564(x7673,x7674,x7675,x7676,x7671),f564(x7673,x7674,x7675,x7676,x7672)) % 19.23/19.05 [768]~E(x7681,x7682)+E(f736(x7681,x7683,x7684,x7685),f736(x7682,x7683,x7684,x7685)) % 19.23/19.05 [769]~E(x7691,x7692)+E(f736(x7693,x7691,x7694,x7695),f736(x7693,x7692,x7694,x7695)) % 19.23/19.05 [770]~E(x7701,x7702)+E(f736(x7703,x7704,x7701,x7705),f736(x7703,x7704,x7702,x7705)) % 19.23/19.05 [771]~E(x7711,x7712)+E(f736(x7713,x7714,x7715,x7711),f736(x7713,x7714,x7715,x7712)) % 19.23/19.05 [772]~E(x7721,x7722)+E(f400(x7721,x7723),f400(x7722,x7723)) % 19.23/19.05 [773]~E(x7731,x7732)+E(f400(x7733,x7731),f400(x7733,x7732)) % 19.23/19.05 [774]~E(x7741,x7742)+E(f841(x7741,x7743,x7744),f841(x7742,x7743,x7744)) % 19.23/19.05 [775]~E(x7751,x7752)+E(f841(x7753,x7751,x7754),f841(x7753,x7752,x7754)) % 19.23/19.05 [776]~E(x7761,x7762)+E(f841(x7763,x7764,x7761),f841(x7763,x7764,x7762)) % 19.23/19.05 [777]~E(x7771,x7772)+E(f353(x7771,x7773),f353(x7772,x7773)) % 19.23/19.05 [778]~E(x7781,x7782)+E(f353(x7783,x7781),f353(x7783,x7782)) % 19.23/19.05 [779]~E(x7791,x7792)+E(f72(x7791,x7793,x7794),f72(x7792,x7793,x7794)) % 19.23/19.05 [780]~E(x7801,x7802)+E(f72(x7803,x7801,x7804),f72(x7803,x7802,x7804)) % 19.23/19.05 [781]~E(x7811,x7812)+E(f72(x7813,x7814,x7811),f72(x7813,x7814,x7812)) % 19.23/19.05 [782]~E(x7821,x7822)+E(f76(x7821,x7823,x7824,x7825,x7826),f76(x7822,x7823,x7824,x7825,x7826)) % 19.23/19.05 [783]~E(x7831,x7832)+E(f76(x7833,x7831,x7834,x7835,x7836),f76(x7833,x7832,x7834,x7835,x7836)) % 19.23/19.05 [784]~E(x7841,x7842)+E(f76(x7843,x7844,x7841,x7845,x7846),f76(x7843,x7844,x7842,x7845,x7846)) % 19.23/19.05 [785]~E(x7851,x7852)+E(f76(x7853,x7854,x7855,x7851,x7856),f76(x7853,x7854,x7855,x7852,x7856)) % 19.23/19.05 [786]~E(x7861,x7862)+E(f76(x7863,x7864,x7865,x7866,x7861),f76(x7863,x7864,x7865,x7866,x7862)) % 19.23/19.05 [787]~E(x7871,x7872)+E(f614(x7871,x7873,x7874),f614(x7872,x7873,x7874)) % 19.23/19.05 [788]~E(x7881,x7882)+E(f614(x7883,x7881,x7884),f614(x7883,x7882,x7884)) % 19.23/19.05 [789]~E(x7891,x7892)+E(f614(x7893,x7894,x7891),f614(x7893,x7894,x7892)) % 19.23/19.05 [790]~E(x7901,x7902)+E(f268(x7901,x7903),f268(x7902,x7903)) % 19.23/19.05 [791]~E(x7911,x7912)+E(f268(x7913,x7911),f268(x7913,x7912)) % 19.23/19.05 [792]~E(x7921,x7922)+E(f77(x7921,x7923,x7924),f77(x7922,x7923,x7924)) % 19.23/19.05 [793]~E(x7931,x7932)+E(f77(x7933,x7931,x7934),f77(x7933,x7932,x7934)) % 19.23/19.05 [794]~E(x7941,x7942)+E(f77(x7943,x7944,x7941),f77(x7943,x7944,x7942)) % 19.23/19.05 [795]~E(x7951,x7952)+E(f301(x7951,x7953,x7954,x7955,x7956),f301(x7952,x7953,x7954,x7955,x7956)) % 19.23/19.05 [796]~E(x7961,x7962)+E(f301(x7963,x7961,x7964,x7965,x7966),f301(x7963,x7962,x7964,x7965,x7966)) % 19.23/19.05 [797]~E(x7971,x7972)+E(f301(x7973,x7974,x7971,x7975,x7976),f301(x7973,x7974,x7972,x7975,x7976)) % 19.23/19.05 [798]~E(x7981,x7982)+E(f301(x7983,x7984,x7985,x7981,x7986),f301(x7983,x7984,x7985,x7982,x7986)) % 19.23/19.05 [799]~E(x7991,x7992)+E(f301(x7993,x7994,x7995,x7996,x7991),f301(x7993,x7994,x7995,x7996,x7992)) % 19.23/19.05 [800]~E(x8001,x8002)+E(f837(x8001,x8003,x8004),f837(x8002,x8003,x8004)) % 19.23/19.05 [801]~E(x8011,x8012)+E(f837(x8013,x8011,x8014),f837(x8013,x8012,x8014)) % 19.23/19.05 [802]~E(x8021,x8022)+E(f837(x8023,x8024,x8021),f837(x8023,x8024,x8022)) % 19.23/19.05 [803]~E(x8031,x8032)+E(f65(x8031,x8033),f65(x8032,x8033)) % 19.23/19.05 [804]~E(x8041,x8042)+E(f65(x8043,x8041),f65(x8043,x8042)) % 19.23/19.05 [805]~E(x8051,x8052)+E(f478(x8051,x8053,x8054,x8055),f478(x8052,x8053,x8054,x8055)) % 19.23/19.05 [806]~E(x8061,x8062)+E(f478(x8063,x8061,x8064,x8065),f478(x8063,x8062,x8064,x8065)) % 19.23/19.05 [807]~E(x8071,x8072)+E(f478(x8073,x8074,x8071,x8075),f478(x8073,x8074,x8072,x8075)) % 19.23/19.05 [808]~E(x8081,x8082)+E(f478(x8083,x8084,x8085,x8081),f478(x8083,x8084,x8085,x8082)) % 19.23/19.05 [809]~E(x8091,x8092)+E(f327(x8091,x8093,x8094,x8095,x8096),f327(x8092,x8093,x8094,x8095,x8096)) % 19.23/19.05 [810]~E(x8101,x8102)+E(f327(x8103,x8101,x8104,x8105,x8106),f327(x8103,x8102,x8104,x8105,x8106)) % 19.23/19.05 [811]~E(x8111,x8112)+E(f327(x8113,x8114,x8111,x8115,x8116),f327(x8113,x8114,x8112,x8115,x8116)) % 19.23/19.05 [812]~E(x8121,x8122)+E(f327(x8123,x8124,x8125,x8121,x8126),f327(x8123,x8124,x8125,x8122,x8126)) % 19.23/19.05 [813]~E(x8131,x8132)+E(f327(x8133,x8134,x8135,x8136,x8131),f327(x8133,x8134,x8135,x8136,x8132)) % 19.23/19.05 [814]~E(x8141,x8142)+E(f368(x8141,x8143,x8144,x8145,x8146),f368(x8142,x8143,x8144,x8145,x8146)) % 19.23/19.05 [815]~E(x8151,x8152)+E(f368(x8153,x8151,x8154,x8155,x8156),f368(x8153,x8152,x8154,x8155,x8156)) % 19.23/19.05 [816]~E(x8161,x8162)+E(f368(x8163,x8164,x8161,x8165,x8166),f368(x8163,x8164,x8162,x8165,x8166)) % 19.23/19.05 [817]~E(x8171,x8172)+E(f368(x8173,x8174,x8175,x8171,x8176),f368(x8173,x8174,x8175,x8172,x8176)) % 19.23/19.05 [818]~E(x8181,x8182)+E(f368(x8183,x8184,x8185,x8186,x8181),f368(x8183,x8184,x8185,x8186,x8182)) % 19.23/19.05 [819]~E(x8191,x8192)+E(f378(x8191,x8193),f378(x8192,x8193)) % 19.23/19.05 [820]~E(x8201,x8202)+E(f378(x8203,x8201),f378(x8203,x8202)) % 19.23/19.05 [821]~E(x8211,x8212)+E(f547(x8211,x8213,x8214,x8215,x8216),f547(x8212,x8213,x8214,x8215,x8216)) % 19.23/19.05 [822]~E(x8221,x8222)+E(f547(x8223,x8221,x8224,x8225,x8226),f547(x8223,x8222,x8224,x8225,x8226)) % 19.23/19.05 [823]~E(x8231,x8232)+E(f547(x8233,x8234,x8231,x8235,x8236),f547(x8233,x8234,x8232,x8235,x8236)) % 19.23/19.05 [824]~E(x8241,x8242)+E(f547(x8243,x8244,x8245,x8241,x8246),f547(x8243,x8244,x8245,x8242,x8246)) % 19.23/19.05 [825]~E(x8251,x8252)+E(f547(x8253,x8254,x8255,x8256,x8251),f547(x8253,x8254,x8255,x8256,x8252)) % 19.23/19.05 [826]~E(x8261,x8262)+E(f95(x8261,x8263),f95(x8262,x8263)) % 19.23/19.05 [827]~E(x8271,x8272)+E(f95(x8273,x8271),f95(x8273,x8272)) % 19.23/19.05 [828]~E(x8281,x8282)+E(f526(x8281,x8283,x8284,x8285,x8286),f526(x8282,x8283,x8284,x8285,x8286)) % 19.23/19.05 [829]~E(x8291,x8292)+E(f526(x8293,x8291,x8294,x8295,x8296),f526(x8293,x8292,x8294,x8295,x8296)) % 19.23/19.05 [830]~E(x8301,x8302)+E(f526(x8303,x8304,x8301,x8305,x8306),f526(x8303,x8304,x8302,x8305,x8306)) % 19.23/19.05 [831]~E(x8311,x8312)+E(f526(x8313,x8314,x8315,x8311,x8316),f526(x8313,x8314,x8315,x8312,x8316)) % 19.23/19.05 [832]~E(x8321,x8322)+E(f526(x8323,x8324,x8325,x8326,x8321),f526(x8323,x8324,x8325,x8326,x8322)) % 19.23/19.05 [833]~E(x8331,x8332)+E(f376(x8331),f376(x8332)) % 19.23/19.05 [834]~E(x8341,x8342)+E(f369(x8341,x8343),f369(x8342,x8343)) % 19.23/19.05 [835]~E(x8351,x8352)+E(f369(x8353,x8351),f369(x8353,x8352)) % 19.23/19.05 [836]~E(x8361,x8362)+E(f150(x8361,x8363,x8364),f150(x8362,x8363,x8364)) % 19.23/19.05 [837]~E(x8371,x8372)+E(f150(x8373,x8371,x8374),f150(x8373,x8372,x8374)) % 19.23/19.05 [838]~E(x8381,x8382)+E(f150(x8383,x8384,x8381),f150(x8383,x8384,x8382)) % 19.23/19.05 [839]~E(x8391,x8392)+E(f510(x8391,x8393,x8394,x8395),f510(x8392,x8393,x8394,x8395)) % 19.23/19.05 [840]~E(x8401,x8402)+E(f510(x8403,x8401,x8404,x8405),f510(x8403,x8402,x8404,x8405)) % 19.23/19.05 [841]~E(x8411,x8412)+E(f510(x8413,x8414,x8411,x8415),f510(x8413,x8414,x8412,x8415)) % 19.23/19.05 [842]~E(x8421,x8422)+E(f510(x8423,x8424,x8425,x8421),f510(x8423,x8424,x8425,x8422)) % 19.23/19.05 [843]~E(x8431,x8432)+E(f817(x8431,x8433,x8434),f817(x8432,x8433,x8434)) % 19.23/19.05 [844]~E(x8441,x8442)+E(f817(x8443,x8441,x8444),f817(x8443,x8442,x8444)) % 19.23/19.05 [845]~E(x8451,x8452)+E(f817(x8453,x8454,x8451),f817(x8453,x8454,x8452)) % 19.23/19.05 [846]~E(x8461,x8462)+E(f610(x8461,x8463,x8464),f610(x8462,x8463,x8464)) % 19.23/19.05 [847]~E(x8471,x8472)+E(f610(x8473,x8471,x8474),f610(x8473,x8472,x8474)) % 19.23/19.05 [848]~E(x8481,x8482)+E(f610(x8483,x8484,x8481),f610(x8483,x8484,x8482)) % 19.23/19.05 [849]~E(x8491,x8492)+E(f384(x8491,x8493,x8494),f384(x8492,x8493,x8494)) % 19.23/19.05 [850]~E(x8501,x8502)+E(f384(x8503,x8501,x8504),f384(x8503,x8502,x8504)) % 19.23/19.05 [851]~E(x8511,x8512)+E(f384(x8513,x8514,x8511),f384(x8513,x8514,x8512)) % 19.23/19.05 [852]~E(x8521,x8522)+E(f411(x8521,x8523,x8524,x8525,x8526),f411(x8522,x8523,x8524,x8525,x8526)) % 19.23/19.05 [853]~E(x8531,x8532)+E(f411(x8533,x8531,x8534,x8535,x8536),f411(x8533,x8532,x8534,x8535,x8536)) % 19.23/19.05 [854]~E(x8541,x8542)+E(f411(x8543,x8544,x8541,x8545,x8546),f411(x8543,x8544,x8542,x8545,x8546)) % 19.23/19.05 [855]~E(x8551,x8552)+E(f411(x8553,x8554,x8555,x8551,x8556),f411(x8553,x8554,x8555,x8552,x8556)) % 19.23/19.05 [856]~E(x8561,x8562)+E(f411(x8563,x8564,x8565,x8566,x8561),f411(x8563,x8564,x8565,x8566,x8562)) % 19.23/19.05 [857]~E(x8571,x8572)+E(f62(x8571,x8573),f62(x8572,x8573)) % 19.23/19.05 [858]~E(x8581,x8582)+E(f62(x8583,x8581),f62(x8583,x8582)) % 19.23/19.05 [859]~E(x8591,x8592)+E(f85(x8591,x8593,x8594,x8595,x8596),f85(x8592,x8593,x8594,x8595,x8596)) % 19.23/19.05 [860]~E(x8601,x8602)+E(f85(x8603,x8601,x8604,x8605,x8606),f85(x8603,x8602,x8604,x8605,x8606)) % 19.23/19.05 [861]~E(x8611,x8612)+E(f85(x8613,x8614,x8611,x8615,x8616),f85(x8613,x8614,x8612,x8615,x8616)) % 19.23/19.05 [862]~E(x8621,x8622)+E(f85(x8623,x8624,x8625,x8621,x8626),f85(x8623,x8624,x8625,x8622,x8626)) % 19.23/19.05 [863]~E(x8631,x8632)+E(f85(x8633,x8634,x8635,x8636,x8631),f85(x8633,x8634,x8635,x8636,x8632)) % 19.23/19.05 [864]~E(x8641,x8642)+E(f432(x8641,x8643,x8644,x8645,x8646,x8647,x8648),f432(x8642,x8643,x8644,x8645,x8646,x8647,x8648)) % 19.23/19.05 [865]~E(x8651,x8652)+E(f432(x8653,x8651,x8654,x8655,x8656,x8657,x8658),f432(x8653,x8652,x8654,x8655,x8656,x8657,x8658)) % 19.23/19.05 [866]~E(x8661,x8662)+E(f432(x8663,x8664,x8661,x8665,x8666,x8667,x8668),f432(x8663,x8664,x8662,x8665,x8666,x8667,x8668)) % 19.23/19.05 [867]~E(x8671,x8672)+E(f432(x8673,x8674,x8675,x8671,x8676,x8677,x8678),f432(x8673,x8674,x8675,x8672,x8676,x8677,x8678)) % 19.23/19.05 [868]~E(x8681,x8682)+E(f432(x8683,x8684,x8685,x8686,x8681,x8687,x8688),f432(x8683,x8684,x8685,x8686,x8682,x8687,x8688)) % 19.23/19.05 [869]~E(x8691,x8692)+E(f432(x8693,x8694,x8695,x8696,x8697,x8691,x8698),f432(x8693,x8694,x8695,x8696,x8697,x8692,x8698)) % 19.23/19.05 [870]~E(x8701,x8702)+E(f432(x8703,x8704,x8705,x8706,x8707,x8708,x8701),f432(x8703,x8704,x8705,x8706,x8707,x8708,x8702)) % 19.23/19.05 [871]~E(x8711,x8712)+E(f474(x8711,x8713,x8714,x8715),f474(x8712,x8713,x8714,x8715)) % 19.23/19.05 [872]~E(x8721,x8722)+E(f474(x8723,x8721,x8724,x8725),f474(x8723,x8722,x8724,x8725)) % 19.23/19.05 [873]~E(x8731,x8732)+E(f474(x8733,x8734,x8731,x8735),f474(x8733,x8734,x8732,x8735)) % 19.23/19.05 [874]~E(x8741,x8742)+E(f474(x8743,x8744,x8745,x8741),f474(x8743,x8744,x8745,x8742)) % 19.23/19.05 [875]~E(x8751,x8752)+E(f205(x8751),f205(x8752)) % 19.23/19.05 [876]~E(x8761,x8762)+E(f328(x8761,x8763,x8764,x8765,x8766),f328(x8762,x8763,x8764,x8765,x8766)) % 19.23/19.05 [877]~E(x8771,x8772)+E(f328(x8773,x8771,x8774,x8775,x8776),f328(x8773,x8772,x8774,x8775,x8776)) % 19.23/19.05 [878]~E(x8781,x8782)+E(f328(x8783,x8784,x8781,x8785,x8786),f328(x8783,x8784,x8782,x8785,x8786)) % 19.23/19.05 [879]~E(x8791,x8792)+E(f328(x8793,x8794,x8795,x8791,x8796),f328(x8793,x8794,x8795,x8792,x8796)) % 19.23/19.05 [880]~E(x8801,x8802)+E(f328(x8803,x8804,x8805,x8806,x8801),f328(x8803,x8804,x8805,x8806,x8802)) % 19.23/19.05 [881]~E(x8811,x8812)+E(f720(x8811,x8813,x8814,x8815),f720(x8812,x8813,x8814,x8815)) % 19.23/19.05 [882]~E(x8821,x8822)+E(f720(x8823,x8821,x8824,x8825),f720(x8823,x8822,x8824,x8825)) % 19.23/19.05 [883]~E(x8831,x8832)+E(f720(x8833,x8834,x8831,x8835),f720(x8833,x8834,x8832,x8835)) % 19.23/19.05 [884]~E(x8841,x8842)+E(f720(x8843,x8844,x8845,x8841),f720(x8843,x8844,x8845,x8842)) % 19.23/19.05 [885]~E(x8851,x8852)+E(f350(x8851,x8853,x8854),f350(x8852,x8853,x8854)) % 19.23/19.05 [886]~E(x8861,x8862)+E(f350(x8863,x8861,x8864),f350(x8863,x8862,x8864)) % 19.23/19.05 [887]~E(x8871,x8872)+E(f350(x8873,x8874,x8871),f350(x8873,x8874,x8872)) % 19.23/19.05 [888]~E(x8881,x8882)+E(f734(x8881,x8883,x8884),f734(x8882,x8883,x8884)) % 19.23/19.05 [889]~E(x8891,x8892)+E(f734(x8893,x8891,x8894),f734(x8893,x8892,x8894)) % 19.23/19.05 [890]~E(x8901,x8902)+E(f734(x8903,x8904,x8901),f734(x8903,x8904,x8902)) % 19.23/19.05 [891]~E(x8911,x8912)+E(f323(x8911,x8913,x8914,x8915),f323(x8912,x8913,x8914,x8915)) % 19.23/19.05 [892]~E(x8921,x8922)+E(f323(x8923,x8921,x8924,x8925),f323(x8923,x8922,x8924,x8925)) % 19.23/19.05 [893]~E(x8931,x8932)+E(f323(x8933,x8934,x8931,x8935),f323(x8933,x8934,x8932,x8935)) % 19.23/19.05 [894]~E(x8941,x8942)+E(f323(x8943,x8944,x8945,x8941),f323(x8943,x8944,x8945,x8942)) % 19.23/19.05 [895]~E(x8951,x8952)+E(f507(x8951,x8953,x8954,x8955,x8956),f507(x8952,x8953,x8954,x8955,x8956)) % 19.23/19.05 [896]~E(x8961,x8962)+E(f507(x8963,x8961,x8964,x8965,x8966),f507(x8963,x8962,x8964,x8965,x8966)) % 19.23/19.05 [897]~E(x8971,x8972)+E(f507(x8973,x8974,x8971,x8975,x8976),f507(x8973,x8974,x8972,x8975,x8976)) % 19.23/19.05 [898]~E(x8981,x8982)+E(f507(x8983,x8984,x8985,x8981,x8986),f507(x8983,x8984,x8985,x8982,x8986)) % 19.23/19.05 [899]~E(x8991,x8992)+E(f507(x8993,x8994,x8995,x8996,x8991),f507(x8993,x8994,x8995,x8996,x8992)) % 19.23/19.05 [900]~E(x9001,x9002)+E(f86(x9001,x9003,x9004,x9005),f86(x9002,x9003,x9004,x9005)) % 19.23/19.05 [901]~E(x9011,x9012)+E(f86(x9013,x9011,x9014,x9015),f86(x9013,x9012,x9014,x9015)) % 19.23/19.05 [902]~E(x9021,x9022)+E(f86(x9023,x9024,x9021,x9025),f86(x9023,x9024,x9022,x9025)) % 19.23/19.05 [903]~E(x9031,x9032)+E(f86(x9033,x9034,x9035,x9031),f86(x9033,x9034,x9035,x9032)) % 19.23/19.05 [904]~E(x9041,x9042)+E(f613(x9041,x9043),f613(x9042,x9043)) % 19.23/19.05 [905]~E(x9051,x9052)+E(f613(x9053,x9051),f613(x9053,x9052)) % 19.23/19.05 [906]~E(x9061,x9062)+E(f463(x9061,x9063,x9064),f463(x9062,x9063,x9064)) % 19.23/19.05 [907]~E(x9071,x9072)+E(f463(x9073,x9071,x9074),f463(x9073,x9072,x9074)) % 19.23/19.05 [908]~E(x9081,x9082)+E(f463(x9083,x9084,x9081),f463(x9083,x9084,x9082)) % 19.23/19.05 [909]~E(x9091,x9092)+E(f322(x9091,x9093),f322(x9092,x9093)) % 19.23/19.05 [910]~E(x9101,x9102)+E(f322(x9103,x9101),f322(x9103,x9102)) % 19.23/19.05 [911]~E(x9111,x9112)+E(f423(x9111,x9113,x9114,x9115),f423(x9112,x9113,x9114,x9115)) % 19.23/19.05 [912]~E(x9121,x9122)+E(f423(x9123,x9121,x9124,x9125),f423(x9123,x9122,x9124,x9125)) % 19.23/19.05 [913]~E(x9131,x9132)+E(f423(x9133,x9134,x9131,x9135),f423(x9133,x9134,x9132,x9135)) % 19.23/19.05 [914]~E(x9141,x9142)+E(f423(x9143,x9144,x9145,x9141),f423(x9143,x9144,x9145,x9142)) % 19.23/19.05 [915]~E(x9151,x9152)+E(f278(x9151,x9153,x9154),f278(x9152,x9153,x9154)) % 19.23/19.05 [916]~E(x9161,x9162)+E(f278(x9163,x9161,x9164),f278(x9163,x9162,x9164)) % 19.23/19.05 [917]~E(x9171,x9172)+E(f278(x9173,x9174,x9171),f278(x9173,x9174,x9172)) % 19.23/19.05 [918]~E(x9181,x9182)+E(f448(x9181,x9183,x9184,x9185,x9186),f448(x9182,x9183,x9184,x9185,x9186)) % 19.23/19.05 [919]~E(x9191,x9192)+E(f448(x9193,x9191,x9194,x9195,x9196),f448(x9193,x9192,x9194,x9195,x9196)) % 19.23/19.05 [920]~E(x9201,x9202)+E(f448(x9203,x9204,x9201,x9205,x9206),f448(x9203,x9204,x9202,x9205,x9206)) % 19.23/19.05 [921]~E(x9211,x9212)+E(f448(x9213,x9214,x9215,x9211,x9216),f448(x9213,x9214,x9215,x9212,x9216)) % 19.23/19.05 [922]~E(x9221,x9222)+E(f448(x9223,x9224,x9225,x9226,x9221),f448(x9223,x9224,x9225,x9226,x9222)) % 19.23/19.05 [923]~E(x9231,x9232)+E(f628(x9231,x9233,x9234),f628(x9232,x9233,x9234)) % 19.23/19.05 [924]~E(x9241,x9242)+E(f628(x9243,x9241,x9244),f628(x9243,x9242,x9244)) % 19.23/19.05 [925]~E(x9251,x9252)+E(f628(x9253,x9254,x9251),f628(x9253,x9254,x9252)) % 19.23/19.05 [926]~E(x9261,x9262)+E(f666(x9261,x9263,x9264,x9265,x9266),f666(x9262,x9263,x9264,x9265,x9266)) % 19.23/19.05 [927]~E(x9271,x9272)+E(f666(x9273,x9271,x9274,x9275,x9276),f666(x9273,x9272,x9274,x9275,x9276)) % 19.23/19.05 [928]~E(x9281,x9282)+E(f666(x9283,x9284,x9281,x9285,x9286),f666(x9283,x9284,x9282,x9285,x9286)) % 19.23/19.05 [929]~E(x9291,x9292)+E(f666(x9293,x9294,x9295,x9291,x9296),f666(x9293,x9294,x9295,x9292,x9296)) % 19.23/19.05 [930]~E(x9301,x9302)+E(f666(x9303,x9304,x9305,x9306,x9301),f666(x9303,x9304,x9305,x9306,x9302)) % 19.23/19.05 [931]~E(x9311,x9312)+E(f719(x9311,x9313,x9314,x9315),f719(x9312,x9313,x9314,x9315)) % 19.23/19.05 [932]~E(x9321,x9322)+E(f719(x9323,x9321,x9324,x9325),f719(x9323,x9322,x9324,x9325)) % 19.23/19.05 [933]~E(x9331,x9332)+E(f719(x9333,x9334,x9331,x9335),f719(x9333,x9334,x9332,x9335)) % 19.23/19.05 [934]~E(x9341,x9342)+E(f719(x9343,x9344,x9345,x9341),f719(x9343,x9344,x9345,x9342)) % 19.23/19.05 [935]~E(x9351,x9352)+E(f190(x9351,x9353),f190(x9352,x9353)) % 19.23/19.05 [936]~E(x9361,x9362)+E(f190(x9363,x9361),f190(x9363,x9362)) % 19.23/19.05 [937]~E(x9371,x9372)+E(f408(x9371,x9373,x9374),f408(x9372,x9373,x9374)) % 19.23/19.05 [938]~E(x9381,x9382)+E(f408(x9383,x9381,x9384),f408(x9383,x9382,x9384)) % 19.23/19.05 [939]~E(x9391,x9392)+E(f408(x9393,x9394,x9391),f408(x9393,x9394,x9392)) % 19.23/19.05 [940]~E(x9401,x9402)+E(f127(x9401,x9403),f127(x9402,x9403)) % 19.23/19.05 [941]~E(x9411,x9412)+E(f127(x9413,x9411),f127(x9413,x9412)) % 19.23/19.05 [942]~E(x9421,x9422)+E(f202(x9421,x9423),f202(x9422,x9423)) % 19.23/19.05 [943]~E(x9431,x9432)+E(f202(x9433,x9431),f202(x9433,x9432)) % 19.23/19.05 [944]~E(x9441,x9442)+E(f233(x9441,x9443,x9444,x9445),f233(x9442,x9443,x9444,x9445)) % 19.23/19.05 [945]~E(x9451,x9452)+E(f233(x9453,x9451,x9454,x9455),f233(x9453,x9452,x9454,x9455)) % 19.23/19.05 [946]~E(x9461,x9462)+E(f233(x9463,x9464,x9461,x9465),f233(x9463,x9464,x9462,x9465)) % 19.23/19.05 [947]~E(x9471,x9472)+E(f233(x9473,x9474,x9475,x9471),f233(x9473,x9474,x9475,x9472)) % 19.23/19.05 [948]~E(x9481,x9482)+E(f130(x9481,x9483),f130(x9482,x9483)) % 19.23/19.05 [949]~E(x9491,x9492)+E(f130(x9493,x9491),f130(x9493,x9492)) % 19.23/19.05 [950]~E(x9501,x9502)+E(f502(x9501,x9503,x9504,x9505,x9506),f502(x9502,x9503,x9504,x9505,x9506)) % 19.23/19.05 [951]~E(x9511,x9512)+E(f502(x9513,x9511,x9514,x9515,x9516),f502(x9513,x9512,x9514,x9515,x9516)) % 19.23/19.05 [952]~E(x9521,x9522)+E(f502(x9523,x9524,x9521,x9525,x9526),f502(x9523,x9524,x9522,x9525,x9526)) % 19.23/19.05 [953]~E(x9531,x9532)+E(f502(x9533,x9534,x9535,x9531,x9536),f502(x9533,x9534,x9535,x9532,x9536)) % 19.23/19.05 [954]~E(x9541,x9542)+E(f502(x9543,x9544,x9545,x9546,x9541),f502(x9543,x9544,x9545,x9546,x9542)) % 19.23/19.05 [955]~E(x9551,x9552)+E(f577(x9551,x9553,x9554,x9555,x9556,x9557,x9558),f577(x9552,x9553,x9554,x9555,x9556,x9557,x9558)) % 19.23/19.05 [956]~E(x9561,x9562)+E(f577(x9563,x9561,x9564,x9565,x9566,x9567,x9568),f577(x9563,x9562,x9564,x9565,x9566,x9567,x9568)) % 19.23/19.05 [957]~E(x9571,x9572)+E(f577(x9573,x9574,x9571,x9575,x9576,x9577,x9578),f577(x9573,x9574,x9572,x9575,x9576,x9577,x9578)) % 19.23/19.05 [958]~E(x9581,x9582)+E(f577(x9583,x9584,x9585,x9581,x9586,x9587,x9588),f577(x9583,x9584,x9585,x9582,x9586,x9587,x9588)) % 19.23/19.05 [959]~E(x9591,x9592)+E(f577(x9593,x9594,x9595,x9596,x9591,x9597,x9598),f577(x9593,x9594,x9595,x9596,x9592,x9597,x9598)) % 19.23/19.05 [960]~E(x9601,x9602)+E(f577(x9603,x9604,x9605,x9606,x9607,x9601,x9608),f577(x9603,x9604,x9605,x9606,x9607,x9602,x9608)) % 19.23/19.05 [961]~E(x9611,x9612)+E(f577(x9613,x9614,x9615,x9616,x9617,x9618,x9611),f577(x9613,x9614,x9615,x9616,x9617,x9618,x9612)) % 19.23/19.05 [962]~E(x9621,x9622)+E(f166(x9621,x9623,x9624),f166(x9622,x9623,x9624)) % 19.23/19.05 [963]~E(x9631,x9632)+E(f166(x9633,x9631,x9634),f166(x9633,x9632,x9634)) % 19.23/19.05 [964]~E(x9641,x9642)+E(f166(x9643,x9644,x9641),f166(x9643,x9644,x9642)) % 19.23/19.05 [965]~E(x9651,x9652)+E(f765(x9651,x9653,x9654),f765(x9652,x9653,x9654)) % 19.23/19.05 [966]~E(x9661,x9662)+E(f765(x9663,x9661,x9664),f765(x9663,x9662,x9664)) % 19.23/19.05 [967]~E(x9671,x9672)+E(f765(x9673,x9674,x9671),f765(x9673,x9674,x9672)) % 19.23/19.05 [968]~E(x9681,x9682)+E(f597(x9681,x9683),f597(x9682,x9683)) % 19.23/19.05 [969]~E(x9691,x9692)+E(f597(x9693,x9691),f597(x9693,x9692)) % 19.23/19.05 [970]~E(x9701,x9702)+E(f398(x9701,x9703,x9704,x9705),f398(x9702,x9703,x9704,x9705)) % 19.23/19.05 [971]~E(x9711,x9712)+E(f398(x9713,x9711,x9714,x9715),f398(x9713,x9712,x9714,x9715)) % 19.23/19.05 [972]~E(x9721,x9722)+E(f398(x9723,x9724,x9721,x9725),f398(x9723,x9724,x9722,x9725)) % 19.23/19.05 [973]~E(x9731,x9732)+E(f398(x9733,x9734,x9735,x9731),f398(x9733,x9734,x9735,x9732)) % 19.23/19.05 [974]~E(x9741,x9742)+E(f836(x9741,x9743,x9744),f836(x9742,x9743,x9744)) % 19.23/19.05 [975]~E(x9751,x9752)+E(f836(x9753,x9751,x9754),f836(x9753,x9752,x9754)) % 19.23/19.05 [976]~E(x9761,x9762)+E(f836(x9763,x9764,x9761),f836(x9763,x9764,x9762)) % 19.23/19.05 [977]~E(x9771,x9772)+E(f638(x9771,x9773,x9774),f638(x9772,x9773,x9774)) % 19.23/19.05 [978]~E(x9781,x9782)+E(f638(x9783,x9781,x9784),f638(x9783,x9782,x9784)) % 19.23/19.05 [979]~E(x9791,x9792)+E(f638(x9793,x9794,x9791),f638(x9793,x9794,x9792)) % 19.23/19.05 [980]~E(x9801,x9802)+E(f454(x9801,x9803,x9804,x9805),f454(x9802,x9803,x9804,x9805)) % 19.23/19.05 [981]~E(x9811,x9812)+E(f454(x9813,x9811,x9814,x9815),f454(x9813,x9812,x9814,x9815)) % 19.23/19.05 [982]~E(x9821,x9822)+E(f454(x9823,x9824,x9821,x9825),f454(x9823,x9824,x9822,x9825)) % 19.23/19.05 [983]~E(x9831,x9832)+E(f454(x9833,x9834,x9835,x9831),f454(x9833,x9834,x9835,x9832)) % 19.23/19.05 [984]~E(x9841,x9842)+E(f707(x9841,x9843),f707(x9842,x9843)) % 19.23/19.05 [985]~E(x9851,x9852)+E(f707(x9853,x9851),f707(x9853,x9852)) % 19.23/19.05 [986]~E(x9861,x9862)+E(f830(x9861,x9863,x9864,x9865),f830(x9862,x9863,x9864,x9865)) % 19.23/19.05 [987]~E(x9871,x9872)+E(f830(x9873,x9871,x9874,x9875),f830(x9873,x9872,x9874,x9875)) % 19.23/19.05 [988]~E(x9881,x9882)+E(f830(x9883,x9884,x9881,x9885),f830(x9883,x9884,x9882,x9885)) % 19.23/19.05 [989]~E(x9891,x9892)+E(f830(x9893,x9894,x9895,x9891),f830(x9893,x9894,x9895,x9892)) % 19.23/19.05 [990]~E(x9901,x9902)+E(f299(x9901,x9903,x9904),f299(x9902,x9903,x9904)) % 19.23/19.05 [991]~E(x9911,x9912)+E(f299(x9913,x9911,x9914),f299(x9913,x9912,x9914)) % 19.23/19.05 [992]~E(x9921,x9922)+E(f299(x9923,x9924,x9921),f299(x9923,x9924,x9922)) % 19.23/19.05 [993]~E(x9931,x9932)+E(f693(x9931,x9933,x9934),f693(x9932,x9933,x9934)) % 19.23/19.05 [994]~E(x9941,x9942)+E(f693(x9943,x9941,x9944),f693(x9943,x9942,x9944)) % 19.23/19.05 [995]~E(x9951,x9952)+E(f693(x9953,x9954,x9951),f693(x9953,x9954,x9952)) % 19.23/19.05 [996]~E(x9961,x9962)+E(f703(x9961,x9963,x9964),f703(x9962,x9963,x9964)) % 19.23/19.05 [997]~E(x9971,x9972)+E(f703(x9973,x9971,x9974),f703(x9973,x9972,x9974)) % 19.23/19.05 [998]~E(x9981,x9982)+E(f703(x9983,x9984,x9981),f703(x9983,x9984,x9982)) % 19.23/19.05 [999]~E(x9991,x9992)+E(f468(x9991,x9993,x9994,x9995),f468(x9992,x9993,x9994,x9995)) % 19.23/19.05 [1000]~E(x10001,x10002)+E(f468(x10003,x10001,x10004,x10005),f468(x10003,x10002,x10004,x10005)) % 19.23/19.05 [1001]~E(x10011,x10012)+E(f468(x10013,x10014,x10011,x10015),f468(x10013,x10014,x10012,x10015)) % 19.23/19.05 [1002]~E(x10021,x10022)+E(f468(x10023,x10024,x10025,x10021),f468(x10023,x10024,x10025,x10022)) % 19.23/19.05 [1003]~E(x10031,x10032)+E(f655(x10031,x10033,x10034,x10035,x10036),f655(x10032,x10033,x10034,x10035,x10036)) % 19.23/19.05 [1004]~E(x10041,x10042)+E(f655(x10043,x10041,x10044,x10045,x10046),f655(x10043,x10042,x10044,x10045,x10046)) % 19.23/19.05 [1005]~E(x10051,x10052)+E(f655(x10053,x10054,x10051,x10055,x10056),f655(x10053,x10054,x10052,x10055,x10056)) % 19.23/19.05 [1006]~E(x10061,x10062)+E(f655(x10063,x10064,x10065,x10061,x10066),f655(x10063,x10064,x10065,x10062,x10066)) % 19.23/19.05 [1007]~E(x10071,x10072)+E(f655(x10073,x10074,x10075,x10076,x10071),f655(x10073,x10074,x10075,x10076,x10072)) % 19.23/19.05 [1008]~E(x10081,x10082)+E(f702(x10081,x10083),f702(x10082,x10083)) % 19.23/19.05 [1009]~E(x10091,x10092)+E(f702(x10093,x10091),f702(x10093,x10092)) % 19.23/19.05 [1010]~E(x10101,x10102)+E(f83(x10101,x10103),f83(x10102,x10103)) % 19.23/19.05 [1011]~E(x10111,x10112)+E(f83(x10113,x10111),f83(x10113,x10112)) % 19.23/19.05 [1012]~E(x10121,x10122)+E(f769(x10121,x10123,x10124,x10125),f769(x10122,x10123,x10124,x10125)) % 19.23/19.05 [1013]~E(x10131,x10132)+E(f769(x10133,x10131,x10134,x10135),f769(x10133,x10132,x10134,x10135)) % 19.23/19.05 [1014]~E(x10141,x10142)+E(f769(x10143,x10144,x10141,x10145),f769(x10143,x10144,x10142,x10145)) % 19.23/19.05 [1015]~E(x10151,x10152)+E(f769(x10153,x10154,x10155,x10151),f769(x10153,x10154,x10155,x10152)) % 19.23/19.05 [1016]~E(x10161,x10162)+E(f604(x10161,x10163,x10164,x10165),f604(x10162,x10163,x10164,x10165)) % 19.23/19.05 [1017]~E(x10171,x10172)+E(f604(x10173,x10171,x10174,x10175),f604(x10173,x10172,x10174,x10175)) % 19.23/19.05 [1018]~E(x10181,x10182)+E(f604(x10183,x10184,x10181,x10185),f604(x10183,x10184,x10182,x10185)) % 19.23/19.05 [1019]~E(x10191,x10192)+E(f604(x10193,x10194,x10195,x10191),f604(x10193,x10194,x10195,x10192)) % 19.23/19.05 [1020]~E(x10201,x10202)+E(f238(x10201,x10203,x10204,x10205,x10206),f238(x10202,x10203,x10204,x10205,x10206)) % 19.23/19.05 [1021]~E(x10211,x10212)+E(f238(x10213,x10211,x10214,x10215,x10216),f238(x10213,x10212,x10214,x10215,x10216)) % 19.23/19.05 [1022]~E(x10221,x10222)+E(f238(x10223,x10224,x10221,x10225,x10226),f238(x10223,x10224,x10222,x10225,x10226)) % 19.23/19.05 [1023]~E(x10231,x10232)+E(f238(x10233,x10234,x10235,x10231,x10236),f238(x10233,x10234,x10235,x10232,x10236)) % 19.23/19.05 [1024]~E(x10241,x10242)+E(f238(x10243,x10244,x10245,x10246,x10241),f238(x10243,x10244,x10245,x10246,x10242)) % 19.23/19.05 [1025]~E(x10251,x10252)+E(f750(x10251,x10253,x10254,x10255,x10256),f750(x10252,x10253,x10254,x10255,x10256)) % 19.23/19.05 [1026]~E(x10261,x10262)+E(f750(x10263,x10261,x10264,x10265,x10266),f750(x10263,x10262,x10264,x10265,x10266)) % 19.23/19.05 [1027]~E(x10271,x10272)+E(f750(x10273,x10274,x10271,x10275,x10276),f750(x10273,x10274,x10272,x10275,x10276)) % 19.23/19.05 [1028]~E(x10281,x10282)+E(f750(x10283,x10284,x10285,x10281,x10286),f750(x10283,x10284,x10285,x10282,x10286)) % 19.23/19.05 [1029]~E(x10291,x10292)+E(f750(x10293,x10294,x10295,x10296,x10291),f750(x10293,x10294,x10295,x10296,x10292)) % 19.23/19.05 [1030]~E(x10301,x10302)+E(f660(x10301,x10303),f660(x10302,x10303)) % 19.23/19.05 [1031]~E(x10311,x10312)+E(f660(x10313,x10311),f660(x10313,x10312)) % 19.23/19.05 [1032]~E(x10321,x10322)+E(f508(x10321,x10323,x10324,x10325,x10326),f508(x10322,x10323,x10324,x10325,x10326)) % 19.23/19.05 [1033]~E(x10331,x10332)+E(f508(x10333,x10331,x10334,x10335,x10336),f508(x10333,x10332,x10334,x10335,x10336)) % 19.23/19.05 [1034]~E(x10341,x10342)+E(f508(x10343,x10344,x10341,x10345,x10346),f508(x10343,x10344,x10342,x10345,x10346)) % 19.23/19.05 [1035]~E(x10351,x10352)+E(f508(x10353,x10354,x10355,x10351,x10356),f508(x10353,x10354,x10355,x10352,x10356)) % 19.23/19.05 [1036]~E(x10361,x10362)+E(f508(x10363,x10364,x10365,x10366,x10361),f508(x10363,x10364,x10365,x10366,x10362)) % 19.23/19.05 [1037]~E(x10371,x10372)+E(f218(x10371,x10373),f218(x10372,x10373)) % 19.23/19.05 [1038]~E(x10381,x10382)+E(f218(x10383,x10381),f218(x10383,x10382)) % 19.23/19.05 [1039]~E(x10391,x10392)+E(f743(x10391,x10393,x10394,x10395),f743(x10392,x10393,x10394,x10395)) % 19.23/19.05 [1040]~E(x10401,x10402)+E(f743(x10403,x10401,x10404,x10405),f743(x10403,x10402,x10404,x10405)) % 19.23/19.05 [1041]~E(x10411,x10412)+E(f743(x10413,x10414,x10411,x10415),f743(x10413,x10414,x10412,x10415)) % 19.23/19.05 [1042]~E(x10421,x10422)+E(f743(x10423,x10424,x10425,x10421),f743(x10423,x10424,x10425,x10422)) % 19.23/19.05 [1043]~E(x10431,x10432)+E(f58(x10431),f58(x10432)) % 19.23/19.05 [1044]~E(x10441,x10442)+E(f601(x10441,x10443,x10444),f601(x10442,x10443,x10444)) % 19.23/19.05 [1045]~E(x10451,x10452)+E(f601(x10453,x10451,x10454),f601(x10453,x10452,x10454)) % 19.23/19.05 [1046]~E(x10461,x10462)+E(f601(x10463,x10464,x10461),f601(x10463,x10464,x10462)) % 19.23/19.05 [1047]~E(x10471,x10472)+E(f804(x10471,x10473),f804(x10472,x10473)) % 19.23/19.05 [1048]~E(x10481,x10482)+E(f804(x10483,x10481),f804(x10483,x10482)) % 19.23/19.05 [1049]~E(x10491,x10492)+E(f708(x10491,x10493,x10494,x10495,x10496),f708(x10492,x10493,x10494,x10495,x10496)) % 19.23/19.05 [1050]~E(x10501,x10502)+E(f708(x10503,x10501,x10504,x10505,x10506),f708(x10503,x10502,x10504,x10505,x10506)) % 19.23/19.05 [1051]~E(x10511,x10512)+E(f708(x10513,x10514,x10511,x10515,x10516),f708(x10513,x10514,x10512,x10515,x10516)) % 19.23/19.05 [1052]~E(x10521,x10522)+E(f708(x10523,x10524,x10525,x10521,x10526),f708(x10523,x10524,x10525,x10522,x10526)) % 19.23/19.05 [1053]~E(x10531,x10532)+E(f708(x10533,x10534,x10535,x10536,x10531),f708(x10533,x10534,x10535,x10536,x10532)) % 19.23/19.05 [1054]~E(x10541,x10542)+E(f40(x10541,x10543,x10544,x10545,x10546,x10547,x10548,x10549,x105410,x105411),f40(x10542,x10543,x10544,x10545,x10546,x10547,x10548,x10549,x105410,x105411)) % 19.23/19.05 [1055]~E(x10551,x10552)+E(f40(x10553,x10551,x10554,x10555,x10556,x10557,x10558,x10559,x105510,x105511),f40(x10553,x10552,x10554,x10555,x10556,x10557,x10558,x10559,x105510,x105511)) % 19.23/19.05 [1056]~E(x10561,x10562)+E(f40(x10563,x10564,x10561,x10565,x10566,x10567,x10568,x10569,x105610,x105611),f40(x10563,x10564,x10562,x10565,x10566,x10567,x10568,x10569,x105610,x105611)) % 19.23/19.05 [1057]~E(x10571,x10572)+E(f40(x10573,x10574,x10575,x10571,x10576,x10577,x10578,x10579,x105710,x105711),f40(x10573,x10574,x10575,x10572,x10576,x10577,x10578,x10579,x105710,x105711)) % 19.23/19.05 [1058]~E(x10581,x10582)+E(f40(x10583,x10584,x10585,x10586,x10581,x10587,x10588,x10589,x105810,x105811),f40(x10583,x10584,x10585,x10586,x10582,x10587,x10588,x10589,x105810,x105811)) % 19.23/19.05 [1059]~E(x10591,x10592)+E(f40(x10593,x10594,x10595,x10596,x10597,x10591,x10598,x10599,x105910,x105911),f40(x10593,x10594,x10595,x10596,x10597,x10592,x10598,x10599,x105910,x105911)) % 19.23/19.05 [1060]~E(x10601,x10602)+E(f40(x10603,x10604,x10605,x10606,x10607,x10608,x10601,x10609,x106010,x106011),f40(x10603,x10604,x10605,x10606,x10607,x10608,x10602,x10609,x106010,x106011)) % 19.23/19.05 [1061]~E(x10611,x10612)+E(f40(x10613,x10614,x10615,x10616,x10617,x10618,x10619,x10611,x106110,x106111),f40(x10613,x10614,x10615,x10616,x10617,x10618,x10619,x10612,x106110,x106111)) % 19.23/19.05 [1062]~E(x10621,x10622)+E(f40(x10623,x10624,x10625,x10626,x10627,x10628,x10629,x106210,x10621,x106211),f40(x10623,x10624,x10625,x10626,x10627,x10628,x10629,x106210,x10622,x106211)) % 19.23/19.05 [1063]~E(x10631,x10632)+E(f40(x10633,x10634,x10635,x10636,x10637,x10638,x10639,x106310,x106311,x10631),f40(x10633,x10634,x10635,x10636,x10637,x10638,x10639,x106310,x106311,x10632)) % 19.23/19.05 [1064]~E(x10641,x10642)+E(f780(x10641,x10643,x10644),f780(x10642,x10643,x10644)) % 19.23/19.05 [1065]~E(x10651,x10652)+E(f780(x10653,x10651,x10654),f780(x10653,x10652,x10654)) % 19.23/19.05 [1066]~E(x10661,x10662)+E(f780(x10663,x10664,x10661),f780(x10663,x10664,x10662)) % 19.23/19.05 [1067]~E(x10671,x10672)+E(f407(x10671,x10673,x10674),f407(x10672,x10673,x10674)) % 19.23/19.05 [1068]~E(x10681,x10682)+E(f407(x10683,x10681,x10684),f407(x10683,x10682,x10684)) % 19.23/19.05 [1069]~E(x10691,x10692)+E(f407(x10693,x10694,x10691),f407(x10693,x10694,x10692)) % 19.23/19.05 [1070]~E(x10701,x10702)+E(f551(x10701,x10703,x10704),f551(x10702,x10703,x10704)) % 19.23/19.05 [1071]~E(x10711,x10712)+E(f551(x10713,x10711,x10714),f551(x10713,x10712,x10714)) % 19.23/19.05 [1072]~E(x10721,x10722)+E(f551(x10723,x10724,x10721),f551(x10723,x10724,x10722)) % 19.23/19.05 [1073]~E(x10731,x10732)+E(f165(x10731,x10733,x10734),f165(x10732,x10733,x10734)) % 19.23/19.05 [1074]~E(x10741,x10742)+E(f165(x10743,x10741,x10744),f165(x10743,x10742,x10744)) % 19.23/19.05 [1075]~E(x10751,x10752)+E(f165(x10753,x10754,x10751),f165(x10753,x10754,x10752)) % 19.23/19.05 [1076]~E(x10761,x10762)+E(f443(x10761,x10763,x10764),f443(x10762,x10763,x10764)) % 19.23/19.05 [1077]~E(x10771,x10772)+E(f443(x10773,x10771,x10774),f443(x10773,x10772,x10774)) % 19.23/19.05 [1078]~E(x10781,x10782)+E(f443(x10783,x10784,x10781),f443(x10783,x10784,x10782)) % 19.23/19.05 [1079]~E(x10791,x10792)+E(f269(x10791,x10793),f269(x10792,x10793)) % 19.23/19.05 [1080]~E(x10801,x10802)+E(f269(x10803,x10801),f269(x10803,x10802)) % 19.23/19.05 [1081]~E(x10811,x10812)+E(f255(x10811,x10813,x10814),f255(x10812,x10813,x10814)) % 19.23/19.05 [1082]~E(x10821,x10822)+E(f255(x10823,x10821,x10824),f255(x10823,x10822,x10824)) % 19.23/19.05 [1083]~E(x10831,x10832)+E(f255(x10833,x10834,x10831),f255(x10833,x10834,x10832)) % 19.23/19.05 [1084]~E(x10841,x10842)+E(f518(x10841,x10843,x10844),f518(x10842,x10843,x10844)) % 19.23/19.05 [1085]~E(x10851,x10852)+E(f518(x10853,x10851,x10854),f518(x10853,x10852,x10854)) % 19.23/19.05 [1086]~E(x10861,x10862)+E(f518(x10863,x10864,x10861),f518(x10863,x10864,x10862)) % 19.23/19.05 [1087]~E(x10871,x10872)+E(f490(x10871),f490(x10872)) % 19.23/19.05 [1088]~E(x10881,x10882)+E(f285(x10881),f285(x10882)) % 19.23/19.05 [1089]~E(x10891,x10892)+E(f775(x10891,x10893),f775(x10892,x10893)) % 19.23/19.05 [1090]~E(x10901,x10902)+E(f775(x10903,x10901),f775(x10903,x10902)) % 19.23/19.05 [1091]~E(x10911,x10912)+E(f180(x10911,x10913,x10914),f180(x10912,x10913,x10914)) % 19.23/19.05 [1092]~E(x10921,x10922)+E(f180(x10923,x10921,x10924),f180(x10923,x10922,x10924)) % 19.23/19.05 [1093]~E(x10931,x10932)+E(f180(x10933,x10934,x10931),f180(x10933,x10934,x10932)) % 19.23/19.05 [1094]~E(x10941,x10942)+E(f476(x10941,x10943,x10944,x10945),f476(x10942,x10943,x10944,x10945)) % 19.23/19.05 [1095]~E(x10951,x10952)+E(f476(x10953,x10951,x10954,x10955),f476(x10953,x10952,x10954,x10955)) % 19.23/19.05 [1096]~E(x10961,x10962)+E(f476(x10963,x10964,x10961,x10965),f476(x10963,x10964,x10962,x10965)) % 19.23/19.05 [1097]~E(x10971,x10972)+E(f476(x10973,x10974,x10975,x10971),f476(x10973,x10974,x10975,x10972)) % 19.23/19.05 [1098]~E(x10981,x10982)+E(f319(x10981),f319(x10982)) % 19.23/19.05 [1099]~E(x10991,x10992)+E(f522(x10991,x10993,x10994,x10995,x10996),f522(x10992,x10993,x10994,x10995,x10996)) % 19.23/19.05 [1100]~E(x11001,x11002)+E(f522(x11003,x11001,x11004,x11005,x11006),f522(x11003,x11002,x11004,x11005,x11006)) % 19.23/19.05 [1101]~E(x11011,x11012)+E(f522(x11013,x11014,x11011,x11015,x11016),f522(x11013,x11014,x11012,x11015,x11016)) % 19.23/19.05 [1102]~E(x11021,x11022)+E(f522(x11023,x11024,x11025,x11021,x11026),f522(x11023,x11024,x11025,x11022,x11026)) % 19.23/19.05 [1103]~E(x11031,x11032)+E(f522(x11033,x11034,x11035,x11036,x11031),f522(x11033,x11034,x11035,x11036,x11032)) % 19.23/19.05 [1104]~E(x11041,x11042)+E(f272(x11041,x11043),f272(x11042,x11043)) % 19.23/19.05 [1105]~E(x11051,x11052)+E(f272(x11053,x11051),f272(x11053,x11052)) % 19.23/19.05 [1106]~E(x11061,x11062)+E(f695(x11061,x11063,x11064,x11065),f695(x11062,x11063,x11064,x11065)) % 19.23/19.05 [1107]~E(x11071,x11072)+E(f695(x11073,x11071,x11074,x11075),f695(x11073,x11072,x11074,x11075)) % 19.23/19.05 [1108]~E(x11081,x11082)+E(f695(x11083,x11084,x11081,x11085),f695(x11083,x11084,x11082,x11085)) % 19.23/19.05 [1109]~E(x11091,x11092)+E(f695(x11093,x11094,x11095,x11091),f695(x11093,x11094,x11095,x11092)) % 19.23/19.05 [1110]~E(x11101,x11102)+E(f844(x11101,x11103,x11104),f844(x11102,x11103,x11104)) % 19.23/19.05 [1111]~E(x11111,x11112)+E(f844(x11113,x11111,x11114),f844(x11113,x11112,x11114)) % 19.23/19.05 [1112]~E(x11121,x11122)+E(f844(x11123,x11124,x11121),f844(x11123,x11124,x11122)) % 19.23/19.05 [1113]~E(x11131,x11132)+E(f252(x11131,x11133,x11134),f252(x11132,x11133,x11134)) % 19.23/19.05 [1114]~E(x11141,x11142)+E(f252(x11143,x11141,x11144),f252(x11143,x11142,x11144)) % 19.23/19.05 [1115]~E(x11151,x11152)+E(f252(x11153,x11154,x11151),f252(x11153,x11154,x11152)) % 19.23/19.05 [1116]~E(x11161,x11162)+E(f807(x11161,x11163,x11164),f807(x11162,x11163,x11164)) % 19.23/19.05 [1117]~E(x11171,x11172)+E(f807(x11173,x11171,x11174),f807(x11173,x11172,x11174)) % 19.23/19.05 [1118]~E(x11181,x11182)+E(f807(x11183,x11184,x11181),f807(x11183,x11184,x11182)) % 19.23/19.05 [1119]~E(x11191,x11192)+E(f650(x11191,x11193,x11194),f650(x11192,x11193,x11194)) % 19.23/19.05 [1120]~E(x11201,x11202)+E(f650(x11203,x11201,x11204),f650(x11203,x11202,x11204)) % 19.23/19.05 [1121]~E(x11211,x11212)+E(f650(x11213,x11214,x11211),f650(x11213,x11214,x11212)) % 19.23/19.05 [1122]~E(x11221,x11222)+E(f814(x11221,x11223,x11224),f814(x11222,x11223,x11224)) % 19.23/19.05 [1123]~E(x11231,x11232)+E(f814(x11233,x11231,x11234),f814(x11233,x11232,x11234)) % 19.23/19.05 [1124]~E(x11241,x11242)+E(f814(x11243,x11244,x11241),f814(x11243,x11244,x11242)) % 19.23/19.05 [1125]~E(x11251,x11252)+E(f790(x11251,x11253,x11254),f790(x11252,x11253,x11254)) % 19.23/19.05 [1126]~E(x11261,x11262)+E(f790(x11263,x11261,x11264),f790(x11263,x11262,x11264)) % 19.23/19.05 [1127]~E(x11271,x11272)+E(f790(x11273,x11274,x11271),f790(x11273,x11274,x11272)) % 19.23/19.05 [1128]~E(x11281,x11282)+E(f598(x11281,x11283,x11284,x11285),f598(x11282,x11283,x11284,x11285)) % 19.23/19.05 [1129]~E(x11291,x11292)+E(f598(x11293,x11291,x11294,x11295),f598(x11293,x11292,x11294,x11295)) % 19.23/19.05 [1130]~E(x11301,x11302)+E(f598(x11303,x11304,x11301,x11305),f598(x11303,x11304,x11302,x11305)) % 19.23/19.05 [1131]~E(x11311,x11312)+E(f598(x11313,x11314,x11315,x11311),f598(x11313,x11314,x11315,x11312)) % 19.23/19.05 [1132]~E(x11321,x11322)+E(f317(x11321,x11323,x11324),f317(x11322,x11323,x11324)) % 19.23/19.05 [1133]~E(x11331,x11332)+E(f317(x11333,x11331,x11334),f317(x11333,x11332,x11334)) % 19.23/19.05 [1134]~E(x11341,x11342)+E(f317(x11343,x11344,x11341),f317(x11343,x11344,x11342)) % 19.23/19.05 [1135]~E(x11351,x11352)+E(f724(x11351,x11353,x11354,x11355),f724(x11352,x11353,x11354,x11355)) % 19.23/19.05 [1136]~E(x11361,x11362)+E(f724(x11363,x11361,x11364,x11365),f724(x11363,x11362,x11364,x11365)) % 19.23/19.05 [1137]~E(x11371,x11372)+E(f724(x11373,x11374,x11371,x11375),f724(x11373,x11374,x11372,x11375)) % 19.23/19.05 [1138]~E(x11381,x11382)+E(f724(x11383,x11384,x11385,x11381),f724(x11383,x11384,x11385,x11382)) % 19.23/19.05 [1139]~E(x11391,x11392)+E(f828(x11391,x11393,x11394),f828(x11392,x11393,x11394)) % 19.23/19.05 [1140]~E(x11401,x11402)+E(f828(x11403,x11401,x11404),f828(x11403,x11402,x11404)) % 19.23/19.05 [1141]~E(x11411,x11412)+E(f828(x11413,x11414,x11411),f828(x11413,x11414,x11412)) % 19.23/19.05 [1142]~E(x11421,x11422)+E(f738(x11421,x11423),f738(x11422,x11423)) % 19.23/19.05 [1143]~E(x11431,x11432)+E(f738(x11433,x11431),f738(x11433,x11432)) % 19.23/19.05 [1144]~E(x11441,x11442)+E(f791(x11441),f791(x11442)) % 19.23/19.05 [1145]~E(x11451,x11452)+E(f540(x11451,x11453,x11454),f540(x11452,x11453,x11454)) % 19.23/19.05 [1146]~E(x11461,x11462)+E(f540(x11463,x11461,x11464),f540(x11463,x11462,x11464)) % 19.23/19.05 [1147]~E(x11471,x11472)+E(f540(x11473,x11474,x11471),f540(x11473,x11474,x11472)) % 19.23/19.05 [1148]~E(x11481,x11482)+E(f798(x11481),f798(x11482)) % 19.23/19.05 [1149]~E(x11491,x11492)+E(f293(x11491,x11493),f293(x11492,x11493)) % 19.23/19.05 [1150]~E(x11501,x11502)+E(f293(x11503,x11501),f293(x11503,x11502)) % 19.23/19.05 [1151]~E(x11511,x11512)+E(f495(x11511,x11513,x11514,x11515,x11516),f495(x11512,x11513,x11514,x11515,x11516)) % 19.23/19.05 [1152]~E(x11521,x11522)+E(f495(x11523,x11521,x11524,x11525,x11526),f495(x11523,x11522,x11524,x11525,x11526)) % 19.23/19.05 [1153]~E(x11531,x11532)+E(f495(x11533,x11534,x11531,x11535,x11536),f495(x11533,x11534,x11532,x11535,x11536)) % 19.23/19.05 [1154]~E(x11541,x11542)+E(f495(x11543,x11544,x11545,x11541,x11546),f495(x11543,x11544,x11545,x11542,x11546)) % 19.23/19.05 [1155]~E(x11551,x11552)+E(f495(x11553,x11554,x11555,x11556,x11551),f495(x11553,x11554,x11555,x11556,x11552)) % 19.23/19.05 [1156]~E(x11561,x11562)+E(f686(x11561,x11563,x11564),f686(x11562,x11563,x11564)) % 19.23/19.05 [1157]~E(x11571,x11572)+E(f686(x11573,x11571,x11574),f686(x11573,x11572,x11574)) % 19.23/19.05 [1158]~E(x11581,x11582)+E(f686(x11583,x11584,x11581),f686(x11583,x11584,x11582)) % 19.23/19.05 [1159]~E(x11591,x11592)+E(f744(x11591,x11593,x11594),f744(x11592,x11593,x11594)) % 19.23/19.05 [1160]~E(x11601,x11602)+E(f744(x11603,x11601,x11604),f744(x11603,x11602,x11604)) % 19.23/19.05 [1161]~E(x11611,x11612)+E(f744(x11613,x11614,x11611),f744(x11613,x11614,x11612)) % 19.23/19.05 [1162]~E(x11621,x11622)+E(f534(x11621,x11623,x11624),f534(x11622,x11623,x11624)) % 19.23/19.05 [1163]~E(x11631,x11632)+E(f534(x11633,x11631,x11634),f534(x11633,x11632,x11634)) % 19.23/19.05 [1164]~E(x11641,x11642)+E(f534(x11643,x11644,x11641),f534(x11643,x11644,x11642)) % 19.23/19.05 [1165]~E(x11651,x11652)+E(f296(x11651,x11653,x11654),f296(x11652,x11653,x11654)) % 19.23/19.05 [1166]~E(x11661,x11662)+E(f296(x11663,x11661,x11664),f296(x11663,x11662,x11664)) % 19.23/19.05 [1167]~E(x11671,x11672)+E(f296(x11673,x11674,x11671),f296(x11673,x11674,x11672)) % 19.23/19.05 [1168]~E(x11681,x11682)+E(f768(x11681,x11683,x11684,x11685),f768(x11682,x11683,x11684,x11685)) % 19.23/19.05 [1169]~E(x11691,x11692)+E(f768(x11693,x11691,x11694,x11695),f768(x11693,x11692,x11694,x11695)) % 19.23/19.05 [1170]~E(x11701,x11702)+E(f768(x11703,x11704,x11701,x11705),f768(x11703,x11704,x11702,x11705)) % 19.23/19.05 [1171]~E(x11711,x11712)+E(f768(x11713,x11714,x11715,x11711),f768(x11713,x11714,x11715,x11712)) % 19.23/19.05 [1172]~E(x11721,x11722)+E(f336(x11721,x11723,x11724),f336(x11722,x11723,x11724)) % 19.23/19.05 [1173]~E(x11731,x11732)+E(f336(x11733,x11731,x11734),f336(x11733,x11732,x11734)) % 19.23/19.05 [1174]~E(x11741,x11742)+E(f336(x11743,x11744,x11741),f336(x11743,x11744,x11742)) % 19.23/19.05 [1175]~E(x11751,x11752)+E(f396(x11751,x11753),f396(x11752,x11753)) % 19.23/19.05 [1176]~E(x11761,x11762)+E(f396(x11763,x11761),f396(x11763,x11762)) % 19.23/19.05 [1177]~E(x11771,x11772)+E(f274(x11771,x11773),f274(x11772,x11773)) % 19.23/19.05 [1178]~E(x11781,x11782)+E(f274(x11783,x11781),f274(x11783,x11782)) % 19.23/19.05 [1179]~E(x11791,x11792)+E(f145(x11791,x11793,x11794,x11795,x11796),f145(x11792,x11793,x11794,x11795,x11796)) % 19.23/19.05 [1180]~E(x11801,x11802)+E(f145(x11803,x11801,x11804,x11805,x11806),f145(x11803,x11802,x11804,x11805,x11806)) % 19.23/19.05 [1181]~E(x11811,x11812)+E(f145(x11813,x11814,x11811,x11815,x11816),f145(x11813,x11814,x11812,x11815,x11816)) % 19.23/19.05 [1182]~E(x11821,x11822)+E(f145(x11823,x11824,x11825,x11821,x11826),f145(x11823,x11824,x11825,x11822,x11826)) % 19.23/19.05 [1183]~E(x11831,x11832)+E(f145(x11833,x11834,x11835,x11836,x11831),f145(x11833,x11834,x11835,x11836,x11832)) % 19.23/19.05 [1184]~E(x11841,x11842)+E(f687(x11841,x11843,x11844),f687(x11842,x11843,x11844)) % 19.23/19.05 [1185]~E(x11851,x11852)+E(f687(x11853,x11851,x11854),f687(x11853,x11852,x11854)) % 19.23/19.05 [1186]~E(x11861,x11862)+E(f687(x11863,x11864,x11861),f687(x11863,x11864,x11862)) % 19.23/19.05 [1187]~E(x11871,x11872)+E(f764(x11871,x11873,x11874,x11875),f764(x11872,x11873,x11874,x11875)) % 19.23/19.05 [1188]~E(x11881,x11882)+E(f764(x11883,x11881,x11884,x11885),f764(x11883,x11882,x11884,x11885)) % 19.23/19.05 [1189]~E(x11891,x11892)+E(f764(x11893,x11894,x11891,x11895),f764(x11893,x11894,x11892,x11895)) % 19.23/19.05 [1190]~E(x11901,x11902)+E(f764(x11903,x11904,x11905,x11901),f764(x11903,x11904,x11905,x11902)) % 19.23/19.05 [1191]~E(x11911,x11912)+E(f279(x11911,x11913),f279(x11912,x11913)) % 19.23/19.05 [1192]~E(x11921,x11922)+E(f279(x11923,x11921),f279(x11923,x11922)) % 19.23/19.05 [1193]~E(x11931,x11932)+E(f654(x11931,x11933,x11934,x11935,x11936),f654(x11932,x11933,x11934,x11935,x11936)) % 19.23/19.05 [1194]~E(x11941,x11942)+E(f654(x11943,x11941,x11944,x11945,x11946),f654(x11943,x11942,x11944,x11945,x11946)) % 19.23/19.05 [1195]~E(x11951,x11952)+E(f654(x11953,x11954,x11951,x11955,x11956),f654(x11953,x11954,x11952,x11955,x11956)) % 19.23/19.06 [1196]~E(x11961,x11962)+E(f654(x11963,x11964,x11965,x11961,x11966),f654(x11963,x11964,x11965,x11962,x11966)) % 19.23/19.06 [1197]~E(x11971,x11972)+E(f654(x11973,x11974,x11975,x11976,x11971),f654(x11973,x11974,x11975,x11976,x11972)) % 19.23/19.06 [1198]~E(x11981,x11982)+E(f603(x11981,x11983,x11984,x11985,x11986),f603(x11982,x11983,x11984,x11985,x11986)) % 19.23/19.06 [1199]~E(x11991,x11992)+E(f603(x11993,x11991,x11994,x11995,x11996),f603(x11993,x11992,x11994,x11995,x11996)) % 19.23/19.06 [1200]~E(x12001,x12002)+E(f603(x12003,x12004,x12001,x12005,x12006),f603(x12003,x12004,x12002,x12005,x12006)) % 19.23/19.06 [1201]~E(x12011,x12012)+E(f603(x12013,x12014,x12015,x12011,x12016),f603(x12013,x12014,x12015,x12012,x12016)) % 19.23/19.06 [1202]~E(x12021,x12022)+E(f603(x12023,x12024,x12025,x12026,x12021),f603(x12023,x12024,x12025,x12026,x12022)) % 19.23/19.06 [1203]~E(x12031,x12032)+E(f363(x12031,x12033,x12034,x12035),f363(x12032,x12033,x12034,x12035)) % 19.23/19.06 [1204]~E(x12041,x12042)+E(f363(x12043,x12041,x12044,x12045),f363(x12043,x12042,x12044,x12045)) % 19.23/19.06 [1205]~E(x12051,x12052)+E(f363(x12053,x12054,x12051,x12055),f363(x12053,x12054,x12052,x12055)) % 19.23/19.06 [1206]~E(x12061,x12062)+E(f363(x12063,x12064,x12065,x12061),f363(x12063,x12064,x12065,x12062)) % 19.23/19.06 [1207]~E(x12071,x12072)+E(f402(x12071,x12073,x12074),f402(x12072,x12073,x12074)) % 19.23/19.06 [1208]~E(x12081,x12082)+E(f402(x12083,x12081,x12084),f402(x12083,x12082,x12084)) % 19.23/19.06 [1209]~E(x12091,x12092)+E(f402(x12093,x12094,x12091),f402(x12093,x12094,x12092)) % 19.23/19.06 [1210]~E(x12101,x12102)+E(f412(x12101,x12103,x12104,x12105,x12106),f412(x12102,x12103,x12104,x12105,x12106)) % 19.23/19.06 [1211]~E(x12111,x12112)+E(f412(x12113,x12111,x12114,x12115,x12116),f412(x12113,x12112,x12114,x12115,x12116)) % 19.23/19.06 [1212]~E(x12121,x12122)+E(f412(x12123,x12124,x12121,x12125,x12126),f412(x12123,x12124,x12122,x12125,x12126)) % 19.23/19.06 [1213]~E(x12131,x12132)+E(f412(x12133,x12134,x12135,x12131,x12136),f412(x12133,x12134,x12135,x12132,x12136)) % 19.23/19.06 [1214]~E(x12141,x12142)+E(f412(x12143,x12144,x12145,x12146,x12141),f412(x12143,x12144,x12145,x12146,x12142)) % 19.23/19.06 [1215]~E(x12151,x12152)+E(f834(x12151,x12153,x12154),f834(x12152,x12153,x12154)) % 19.23/19.06 [1216]~E(x12161,x12162)+E(f834(x12163,x12161,x12164),f834(x12163,x12162,x12164)) % 19.23/19.06 [1217]~E(x12171,x12172)+E(f834(x12173,x12174,x12171),f834(x12173,x12174,x12172)) % 19.23/19.06 [1218]~E(x12181,x12182)+E(f516(x12181,x12183,x12184,x12185,x12186),f516(x12182,x12183,x12184,x12185,x12186)) % 19.23/19.06 [1219]~E(x12191,x12192)+E(f516(x12193,x12191,x12194,x12195,x12196),f516(x12193,x12192,x12194,x12195,x12196)) % 19.23/19.06 [1220]~E(x12201,x12202)+E(f516(x12203,x12204,x12201,x12205,x12206),f516(x12203,x12204,x12202,x12205,x12206)) % 19.23/19.06 [1221]~E(x12211,x12212)+E(f516(x12213,x12214,x12215,x12211,x12216),f516(x12213,x12214,x12215,x12212,x12216)) % 19.23/19.06 [1222]~E(x12221,x12222)+E(f516(x12223,x12224,x12225,x12226,x12221),f516(x12223,x12224,x12225,x12226,x12222)) % 19.23/19.06 [1223]~E(x12231,x12232)+E(f413(x12231,x12233,x12234,x12235,x12236),f413(x12232,x12233,x12234,x12235,x12236)) % 19.23/19.06 [1224]~E(x12241,x12242)+E(f413(x12243,x12241,x12244,x12245,x12246),f413(x12243,x12242,x12244,x12245,x12246)) % 19.23/19.06 [1225]~E(x12251,x12252)+E(f413(x12253,x12254,x12251,x12255,x12256),f413(x12253,x12254,x12252,x12255,x12256)) % 19.23/19.06 [1226]~E(x12261,x12262)+E(f413(x12263,x12264,x12265,x12261,x12266),f413(x12263,x12264,x12265,x12262,x12266)) % 19.23/19.06 [1227]~E(x12271,x12272)+E(f413(x12273,x12274,x12275,x12276,x12271),f413(x12273,x12274,x12275,x12276,x12272)) % 19.23/19.06 [1228]~E(x12281,x12282)+E(f512(x12281,x12283,x12284,x12285),f512(x12282,x12283,x12284,x12285)) % 19.23/19.06 [1229]~E(x12291,x12292)+E(f512(x12293,x12291,x12294,x12295),f512(x12293,x12292,x12294,x12295)) % 19.23/19.06 [1230]~E(x12301,x12302)+E(f512(x12303,x12304,x12301,x12305),f512(x12303,x12304,x12302,x12305)) % 19.23/19.06 [1231]~E(x12311,x12312)+E(f512(x12313,x12314,x12315,x12311),f512(x12313,x12314,x12315,x12312)) % 19.23/19.06 [1232]~E(x12321,x12322)+E(f505(x12321,x12323,x12324,x12325,x12326),f505(x12322,x12323,x12324,x12325,x12326)) % 19.23/19.06 [1233]~E(x12331,x12332)+E(f505(x12333,x12331,x12334,x12335,x12336),f505(x12333,x12332,x12334,x12335,x12336)) % 19.23/19.06 [1234]~E(x12341,x12342)+E(f505(x12343,x12344,x12341,x12345,x12346),f505(x12343,x12344,x12342,x12345,x12346)) % 19.23/19.06 [1235]~E(x12351,x12352)+E(f505(x12353,x12354,x12355,x12351,x12356),f505(x12353,x12354,x12355,x12352,x12356)) % 19.23/19.06 [1236]~E(x12361,x12362)+E(f505(x12363,x12364,x12365,x12366,x12361),f505(x12363,x12364,x12365,x12366,x12362)) % 19.23/19.06 [1237]~E(x12371,x12372)+E(f642(x12371,x12373,x12374,x12375,x12376,x12377,x12378,x12379),f642(x12372,x12373,x12374,x12375,x12376,x12377,x12378,x12379)) % 19.23/19.06 [1238]~E(x12381,x12382)+E(f642(x12383,x12381,x12384,x12385,x12386,x12387,x12388,x12389),f642(x12383,x12382,x12384,x12385,x12386,x12387,x12388,x12389)) % 19.23/19.06 [1239]~E(x12391,x12392)+E(f642(x12393,x12394,x12391,x12395,x12396,x12397,x12398,x12399),f642(x12393,x12394,x12392,x12395,x12396,x12397,x12398,x12399)) % 19.23/19.06 [1240]~E(x12401,x12402)+E(f642(x12403,x12404,x12405,x12401,x12406,x12407,x12408,x12409),f642(x12403,x12404,x12405,x12402,x12406,x12407,x12408,x12409)) % 19.23/19.06 [1241]~E(x12411,x12412)+E(f642(x12413,x12414,x12415,x12416,x12411,x12417,x12418,x12419),f642(x12413,x12414,x12415,x12416,x12412,x12417,x12418,x12419)) % 19.23/19.06 [1242]~E(x12421,x12422)+E(f642(x12423,x12424,x12425,x12426,x12427,x12421,x12428,x12429),f642(x12423,x12424,x12425,x12426,x12427,x12422,x12428,x12429)) % 19.23/19.06 [1243]~E(x12431,x12432)+E(f642(x12433,x12434,x12435,x12436,x12437,x12438,x12431,x12439),f642(x12433,x12434,x12435,x12436,x12437,x12438,x12432,x12439)) % 19.23/19.06 [1244]~E(x12441,x12442)+E(f642(x12443,x12444,x12445,x12446,x12447,x12448,x12449,x12441),f642(x12443,x12444,x12445,x12446,x12447,x12448,x12449,x12442)) % 19.23/19.06 [1245]~E(x12451,x12452)+E(f536(x12451,x12453,x12454,x12455),f536(x12452,x12453,x12454,x12455)) % 19.23/19.06 [1246]~E(x12461,x12462)+E(f536(x12463,x12461,x12464,x12465),f536(x12463,x12462,x12464,x12465)) % 19.23/19.06 [1247]~E(x12471,x12472)+E(f536(x12473,x12474,x12471,x12475),f536(x12473,x12474,x12472,x12475)) % 19.23/19.06 [1248]~E(x12481,x12482)+E(f536(x12483,x12484,x12485,x12481),f536(x12483,x12484,x12485,x12482)) % 19.23/19.06 [1249]~E(x12491,x12492)+E(f818(x12491,x12493,x12494),f818(x12492,x12493,x12494)) % 19.23/19.06 [1250]~E(x12501,x12502)+E(f818(x12503,x12501,x12504),f818(x12503,x12502,x12504)) % 19.23/19.06 [1251]~E(x12511,x12512)+E(f818(x12513,x12514,x12511),f818(x12513,x12514,x12512)) % 19.23/19.06 [1252]~E(x12521,x12522)+E(f359(x12521,x12523,x12524,x12525),f359(x12522,x12523,x12524,x12525)) % 19.23/19.06 [1253]~E(x12531,x12532)+E(f359(x12533,x12531,x12534,x12535),f359(x12533,x12532,x12534,x12535)) % 19.23/19.06 [1254]~E(x12541,x12542)+E(f359(x12543,x12544,x12541,x12545),f359(x12543,x12544,x12542,x12545)) % 19.23/19.06 [1255]~E(x12551,x12552)+E(f359(x12553,x12554,x12555,x12551),f359(x12553,x12554,x12555,x12552)) % 19.23/19.06 [1256]~E(x12561,x12562)+E(f254(x12561,x12563),f254(x12562,x12563)) % 19.23/19.06 [1257]~E(x12571,x12572)+E(f254(x12573,x12571),f254(x12573,x12572)) % 19.23/19.06 [1258]~E(x12581,x12582)+E(f832(x12581,x12583,x12584),f832(x12582,x12583,x12584)) % 19.23/19.06 [1259]~E(x12591,x12592)+E(f832(x12593,x12591,x12594),f832(x12593,x12592,x12594)) % 19.23/19.06 [1260]~E(x12601,x12602)+E(f832(x12603,x12604,x12601),f832(x12603,x12604,x12602)) % 19.23/19.06 [1261]~E(x12611,x12612)+E(f480(x12611,x12613,x12614,x12615),f480(x12612,x12613,x12614,x12615)) % 19.23/19.06 [1262]~E(x12621,x12622)+E(f480(x12623,x12621,x12624,x12625),f480(x12623,x12622,x12624,x12625)) % 19.23/19.06 [1263]~E(x12631,x12632)+E(f480(x12633,x12634,x12631,x12635),f480(x12633,x12634,x12632,x12635)) % 19.23/19.06 [1264]~E(x12641,x12642)+E(f480(x12643,x12644,x12645,x12641),f480(x12643,x12644,x12645,x12642)) % 19.23/19.06 [1265]~E(x12651,x12652)+E(f728(x12651,x12653,x12654,x12655,x12656),f728(x12652,x12653,x12654,x12655,x12656)) % 19.23/19.06 [1266]~E(x12661,x12662)+E(f728(x12663,x12661,x12664,x12665,x12666),f728(x12663,x12662,x12664,x12665,x12666)) % 19.23/19.06 [1267]~E(x12671,x12672)+E(f728(x12673,x12674,x12671,x12675,x12676),f728(x12673,x12674,x12672,x12675,x12676)) % 19.23/19.06 [1268]~E(x12681,x12682)+E(f728(x12683,x12684,x12685,x12681,x12686),f728(x12683,x12684,x12685,x12682,x12686)) % 19.23/19.06 [1269]~E(x12691,x12692)+E(f728(x12693,x12694,x12695,x12696,x12691),f728(x12693,x12694,x12695,x12696,x12692)) % 19.23/19.06 [1270]~E(x12701,x12702)+E(f461(x12701,x12703,x12704),f461(x12702,x12703,x12704)) % 19.23/19.06 [1271]~E(x12711,x12712)+E(f461(x12713,x12711,x12714),f461(x12713,x12712,x12714)) % 19.23/19.06 [1272]~E(x12721,x12722)+E(f461(x12723,x12724,x12721),f461(x12723,x12724,x12722)) % 19.23/19.06 [1273]~E(x12731,x12732)+E(f514(x12731,x12733,x12734,x12735,x12736),f514(x12732,x12733,x12734,x12735,x12736)) % 19.23/19.06 [1274]~E(x12741,x12742)+E(f514(x12743,x12741,x12744,x12745,x12746),f514(x12743,x12742,x12744,x12745,x12746)) % 19.23/19.06 [1275]~E(x12751,x12752)+E(f514(x12753,x12754,x12751,x12755,x12756),f514(x12753,x12754,x12752,x12755,x12756)) % 19.23/19.06 [1276]~E(x12761,x12762)+E(f514(x12763,x12764,x12765,x12761,x12766),f514(x12763,x12764,x12765,x12762,x12766)) % 19.23/19.06 [1277]~E(x12771,x12772)+E(f514(x12773,x12774,x12775,x12776,x12771),f514(x12773,x12774,x12775,x12776,x12772)) % 19.23/19.06 [1278]~E(x12781,x12782)+E(f662(x12781,x12783,x12784,x12785),f662(x12782,x12783,x12784,x12785)) % 19.23/19.06 [1279]~E(x12791,x12792)+E(f662(x12793,x12791,x12794,x12795),f662(x12793,x12792,x12794,x12795)) % 19.23/19.06 [1280]~E(x12801,x12802)+E(f662(x12803,x12804,x12801,x12805),f662(x12803,x12804,x12802,x12805)) % 19.23/19.06 [1281]~E(x12811,x12812)+E(f662(x12813,x12814,x12815,x12811),f662(x12813,x12814,x12815,x12812)) % 19.23/19.06 [1282]~E(x12821,x12822)+E(f627(x12821,x12823),f627(x12822,x12823)) % 19.23/19.06 [1283]~E(x12831,x12832)+E(f627(x12833,x12831),f627(x12833,x12832)) % 19.23/19.06 [1284]~E(x12841,x12842)+E(f670(x12841,x12843,x12844),f670(x12842,x12843,x12844)) % 19.23/19.06 [1285]~E(x12851,x12852)+E(f670(x12853,x12851,x12854),f670(x12853,x12852,x12854)) % 19.23/19.06 [1286]~E(x12861,x12862)+E(f670(x12863,x12864,x12861),f670(x12863,x12864,x12862)) % 19.23/19.06 [1287]~E(x12871,x12872)+E(f549(x12871,x12873,x12874,x12875,x12876),f549(x12872,x12873,x12874,x12875,x12876)) % 19.23/19.06 [1288]~E(x12881,x12882)+E(f549(x12883,x12881,x12884,x12885,x12886),f549(x12883,x12882,x12884,x12885,x12886)) % 19.23/19.06 [1289]~E(x12891,x12892)+E(f549(x12893,x12894,x12891,x12895,x12896),f549(x12893,x12894,x12892,x12895,x12896)) % 19.23/19.06 [1290]~E(x12901,x12902)+E(f549(x12903,x12904,x12905,x12901,x12906),f549(x12903,x12904,x12905,x12902,x12906)) % 19.23/19.06 [1291]~E(x12911,x12912)+E(f549(x12913,x12914,x12915,x12916,x12911),f549(x12913,x12914,x12915,x12916,x12912)) % 19.23/19.06 [1292]~E(x12921,x12922)+E(f316(x12921,x12923,x12924),f316(x12922,x12923,x12924)) % 19.23/19.06 [1293]~E(x12931,x12932)+E(f316(x12933,x12931,x12934),f316(x12933,x12932,x12934)) % 19.23/19.06 [1294]~E(x12941,x12942)+E(f316(x12943,x12944,x12941),f316(x12943,x12944,x12942)) % 19.23/19.06 [1295]~E(x12951,x12952)+E(f125(x12951,x12953,x12954,x12955),f125(x12952,x12953,x12954,x12955)) % 19.23/19.06 [1296]~E(x12961,x12962)+E(f125(x12963,x12961,x12964,x12965),f125(x12963,x12962,x12964,x12965)) % 19.23/19.06 [1297]~E(x12971,x12972)+E(f125(x12973,x12974,x12971,x12975),f125(x12973,x12974,x12972,x12975)) % 19.23/19.06 [1298]~E(x12981,x12982)+E(f125(x12983,x12984,x12985,x12981),f125(x12983,x12984,x12985,x12982)) % 19.23/19.06 [1299]~E(x12991,x12992)+E(f492(x12991,x12993),f492(x12992,x12993)) % 19.23/19.06 [1300]~E(x13001,x13002)+E(f492(x13003,x13001),f492(x13003,x13002)) % 19.23/19.06 [1301]~E(x13011,x13012)+E(f450(x13011,x13013,x13014,x13015),f450(x13012,x13013,x13014,x13015)) % 19.23/19.06 [1302]~E(x13021,x13022)+E(f450(x13023,x13021,x13024,x13025),f450(x13023,x13022,x13024,x13025)) % 19.23/19.06 [1303]~E(x13031,x13032)+E(f450(x13033,x13034,x13031,x13035),f450(x13033,x13034,x13032,x13035)) % 19.23/19.06 [1304]~E(x13041,x13042)+E(f450(x13043,x13044,x13045,x13041),f450(x13043,x13044,x13045,x13042)) % 19.23/19.06 [1305]~E(x13051,x13052)+E(f747(x13051,x13053,x13054,x13055),f747(x13052,x13053,x13054,x13055)) % 19.23/19.06 [1306]~E(x13061,x13062)+E(f747(x13063,x13061,x13064,x13065),f747(x13063,x13062,x13064,x13065)) % 19.23/19.06 [1307]~E(x13071,x13072)+E(f747(x13073,x13074,x13071,x13075),f747(x13073,x13074,x13072,x13075)) % 19.23/19.06 [1308]~E(x13081,x13082)+E(f747(x13083,x13084,x13085,x13081),f747(x13083,x13084,x13085,x13082)) % 19.23/19.06 [1309]~E(x13091,x13092)+E(f665(x13091,x13093,x13094,x13095,x13096),f665(x13092,x13093,x13094,x13095,x13096)) % 19.23/19.06 [1310]~E(x13101,x13102)+E(f665(x13103,x13101,x13104,x13105,x13106),f665(x13103,x13102,x13104,x13105,x13106)) % 19.23/19.06 [1311]~E(x13111,x13112)+E(f665(x13113,x13114,x13111,x13115,x13116),f665(x13113,x13114,x13112,x13115,x13116)) % 19.23/19.06 [1312]~E(x13121,x13122)+E(f665(x13123,x13124,x13125,x13121,x13126),f665(x13123,x13124,x13125,x13122,x13126)) % 19.23/19.06 [1313]~E(x13131,x13132)+E(f665(x13133,x13134,x13135,x13136,x13131),f665(x13133,x13134,x13135,x13136,x13132)) % 19.23/19.06 [1314]~E(x13141,x13142)+E(f539(x13141,x13143,x13144),f539(x13142,x13143,x13144)) % 19.23/19.06 [1315]~E(x13151,x13152)+E(f539(x13153,x13151,x13154),f539(x13153,x13152,x13154)) % 19.23/19.06 [1316]~E(x13161,x13162)+E(f539(x13163,x13164,x13161),f539(x13163,x13164,x13162)) % 19.23/19.06 [1317]~E(x13171,x13172)+E(f781(x13171,x13173,x13174,x13175),f781(x13172,x13173,x13174,x13175)) % 19.23/19.06 [1318]~E(x13181,x13182)+E(f781(x13183,x13181,x13184,x13185),f781(x13183,x13182,x13184,x13185)) % 19.23/19.06 [1319]~E(x13191,x13192)+E(f781(x13193,x13194,x13191,x13195),f781(x13193,x13194,x13192,x13195)) % 19.23/19.06 [1320]~E(x13201,x13202)+E(f781(x13203,x13204,x13205,x13201),f781(x13203,x13204,x13205,x13202)) % 19.23/19.06 [1321]~E(x13211,x13212)+E(f714(x13211,x13213,x13214,x13215,x13216),f714(x13212,x13213,x13214,x13215,x13216)) % 19.23/19.06 [1322]~E(x13221,x13222)+E(f714(x13223,x13221,x13224,x13225,x13226),f714(x13223,x13222,x13224,x13225,x13226)) % 19.23/19.06 [1323]~E(x13231,x13232)+E(f714(x13233,x13234,x13231,x13235,x13236),f714(x13233,x13234,x13232,x13235,x13236)) % 19.23/19.06 [1324]~E(x13241,x13242)+E(f714(x13243,x13244,x13245,x13241,x13246),f714(x13243,x13244,x13245,x13242,x13246)) % 19.23/19.06 [1325]~E(x13251,x13252)+E(f714(x13253,x13254,x13255,x13256,x13251),f714(x13253,x13254,x13255,x13256,x13252)) % 19.23/19.06 [1326]~E(x13261,x13262)+E(f746(x13261,x13263,x13264,x13265,x13266),f746(x13262,x13263,x13264,x13265,x13266)) % 19.23/19.06 [1327]~E(x13271,x13272)+E(f746(x13273,x13271,x13274,x13275,x13276),f746(x13273,x13272,x13274,x13275,x13276)) % 19.23/19.06 [1328]~E(x13281,x13282)+E(f746(x13283,x13284,x13281,x13285,x13286),f746(x13283,x13284,x13282,x13285,x13286)) % 19.23/19.06 [1329]~E(x13291,x13292)+E(f746(x13293,x13294,x13295,x13291,x13296),f746(x13293,x13294,x13295,x13292,x13296)) % 19.23/19.06 [1330]~E(x13301,x13302)+E(f746(x13303,x13304,x13305,x13306,x13301),f746(x13303,x13304,x13305,x13306,x13302)) % 19.23/19.06 [1331]~E(x13311,x13312)+E(f602(x13311,x13313,x13314,x13315),f602(x13312,x13313,x13314,x13315)) % 19.23/19.06 [1332]~E(x13321,x13322)+E(f602(x13323,x13321,x13324,x13325),f602(x13323,x13322,x13324,x13325)) % 19.23/19.06 [1333]~E(x13331,x13332)+E(f602(x13333,x13334,x13331,x13335),f602(x13333,x13334,x13332,x13335)) % 19.23/19.06 [1334]~E(x13341,x13342)+E(f602(x13343,x13344,x13345,x13341),f602(x13343,x13344,x13345,x13342)) % 19.23/19.06 [1335]~E(x13351,x13352)+E(f357(x13351,x13353,x13354,x13355,x13356,x13357,x13358),f357(x13352,x13353,x13354,x13355,x13356,x13357,x13358)) % 19.23/19.06 [1336]~E(x13361,x13362)+E(f357(x13363,x13361,x13364,x13365,x13366,x13367,x13368),f357(x13363,x13362,x13364,x13365,x13366,x13367,x13368)) % 19.23/19.06 [1337]~E(x13371,x13372)+E(f357(x13373,x13374,x13371,x13375,x13376,x13377,x13378),f357(x13373,x13374,x13372,x13375,x13376,x13377,x13378)) % 19.23/19.06 [1338]~E(x13381,x13382)+E(f357(x13383,x13384,x13385,x13381,x13386,x13387,x13388),f357(x13383,x13384,x13385,x13382,x13386,x13387,x13388)) % 19.23/19.06 [1339]~E(x13391,x13392)+E(f357(x13393,x13394,x13395,x13396,x13391,x13397,x13398),f357(x13393,x13394,x13395,x13396,x13392,x13397,x13398)) % 19.23/19.06 [1340]~E(x13401,x13402)+E(f357(x13403,x13404,x13405,x13406,x13407,x13401,x13408),f357(x13403,x13404,x13405,x13406,x13407,x13402,x13408)) % 19.23/19.06 [1341]~E(x13411,x13412)+E(f357(x13413,x13414,x13415,x13416,x13417,x13418,x13411),f357(x13413,x13414,x13415,x13416,x13417,x13418,x13412)) % 19.23/19.06 [1342]~E(x13421,x13422)+E(f609(x13421,x13423,x13424,x13425),f609(x13422,x13423,x13424,x13425)) % 19.23/19.06 [1343]~E(x13431,x13432)+E(f609(x13433,x13431,x13434,x13435),f609(x13433,x13432,x13434,x13435)) % 19.23/19.06 [1344]~E(x13441,x13442)+E(f609(x13443,x13444,x13441,x13445),f609(x13443,x13444,x13442,x13445)) % 19.23/19.06 [1345]~E(x13451,x13452)+E(f609(x13453,x13454,x13455,x13451),f609(x13453,x13454,x13455,x13452)) % 19.23/19.06 [1346]~E(x13461,x13462)+E(f513(x13461,x13463,x13464),f513(x13462,x13463,x13464)) % 19.23/19.06 [1347]~E(x13471,x13472)+E(f513(x13473,x13471,x13474),f513(x13473,x13472,x13474)) % 19.23/19.06 [1348]~E(x13481,x13482)+E(f513(x13483,x13484,x13481),f513(x13483,x13484,x13482)) % 19.23/19.06 [1349]~E(x13491,x13492)+E(f295(x13491,x13493,x13494),f295(x13492,x13493,x13494)) % 19.23/19.06 [1350]~E(x13501,x13502)+E(f295(x13503,x13501,x13504),f295(x13503,x13502,x13504)) % 19.23/19.06 [1351]~E(x13511,x13512)+E(f295(x13513,x13514,x13511),f295(x13513,x13514,x13512)) % 19.23/19.06 [1352]~E(x13521,x13522)+E(f667(x13521,x13523,x13524,x13525,x13526),f667(x13522,x13523,x13524,x13525,x13526)) % 19.23/19.06 [1353]~E(x13531,x13532)+E(f667(x13533,x13531,x13534,x13535,x13536),f667(x13533,x13532,x13534,x13535,x13536)) % 19.23/19.06 [1354]~E(x13541,x13542)+E(f667(x13543,x13544,x13541,x13545,x13546),f667(x13543,x13544,x13542,x13545,x13546)) % 19.23/19.06 [1355]~E(x13551,x13552)+E(f667(x13553,x13554,x13555,x13551,x13556),f667(x13553,x13554,x13555,x13552,x13556)) % 19.23/19.06 [1356]~E(x13561,x13562)+E(f667(x13563,x13564,x13565,x13566,x13561),f667(x13563,x13564,x13565,x13566,x13562)) % 19.23/19.06 [1357]~E(x13571,x13572)+E(f419(x13571,x13573,x13574,x13575,x13576),f419(x13572,x13573,x13574,x13575,x13576)) % 19.23/19.06 [1358]~E(x13581,x13582)+E(f419(x13583,x13581,x13584,x13585,x13586),f419(x13583,x13582,x13584,x13585,x13586)) % 19.23/19.06 [1359]~E(x13591,x13592)+E(f419(x13593,x13594,x13591,x13595,x13596),f419(x13593,x13594,x13592,x13595,x13596)) % 19.23/19.06 [1360]~E(x13601,x13602)+E(f419(x13603,x13604,x13605,x13601,x13606),f419(x13603,x13604,x13605,x13602,x13606)) % 19.23/19.06 [1361]~E(x13611,x13612)+E(f419(x13613,x13614,x13615,x13616,x13611),f419(x13613,x13614,x13615,x13616,x13612)) % 19.23/19.06 [1362]~E(x13621,x13622)+E(f446(x13621,x13623,x13624),f446(x13622,x13623,x13624)) % 19.23/19.06 [1363]~E(x13631,x13632)+E(f446(x13633,x13631,x13634),f446(x13633,x13632,x13634)) % 19.23/19.06 [1364]~E(x13641,x13642)+E(f446(x13643,x13644,x13641),f446(x13643,x13644,x13642)) % 19.23/19.06 [1365]~E(x13651,x13652)+E(f444(x13651,x13653,x13654),f444(x13652,x13653,x13654)) % 19.23/19.06 [1366]~E(x13661,x13662)+E(f444(x13663,x13661,x13664),f444(x13663,x13662,x13664)) % 19.23/19.06 [1367]~E(x13671,x13672)+E(f444(x13673,x13674,x13671),f444(x13673,x13674,x13672)) % 19.23/19.06 [1368]~E(x13681,x13682)+E(f545(x13681,x13683,x13684,x13685),f545(x13682,x13683,x13684,x13685)) % 19.23/19.06 [1369]~E(x13691,x13692)+E(f545(x13693,x13691,x13694,x13695),f545(x13693,x13692,x13694,x13695)) % 19.23/19.06 [1370]~E(x13701,x13702)+E(f545(x13703,x13704,x13701,x13705),f545(x13703,x13704,x13702,x13705)) % 19.23/19.06 [1371]~E(x13711,x13712)+E(f545(x13713,x13714,x13715,x13711),f545(x13713,x13714,x13715,x13712)) % 19.23/19.06 [1372]~E(x13721,x13722)+E(f588(x13721,x13723,x13724,x13725),f588(x13722,x13723,x13724,x13725)) % 19.23/19.06 [1373]~E(x13731,x13732)+E(f588(x13733,x13731,x13734,x13735),f588(x13733,x13732,x13734,x13735)) % 19.23/19.06 [1374]~E(x13741,x13742)+E(f588(x13743,x13744,x13741,x13745),f588(x13743,x13744,x13742,x13745)) % 19.23/19.06 [1375]~E(x13751,x13752)+E(f588(x13753,x13754,x13755,x13751),f588(x13753,x13754,x13755,x13752)) % 19.23/19.06 [1376]~E(x13761,x13762)+E(f668(x13761,x13763,x13764,x13765),f668(x13762,x13763,x13764,x13765)) % 19.23/19.06 [1377]~E(x13771,x13772)+E(f668(x13773,x13771,x13774,x13775),f668(x13773,x13772,x13774,x13775)) % 19.23/19.06 [1378]~E(x13781,x13782)+E(f668(x13783,x13784,x13781,x13785),f668(x13783,x13784,x13782,x13785)) % 19.23/19.06 [1379]~E(x13791,x13792)+E(f668(x13793,x13794,x13795,x13791),f668(x13793,x13794,x13795,x13792)) % 19.23/19.06 [1380]~E(x13801,x13802)+E(f658(x13801,x13803,x13804,x13805,x13806),f658(x13802,x13803,x13804,x13805,x13806)) % 19.23/19.06 [1381]~E(x13811,x13812)+E(f658(x13813,x13811,x13814,x13815,x13816),f658(x13813,x13812,x13814,x13815,x13816)) % 19.23/19.06 [1382]~E(x13821,x13822)+E(f658(x13823,x13824,x13821,x13825,x13826),f658(x13823,x13824,x13822,x13825,x13826)) % 19.23/19.06 [1383]~E(x13831,x13832)+E(f658(x13833,x13834,x13835,x13831,x13836),f658(x13833,x13834,x13835,x13832,x13836)) % 19.23/19.06 [1384]~E(x13841,x13842)+E(f658(x13843,x13844,x13845,x13846,x13841),f658(x13843,x13844,x13845,x13846,x13842)) % 19.23/19.06 [1385]~E(x13851,x13852)+E(f447(x13851,x13853,x13854),f447(x13852,x13853,x13854)) % 19.23/19.06 [1386]~E(x13861,x13862)+E(f447(x13863,x13861,x13864),f447(x13863,x13862,x13864)) % 19.23/19.06 [1387]~E(x13871,x13872)+E(f447(x13873,x13874,x13871),f447(x13873,x13874,x13872)) % 19.23/19.06 [1388]~E(x13881,x13882)+E(f611(x13881,x13883,x13884,x13885),f611(x13882,x13883,x13884,x13885)) % 19.23/19.06 [1389]~E(x13891,x13892)+E(f611(x13893,x13891,x13894,x13895),f611(x13893,x13892,x13894,x13895)) % 19.23/19.06 [1390]~E(x13901,x13902)+E(f611(x13903,x13904,x13901,x13905),f611(x13903,x13904,x13902,x13905)) % 19.23/19.06 [1391]~E(x13911,x13912)+E(f611(x13913,x13914,x13915,x13911),f611(x13913,x13914,x13915,x13912)) % 19.23/19.06 [1392]~E(x13921,x13922)+E(f641(x13921,x13923,x13924,x13925,x13926,x13927,x13928,x13929),f641(x13922,x13923,x13924,x13925,x13926,x13927,x13928,x13929)) % 19.23/19.06 [1393]~E(x13931,x13932)+E(f641(x13933,x13931,x13934,x13935,x13936,x13937,x13938,x13939),f641(x13933,x13932,x13934,x13935,x13936,x13937,x13938,x13939)) % 19.23/19.06 [1394]~E(x13941,x13942)+E(f641(x13943,x13944,x13941,x13945,x13946,x13947,x13948,x13949),f641(x13943,x13944,x13942,x13945,x13946,x13947,x13948,x13949)) % 19.23/19.06 [1395]~E(x13951,x13952)+E(f641(x13953,x13954,x13955,x13951,x13956,x13957,x13958,x13959),f641(x13953,x13954,x13955,x13952,x13956,x13957,x13958,x13959)) % 19.23/19.06 [1396]~E(x13961,x13962)+E(f641(x13963,x13964,x13965,x13966,x13961,x13967,x13968,x13969),f641(x13963,x13964,x13965,x13966,x13962,x13967,x13968,x13969)) % 19.23/19.06 [1397]~E(x13971,x13972)+E(f641(x13973,x13974,x13975,x13976,x13977,x13971,x13978,x13979),f641(x13973,x13974,x13975,x13976,x13977,x13972,x13978,x13979)) % 19.23/19.06 [1398]~E(x13981,x13982)+E(f641(x13983,x13984,x13985,x13986,x13987,x13988,x13981,x13989),f641(x13983,x13984,x13985,x13986,x13987,x13988,x13982,x13989)) % 19.23/19.06 [1399]~E(x13991,x13992)+E(f641(x13993,x13994,x13995,x13996,x13997,x13998,x13999,x13991),f641(x13993,x13994,x13995,x13996,x13997,x13998,x13999,x13992)) % 19.23/19.06 [1400]~E(x14001,x14002)+E(f813(x14001,x14003,x14004),f813(x14002,x14003,x14004)) % 19.23/19.06 [1401]~E(x14011,x14012)+E(f813(x14013,x14011,x14014),f813(x14013,x14012,x14014)) % 19.23/19.06 [1402]~E(x14021,x14022)+E(f813(x14023,x14024,x14021),f813(x14023,x14024,x14022)) % 19.23/19.06 [1403]~E(x14031,x14032)+E(f690(x14031,x14033,x14034),f690(x14032,x14033,x14034)) % 19.23/19.06 [1404]~E(x14041,x14042)+E(f690(x14043,x14041,x14044),f690(x14043,x14042,x14044)) % 19.23/19.06 [1405]~E(x14051,x14052)+E(f690(x14053,x14054,x14051),f690(x14053,x14054,x14052)) % 19.23/19.06 [1406]~E(x14061,x14062)+E(f763(x14061,x14063,x14064,x14065,x14066),f763(x14062,x14063,x14064,x14065,x14066)) % 19.23/19.06 [1407]~E(x14071,x14072)+E(f763(x14073,x14071,x14074,x14075,x14076),f763(x14073,x14072,x14074,x14075,x14076)) % 19.23/19.06 [1408]~E(x14081,x14082)+E(f763(x14083,x14084,x14081,x14085,x14086),f763(x14083,x14084,x14082,x14085,x14086)) % 19.23/19.06 [1409]~E(x14091,x14092)+E(f763(x14093,x14094,x14095,x14091,x14096),f763(x14093,x14094,x14095,x14092,x14096)) % 19.23/19.06 [1410]~E(x14101,x14102)+E(f763(x14103,x14104,x14105,x14106,x14101),f763(x14103,x14104,x14105,x14106,x14102)) % 19.23/19.06 [1411]~E(x14111,x14112)+E(f681(x14111,x14113,x14114),f681(x14112,x14113,x14114)) % 19.23/19.06 [1412]~E(x14121,x14122)+E(f681(x14123,x14121,x14124),f681(x14123,x14122,x14124)) % 19.23/19.06 [1413]~E(x14131,x14132)+E(f681(x14133,x14134,x14131),f681(x14133,x14134,x14132)) % 19.23/19.06 [1414]~E(x14141,x14142)+E(f806(x14141,x14143),f806(x14142,x14143)) % 19.23/19.06 [1415]~E(x14151,x14152)+E(f806(x14153,x14151),f806(x14153,x14152)) % 19.23/19.06 [1416]~E(x14161,x14162)+E(f315(x14161,x14163),f315(x14162,x14163)) % 19.23/19.06 [1417]~E(x14171,x14172)+E(f315(x14173,x14171),f315(x14173,x14172)) % 19.23/19.06 [1418]~E(x14181,x14182)+E(f464(x14181,x14183,x14184,x14185),f464(x14182,x14183,x14184,x14185)) % 19.23/19.06 [1419]~E(x14191,x14192)+E(f464(x14193,x14191,x14194,x14195),f464(x14193,x14192,x14194,x14195)) % 19.23/19.06 [1420]~E(x14201,x14202)+E(f464(x14203,x14204,x14201,x14205),f464(x14203,x14204,x14202,x14205)) % 19.23/19.06 [1421]~E(x14211,x14212)+E(f464(x14213,x14214,x14215,x14211),f464(x14213,x14214,x14215,x14212)) % 19.23/19.06 [1422]~E(x14221,x14222)+E(f685(x14221,x14223,x14224),f685(x14222,x14223,x14224)) % 19.23/19.06 [1423]~E(x14231,x14232)+E(f685(x14233,x14231,x14234),f685(x14233,x14232,x14234)) % 19.23/19.06 [1424]~E(x14241,x14242)+E(f685(x14243,x14244,x14241),f685(x14243,x14244,x14242)) % 19.23/19.06 [1425]~E(x14251,x14252)+E(f428(x14251,x14253,x14254,x14255,x14256,x14257,x14258),f428(x14252,x14253,x14254,x14255,x14256,x14257,x14258)) % 19.23/19.06 [1426]~E(x14261,x14262)+E(f428(x14263,x14261,x14264,x14265,x14266,x14267,x14268),f428(x14263,x14262,x14264,x14265,x14266,x14267,x14268)) % 19.23/19.06 [1427]~E(x14271,x14272)+E(f428(x14273,x14274,x14271,x14275,x14276,x14277,x14278),f428(x14273,x14274,x14272,x14275,x14276,x14277,x14278)) % 19.23/19.06 [1428]~E(x14281,x14282)+E(f428(x14283,x14284,x14285,x14281,x14286,x14287,x14288),f428(x14283,x14284,x14285,x14282,x14286,x14287,x14288)) % 19.23/19.06 [1429]~E(x14291,x14292)+E(f428(x14293,x14294,x14295,x14296,x14291,x14297,x14298),f428(x14293,x14294,x14295,x14296,x14292,x14297,x14298)) % 19.23/19.06 [1430]~E(x14301,x14302)+E(f428(x14303,x14304,x14305,x14306,x14307,x14301,x14308),f428(x14303,x14304,x14305,x14306,x14307,x14302,x14308)) % 19.23/19.06 [1431]~E(x14311,x14312)+E(f428(x14313,x14314,x14315,x14316,x14317,x14318,x14311),f428(x14313,x14314,x14315,x14316,x14317,x14318,x14312)) % 19.23/19.06 [1432]~E(x14321,x14322)+E(f506(x14321,x14323,x14324,x14325,x14326,x14327),f506(x14322,x14323,x14324,x14325,x14326,x14327)) % 19.23/19.06 [1433]~E(x14331,x14332)+E(f506(x14333,x14331,x14334,x14335,x14336,x14337),f506(x14333,x14332,x14334,x14335,x14336,x14337)) % 19.23/19.06 [1434]~E(x14341,x14342)+E(f506(x14343,x14344,x14341,x14345,x14346,x14347),f506(x14343,x14344,x14342,x14345,x14346,x14347)) % 19.23/19.06 [1435]~E(x14351,x14352)+E(f506(x14353,x14354,x14355,x14351,x14356,x14357),f506(x14353,x14354,x14355,x14352,x14356,x14357)) % 19.23/19.06 [1436]~E(x14361,x14362)+E(f506(x14363,x14364,x14365,x14366,x14361,x14367),f506(x14363,x14364,x14365,x14366,x14362,x14367)) % 19.23/19.06 [1437]~E(x14371,x14372)+E(f506(x14373,x14374,x14375,x14376,x14377,x14371),f506(x14373,x14374,x14375,x14376,x14377,x14372)) % 19.23/19.06 [1438]~E(x14381,x14382)+E(f351(x14381,x14383,x14384),f351(x14382,x14383,x14384)) % 19.23/19.06 [1439]~E(x14391,x14392)+E(f351(x14393,x14391,x14394),f351(x14393,x14392,x14394)) % 19.23/19.06 [1440]~E(x14401,x14402)+E(f351(x14403,x14404,x14401),f351(x14403,x14404,x14402)) % 19.23/19.06 [1441]~E(x14411,x14412)+E(f594(x14411,x14413,x14414,x14415),f594(x14412,x14413,x14414,x14415)) % 19.23/19.06 [1442]~E(x14421,x14422)+E(f594(x14423,x14421,x14424,x14425),f594(x14423,x14422,x14424,x14425)) % 19.23/19.06 [1443]~E(x14431,x14432)+E(f594(x14433,x14434,x14431,x14435),f594(x14433,x14434,x14432,x14435)) % 19.23/19.06 [1444]~E(x14441,x14442)+E(f594(x14443,x14444,x14445,x14441),f594(x14443,x14444,x14445,x14442)) % 19.23/19.06 [1445]~E(x14451,x14452)+E(f236(x14451,x14453,x14454),f236(x14452,x14453,x14454)) % 19.23/19.06 [1446]~E(x14461,x14462)+E(f236(x14463,x14461,x14464),f236(x14463,x14462,x14464)) % 19.23/19.06 [1447]~E(x14471,x14472)+E(f236(x14473,x14474,x14471),f236(x14473,x14474,x14472)) % 19.23/19.06 [1448]~E(x14481,x14482)+E(f470(x14481,x14483,x14484,x14485),f470(x14482,x14483,x14484,x14485)) % 19.23/19.06 [1449]~E(x14491,x14492)+E(f470(x14493,x14491,x14494,x14495),f470(x14493,x14492,x14494,x14495)) % 19.23/19.06 [1450]~E(x14501,x14502)+E(f470(x14503,x14504,x14501,x14505),f470(x14503,x14504,x14502,x14505)) % 19.23/19.06 [1451]~E(x14511,x14512)+E(f470(x14513,x14514,x14515,x14511),f470(x14513,x14514,x14515,x14512)) % 19.23/19.06 [1452]~E(x14521,x14522)+E(f755(x14521,x14523,x14524,x14525),f755(x14522,x14523,x14524,x14525)) % 19.23/19.06 [1453]~E(x14531,x14532)+E(f755(x14533,x14531,x14534,x14535),f755(x14533,x14532,x14534,x14535)) % 19.23/19.06 [1454]~E(x14541,x14542)+E(f755(x14543,x14544,x14541,x14545),f755(x14543,x14544,x14542,x14545)) % 19.23/19.06 [1455]~E(x14551,x14552)+E(f755(x14553,x14554,x14555,x14551),f755(x14553,x14554,x14555,x14552)) % 19.23/19.06 [1456]~E(x14561,x14562)+E(f517(x14561,x14563,x14564,x14565,x14566),f517(x14562,x14563,x14564,x14565,x14566)) % 19.23/19.06 [1457]~E(x14571,x14572)+E(f517(x14573,x14571,x14574,x14575,x14576),f517(x14573,x14572,x14574,x14575,x14576)) % 19.23/19.06 [1458]~E(x14581,x14582)+E(f517(x14583,x14584,x14581,x14585,x14586),f517(x14583,x14584,x14582,x14585,x14586)) % 19.23/19.06 [1459]~E(x14591,x14592)+E(f517(x14593,x14594,x14595,x14591,x14596),f517(x14593,x14594,x14595,x14592,x14596)) % 19.23/19.06 [1460]~E(x14601,x14602)+E(f517(x14603,x14604,x14605,x14606,x14601),f517(x14603,x14604,x14605,x14606,x14602)) % 19.23/19.06 [1461]~E(x14611,x14612)+E(f697(x14611,x14613,x14614,x14615,x14616,x14617),f697(x14612,x14613,x14614,x14615,x14616,x14617)) % 19.23/19.06 [1462]~E(x14621,x14622)+E(f697(x14623,x14621,x14624,x14625,x14626,x14627),f697(x14623,x14622,x14624,x14625,x14626,x14627)) % 19.23/19.06 [1463]~E(x14631,x14632)+E(f697(x14633,x14634,x14631,x14635,x14636,x14637),f697(x14633,x14634,x14632,x14635,x14636,x14637)) % 19.23/19.06 [1464]~E(x14641,x14642)+E(f697(x14643,x14644,x14645,x14641,x14646,x14647),f697(x14643,x14644,x14645,x14642,x14646,x14647)) % 19.23/19.06 [1465]~E(x14651,x14652)+E(f697(x14653,x14654,x14655,x14656,x14651,x14657),f697(x14653,x14654,x14655,x14656,x14652,x14657)) % 19.23/19.06 [1466]~E(x14661,x14662)+E(f697(x14663,x14664,x14665,x14666,x14667,x14661),f697(x14663,x14664,x14665,x14666,x14667,x14662)) % 19.23/19.06 [1467]~E(x14671,x14672)+E(f808(x14671,x14673,x14674),f808(x14672,x14673,x14674)) % 19.23/19.06 [1468]~E(x14681,x14682)+E(f808(x14683,x14681,x14684),f808(x14683,x14682,x14684)) % 19.23/19.06 [1469]~E(x14691,x14692)+E(f808(x14693,x14694,x14691),f808(x14693,x14694,x14692)) % 19.23/19.06 [1470]~E(x14701,x14702)+E(f647(x14701,x14703,x14704),f647(x14702,x14703,x14704)) % 19.23/19.06 [1471]~E(x14711,x14712)+E(f647(x14713,x14711,x14714),f647(x14713,x14712,x14714)) % 19.23/19.06 [1472]~E(x14721,x14722)+E(f647(x14723,x14724,x14721),f647(x14723,x14724,x14722)) % 19.23/19.06 [1473]~E(x14731,x14732)+E(f548(x14731,x14733,x14734,x14735,x14736),f548(x14732,x14733,x14734,x14735,x14736)) % 19.23/19.06 [1474]~E(x14741,x14742)+E(f548(x14743,x14741,x14744,x14745,x14746),f548(x14743,x14742,x14744,x14745,x14746)) % 19.23/19.06 [1475]~E(x14751,x14752)+E(f548(x14753,x14754,x14751,x14755,x14756),f548(x14753,x14754,x14752,x14755,x14756)) % 19.23/19.06 [1476]~E(x14761,x14762)+E(f548(x14763,x14764,x14765,x14761,x14766),f548(x14763,x14764,x14765,x14762,x14766)) % 19.23/19.06 [1477]~E(x14771,x14772)+E(f548(x14773,x14774,x14775,x14776,x14771),f548(x14773,x14774,x14775,x14776,x14772)) % 19.23/19.06 [1478]~E(x14781,x14782)+E(f785(x14781,x14783,x14784),f785(x14782,x14783,x14784)) % 19.23/19.06 [1479]~E(x14791,x14792)+E(f785(x14793,x14791,x14794),f785(x14793,x14792,x14794)) % 19.23/19.06 [1480]~E(x14801,x14802)+E(f785(x14803,x14804,x14801),f785(x14803,x14804,x14802)) % 19.23/19.06 [1481]~E(x14811,x14812)+E(f19(x14811,x14813,x14814,x14815),f19(x14812,x14813,x14814,x14815)) % 19.23/19.06 [1482]~E(x14821,x14822)+E(f19(x14823,x14821,x14824,x14825),f19(x14823,x14822,x14824,x14825)) % 19.23/19.06 [1483]~E(x14831,x14832)+E(f19(x14833,x14834,x14831,x14835),f19(x14833,x14834,x14832,x14835)) % 19.23/19.06 [1484]~E(x14841,x14842)+E(f19(x14843,x14844,x14845,x14841),f19(x14843,x14844,x14845,x14842)) % 19.23/19.06 [1485]~E(x14851,x14852)+E(f509(x14851,x14853,x14854),f509(x14852,x14853,x14854)) % 19.23/19.06 [1486]~E(x14861,x14862)+E(f509(x14863,x14861,x14864),f509(x14863,x14862,x14864)) % 19.23/19.06 [1487]~E(x14871,x14872)+E(f509(x14873,x14874,x14871),f509(x14873,x14874,x14872)) % 19.23/19.06 [1488]~E(x14881,x14882)+E(f676(x14881,x14883,x14884,x14885,x14886),f676(x14882,x14883,x14884,x14885,x14886)) % 19.23/19.06 [1489]~E(x14891,x14892)+E(f676(x14893,x14891,x14894,x14895,x14896),f676(x14893,x14892,x14894,x14895,x14896)) % 19.23/19.06 [1490]~E(x14901,x14902)+E(f676(x14903,x14904,x14901,x14905,x14906),f676(x14903,x14904,x14902,x14905,x14906)) % 19.23/19.06 [1491]~E(x14911,x14912)+E(f676(x14913,x14914,x14915,x14911,x14916),f676(x14913,x14914,x14915,x14912,x14916)) % 19.23/19.06 [1492]~E(x14921,x14922)+E(f676(x14923,x14924,x14925,x14926,x14921),f676(x14923,x14924,x14925,x14926,x14922)) % 19.23/19.06 [1493]~E(x14931,x14932)+E(f646(x14931,x14933),f646(x14932,x14933)) % 19.23/19.06 [1494]~E(x14941,x14942)+E(f646(x14943,x14941),f646(x14943,x14942)) % 19.23/19.06 [1495]~E(x14951,x14952)+E(f779(x14951,x14953,x14954),f779(x14952,x14953,x14954)) % 19.23/19.06 [1496]~E(x14961,x14962)+E(f779(x14963,x14961,x14964),f779(x14963,x14962,x14964)) % 19.23/19.06 [1497]~E(x14971,x14972)+E(f779(x14973,x14974,x14971),f779(x14973,x14974,x14972)) % 19.23/19.06 [1498]~E(x14981,x14982)+E(f825(x14981,x14983,x14984),f825(x14982,x14983,x14984)) % 19.23/19.06 [1499]~E(x14991,x14992)+E(f825(x14993,x14991,x14994),f825(x14993,x14992,x14994)) % 19.23/19.06 [1500]~E(x15001,x15002)+E(f825(x15003,x15004,x15001),f825(x15003,x15004,x15002)) % 19.23/19.06 [1501]~E(x15011,x15012)+E(f440(x15011,x15013,x15014),f440(x15012,x15013,x15014)) % 19.23/19.06 [1502]~E(x15021,x15022)+E(f440(x15023,x15021,x15024),f440(x15023,x15022,x15024)) % 19.23/19.06 [1503]~E(x15031,x15032)+E(f440(x15033,x15034,x15031),f440(x15033,x15034,x15032)) % 19.23/19.06 [1504]~E(x15041,x15042)+E(f399(x15041,x15043,x15044,x15045),f399(x15042,x15043,x15044,x15045)) % 19.23/19.06 [1505]~E(x15051,x15052)+E(f399(x15053,x15051,x15054,x15055),f399(x15053,x15052,x15054,x15055)) % 19.23/19.06 [1506]~E(x15061,x15062)+E(f399(x15063,x15064,x15061,x15065),f399(x15063,x15064,x15062,x15065)) % 19.23/19.06 [1507]~E(x15071,x15072)+E(f399(x15073,x15074,x15075,x15071),f399(x15073,x15074,x15075,x15072)) % 19.23/19.06 [1508]~E(x15081,x15082)+E(f471(x15081,x15083,x15084,x15085),f471(x15082,x15083,x15084,x15085)) % 19.23/19.06 [1509]~E(x15091,x15092)+E(f471(x15093,x15091,x15094,x15095),f471(x15093,x15092,x15094,x15095)) % 19.23/19.06 [1510]~E(x15101,x15102)+E(f471(x15103,x15104,x15101,x15105),f471(x15103,x15104,x15102,x15105)) % 19.23/19.06 [1511]~E(x15111,x15112)+E(f471(x15113,x15114,x15115,x15111),f471(x15113,x15114,x15115,x15112)) % 19.23/19.06 [1512]~E(x15121,x15122)+E(f800(x15121),f800(x15122)) % 19.23/19.06 [1513]~E(x15131,x15132)+E(f542(x15131,x15133,x15134,x15135),f542(x15132,x15133,x15134,x15135)) % 19.23/19.06 [1514]~E(x15141,x15142)+E(f542(x15143,x15141,x15144,x15145),f542(x15143,x15142,x15144,x15145)) % 19.23/19.06 [1515]~E(x15151,x15152)+E(f542(x15153,x15154,x15151,x15155),f542(x15153,x15154,x15152,x15155)) % 19.23/19.06 [1516]~E(x15161,x15162)+E(f542(x15163,x15164,x15165,x15161),f542(x15163,x15164,x15165,x15162)) % 19.23/19.06 [1517]~E(x15171,x15172)+E(f679(x15171,x15173,x15174,x15175,x15176,x15177,x15178),f679(x15172,x15173,x15174,x15175,x15176,x15177,x15178)) % 19.23/19.06 [1518]~E(x15181,x15182)+E(f679(x15183,x15181,x15184,x15185,x15186,x15187,x15188),f679(x15183,x15182,x15184,x15185,x15186,x15187,x15188)) % 19.23/19.06 [1519]~E(x15191,x15192)+E(f679(x15193,x15194,x15191,x15195,x15196,x15197,x15198),f679(x15193,x15194,x15192,x15195,x15196,x15197,x15198)) % 19.23/19.06 [1520]~E(x15201,x15202)+E(f679(x15203,x15204,x15205,x15201,x15206,x15207,x15208),f679(x15203,x15204,x15205,x15202,x15206,x15207,x15208)) % 19.23/19.06 [1521]~E(x15211,x15212)+E(f679(x15213,x15214,x15215,x15216,x15211,x15217,x15218),f679(x15213,x15214,x15215,x15216,x15212,x15217,x15218)) % 19.23/19.06 [1522]~E(x15221,x15222)+E(f679(x15223,x15224,x15225,x15226,x15227,x15221,x15228),f679(x15223,x15224,x15225,x15226,x15227,x15222,x15228)) % 19.23/19.06 [1523]~E(x15231,x15232)+E(f679(x15233,x15234,x15235,x15236,x15237,x15238,x15231),f679(x15233,x15234,x15235,x15236,x15237,x15238,x15232)) % 19.23/19.06 [1524]~E(x15241,x15242)+E(f723(x15241,x15243,x15244,x15245,x15246),f723(x15242,x15243,x15244,x15245,x15246)) % 19.23/19.06 [1525]~E(x15251,x15252)+E(f723(x15253,x15251,x15254,x15255,x15256),f723(x15253,x15252,x15254,x15255,x15256)) % 19.23/19.06 [1526]~E(x15261,x15262)+E(f723(x15263,x15264,x15261,x15265,x15266),f723(x15263,x15264,x15262,x15265,x15266)) % 19.23/19.06 [1527]~E(x15271,x15272)+E(f723(x15273,x15274,x15275,x15271,x15276),f723(x15273,x15274,x15275,x15272,x15276)) % 19.23/19.06 [1528]~E(x15281,x15282)+E(f723(x15283,x15284,x15285,x15286,x15281),f723(x15283,x15284,x15285,x15286,x15282)) % 19.23/19.06 [1529]~E(x15291,x15292)+E(f688(x15291,x15293,x15294),f688(x15292,x15293,x15294)) % 19.23/19.06 [1530]~E(x15301,x15302)+E(f688(x15303,x15301,x15304),f688(x15303,x15302,x15304)) % 19.23/19.06 [1531]~E(x15311,x15312)+E(f688(x15313,x15314,x15311),f688(x15313,x15314,x15312)) % 19.23/19.06 [1532]~E(x15321,x15322)+E(f486(x15321,x15323,x15324,x15325),f486(x15322,x15323,x15324,x15325)) % 19.23/19.06 [1533]~E(x15331,x15332)+E(f486(x15333,x15331,x15334,x15335),f486(x15333,x15332,x15334,x15335)) % 19.23/19.06 [1534]~E(x15341,x15342)+E(f486(x15343,x15344,x15341,x15345),f486(x15343,x15344,x15342,x15345)) % 19.23/19.06 [1535]~E(x15351,x15352)+E(f486(x15353,x15354,x15355,x15351),f486(x15353,x15354,x15355,x15352)) % 19.23/19.06 [1536]~E(x15361,x15362)+E(f758(x15361,x15363,x15364),f758(x15362,x15363,x15364)) % 19.23/19.06 [1537]~E(x15371,x15372)+E(f758(x15373,x15371,x15374),f758(x15373,x15372,x15374)) % 19.23/19.06 [1538]~E(x15381,x15382)+E(f758(x15383,x15384,x15381),f758(x15383,x15384,x15382)) % 19.23/19.06 [1539]~E(x15391,x15392)+E(f677(x15391,x15393,x15394,x15395,x15396),f677(x15392,x15393,x15394,x15395,x15396)) % 19.23/19.06 [1540]~E(x15401,x15402)+E(f677(x15403,x15401,x15404,x15405,x15406),f677(x15403,x15402,x15404,x15405,x15406)) % 19.23/19.06 [1541]~E(x15411,x15412)+E(f677(x15413,x15414,x15411,x15415,x15416),f677(x15413,x15414,x15412,x15415,x15416)) % 19.23/19.06 [1542]~E(x15421,x15422)+E(f677(x15423,x15424,x15425,x15421,x15426),f677(x15423,x15424,x15425,x15422,x15426)) % 19.23/19.06 [1543]~E(x15431,x15432)+E(f677(x15433,x15434,x15435,x15436,x15431),f677(x15433,x15434,x15435,x15436,x15432)) % 19.23/19.06 [1544]~E(x15441,x15442)+E(f596(x15441,x15443,x15444),f596(x15442,x15443,x15444)) % 19.23/19.06 [1545]~E(x15451,x15452)+E(f596(x15453,x15451,x15454),f596(x15453,x15452,x15454)) % 19.23/19.06 [1546]~E(x15461,x15462)+E(f596(x15463,x15464,x15461),f596(x15463,x15464,x15462)) % 19.23/19.06 [1547]~E(x15471,x15472)+E(f477(x15471,x15473,x15474,x15475),f477(x15472,x15473,x15474,x15475)) % 19.23/19.06 [1548]~E(x15481,x15482)+E(f477(x15483,x15481,x15484,x15485),f477(x15483,x15482,x15484,x15485)) % 19.23/19.06 [1549]~E(x15491,x15492)+E(f477(x15493,x15494,x15491,x15495),f477(x15493,x15494,x15492,x15495)) % 19.23/19.06 [1550]~E(x15501,x15502)+E(f477(x15503,x15504,x15505,x15501),f477(x15503,x15504,x15505,x15502)) % 19.23/19.06 [1551]~E(x15511,x15512)+E(f556(x15511,x15513,x15514,x15515),f556(x15512,x15513,x15514,x15515)) % 19.23/19.06 [1552]~E(x15521,x15522)+E(f556(x15523,x15521,x15524,x15525),f556(x15523,x15522,x15524,x15525)) % 19.23/19.06 [1553]~E(x15531,x15532)+E(f556(x15533,x15534,x15531,x15535),f556(x15533,x15534,x15532,x15535)) % 19.23/19.06 [1554]~E(x15541,x15542)+E(f556(x15543,x15544,x15545,x15541),f556(x15543,x15544,x15545,x15542)) % 19.23/19.06 [1555]~E(x15551,x15552)+E(f721(x15551,x15553,x15554,x15555,x15556,x15557,x15558),f721(x15552,x15553,x15554,x15555,x15556,x15557,x15558)) % 19.23/19.06 [1556]~E(x15561,x15562)+E(f721(x15563,x15561,x15564,x15565,x15566,x15567,x15568),f721(x15563,x15562,x15564,x15565,x15566,x15567,x15568)) % 19.23/19.06 [1557]~E(x15571,x15572)+E(f721(x15573,x15574,x15571,x15575,x15576,x15577,x15578),f721(x15573,x15574,x15572,x15575,x15576,x15577,x15578)) % 19.23/19.06 [1558]~E(x15581,x15582)+E(f721(x15583,x15584,x15585,x15581,x15586,x15587,x15588),f721(x15583,x15584,x15585,x15582,x15586,x15587,x15588)) % 19.23/19.06 [1559]~E(x15591,x15592)+E(f721(x15593,x15594,x15595,x15596,x15591,x15597,x15598),f721(x15593,x15594,x15595,x15596,x15592,x15597,x15598)) % 19.23/19.06 [1560]~E(x15601,x15602)+E(f721(x15603,x15604,x15605,x15606,x15607,x15601,x15608),f721(x15603,x15604,x15605,x15606,x15607,x15602,x15608)) % 19.23/19.06 [1561]~E(x15611,x15612)+E(f721(x15613,x15614,x15615,x15616,x15617,x15618,x15611),f721(x15613,x15614,x15615,x15616,x15617,x15618,x15612)) % 19.23/19.06 [1562]~E(x15621,x15622)+E(f193(x15621,x15623),f193(x15622,x15623)) % 19.23/19.06 [1563]~E(x15631,x15632)+E(f193(x15633,x15631),f193(x15633,x15632)) % 19.23/19.06 [1564]~E(x15641,x15642)+E(f811(x15641,x15643,x15644),f811(x15642,x15643,x15644)) % 19.23/19.06 [1565]~E(x15651,x15652)+E(f811(x15653,x15651,x15654),f811(x15653,x15652,x15654)) % 19.23/19.06 [1566]~E(x15661,x15662)+E(f811(x15663,x15664,x15661),f811(x15663,x15664,x15662)) % 19.23/19.06 [1567]~E(x15671,x15672)+E(f253(x15671,x15673,x15674),f253(x15672,x15673,x15674)) % 19.23/19.06 [1568]~E(x15681,x15682)+E(f253(x15683,x15681,x15684),f253(x15683,x15682,x15684)) % 19.23/19.06 [1569]~E(x15691,x15692)+E(f253(x15693,x15694,x15691),f253(x15693,x15694,x15692)) % 19.23/19.06 [1570]~E(x15701,x15702)+E(f578(x15701),f578(x15702)) % 19.23/19.06 [1571]~E(x15711,x15712)+E(f749(x15711,x15713,x15714,x15715,x15716),f749(x15712,x15713,x15714,x15715,x15716)) % 19.23/19.06 [1572]~E(x15721,x15722)+E(f749(x15723,x15721,x15724,x15725,x15726),f749(x15723,x15722,x15724,x15725,x15726)) % 19.23/19.06 [1573]~E(x15731,x15732)+E(f749(x15733,x15734,x15731,x15735,x15736),f749(x15733,x15734,x15732,x15735,x15736)) % 19.23/19.06 [1574]~E(x15741,x15742)+E(f749(x15743,x15744,x15745,x15741,x15746),f749(x15743,x15744,x15745,x15742,x15746)) % 19.23/19.06 [1575]~E(x15751,x15752)+E(f749(x15753,x15754,x15755,x15756,x15751),f749(x15753,x15754,x15755,x15756,x15752)) % 19.23/19.06 [1576]~E(x15761,x15762)+E(f757(x15761,x15763),f757(x15762,x15763)) % 19.23/19.06 [1577]~E(x15771,x15772)+E(f757(x15773,x15771),f757(x15773,x15772)) % 19.23/19.06 [1578]~E(x15781,x15782)+E(f375(x15781,x15783),f375(x15782,x15783)) % 19.23/19.06 [1579]~E(x15791,x15792)+E(f375(x15793,x15791),f375(x15793,x15792)) % 19.23/19.06 [1580]~E(x15801,x15802)+E(f589(x15801,x15803),f589(x15802,x15803)) % 19.23/19.06 [1581]~E(x15811,x15812)+E(f589(x15813,x15811),f589(x15813,x15812)) % 19.23/19.06 [1582]~E(x15821,x15822)+E(f429(x15821,x15823,x15824,x15825,x15826,x15827,x15828),f429(x15822,x15823,x15824,x15825,x15826,x15827,x15828)) % 19.23/19.06 [1583]~E(x15831,x15832)+E(f429(x15833,x15831,x15834,x15835,x15836,x15837,x15838),f429(x15833,x15832,x15834,x15835,x15836,x15837,x15838)) % 19.23/19.06 [1584]~E(x15841,x15842)+E(f429(x15843,x15844,x15841,x15845,x15846,x15847,x15848),f429(x15843,x15844,x15842,x15845,x15846,x15847,x15848)) % 19.23/19.06 [1585]~E(x15851,x15852)+E(f429(x15853,x15854,x15855,x15851,x15856,x15857,x15858),f429(x15853,x15854,x15855,x15852,x15856,x15857,x15858)) % 19.23/19.06 [1586]~E(x15861,x15862)+E(f429(x15863,x15864,x15865,x15866,x15861,x15867,x15868),f429(x15863,x15864,x15865,x15866,x15862,x15867,x15868)) % 19.23/19.06 [1587]~E(x15871,x15872)+E(f429(x15873,x15874,x15875,x15876,x15877,x15871,x15878),f429(x15873,x15874,x15875,x15876,x15877,x15872,x15878)) % 19.23/19.06 [1588]~E(x15881,x15882)+E(f429(x15883,x15884,x15885,x15886,x15887,x15888,x15881),f429(x15883,x15884,x15885,x15886,x15887,x15888,x15882)) % 19.23/19.06 [1589]~E(x15891,x15892)+E(f733(x15891,x15893,x15894),f733(x15892,x15893,x15894)) % 19.23/19.06 [1590]~E(x15901,x15902)+E(f733(x15903,x15901,x15904),f733(x15903,x15902,x15904)) % 19.23/19.06 [1591]~E(x15911,x15912)+E(f733(x15913,x15914,x15911),f733(x15913,x15914,x15912)) % 19.23/19.06 [1592]~E(x15921,x15922)+E(f362(x15921,x15923,x15924,x15925),f362(x15922,x15923,x15924,x15925)) % 19.23/19.06 [1593]~E(x15931,x15932)+E(f362(x15933,x15931,x15934,x15935),f362(x15933,x15932,x15934,x15935)) % 19.23/19.06 [1594]~E(x15941,x15942)+E(f362(x15943,x15944,x15941,x15945),f362(x15943,x15944,x15942,x15945)) % 19.23/19.06 [1595]~E(x15951,x15952)+E(f362(x15953,x15954,x15955,x15951),f362(x15953,x15954,x15955,x15952)) % 19.23/19.06 [1596]~E(x15961,x15962)+E(f633(x15961,x15963,x15964,x15965,x15966),f633(x15962,x15963,x15964,x15965,x15966)) % 19.23/19.06 [1597]~E(x15971,x15972)+E(f633(x15973,x15971,x15974,x15975,x15976),f633(x15973,x15972,x15974,x15975,x15976)) % 19.23/19.06 [1598]~E(x15981,x15982)+E(f633(x15983,x15984,x15981,x15985,x15986),f633(x15983,x15984,x15982,x15985,x15986)) % 19.23/19.06 [1599]~E(x15991,x15992)+E(f633(x15993,x15994,x15995,x15991,x15996),f633(x15993,x15994,x15995,x15992,x15996)) % 19.23/19.06 [1600]~E(x16001,x16002)+E(f633(x16003,x16004,x16005,x16006,x16001),f633(x16003,x16004,x16005,x16006,x16002)) % 19.23/19.06 [1601]~E(x16011,x16012)+E(f664(x16011,x16013,x16014,x16015,x16016),f664(x16012,x16013,x16014,x16015,x16016)) % 19.23/19.06 [1602]~E(x16021,x16022)+E(f664(x16023,x16021,x16024,x16025,x16026),f664(x16023,x16022,x16024,x16025,x16026)) % 19.23/19.06 [1603]~E(x16031,x16032)+E(f664(x16033,x16034,x16031,x16035,x16036),f664(x16033,x16034,x16032,x16035,x16036)) % 19.23/19.06 [1604]~E(x16041,x16042)+E(f664(x16043,x16044,x16045,x16041,x16046),f664(x16043,x16044,x16045,x16042,x16046)) % 19.23/19.06 [1605]~E(x16051,x16052)+E(f664(x16053,x16054,x16055,x16056,x16051),f664(x16053,x16054,x16055,x16056,x16052)) % 19.23/19.06 [1606]~E(x16061,x16062)+E(f546(x16061,x16063,x16064,x16065,x16066),f546(x16062,x16063,x16064,x16065,x16066)) % 19.23/19.06 [1607]~E(x16071,x16072)+E(f546(x16073,x16071,x16074,x16075,x16076),f546(x16073,x16072,x16074,x16075,x16076)) % 19.23/19.06 [1608]~E(x16081,x16082)+E(f546(x16083,x16084,x16081,x16085,x16086),f546(x16083,x16084,x16082,x16085,x16086)) % 19.23/19.06 [1609]~E(x16091,x16092)+E(f546(x16093,x16094,x16095,x16091,x16096),f546(x16093,x16094,x16095,x16092,x16096)) % 19.23/19.06 [1610]~E(x16101,x16102)+E(f546(x16103,x16104,x16105,x16106,x16101),f546(x16103,x16104,x16105,x16106,x16102)) % 19.23/19.06 [1611]~E(x16111,x16112)+E(f229(x16111,x16113),f229(x16112,x16113)) % 19.23/19.06 [1612]~E(x16121,x16122)+E(f229(x16123,x16121),f229(x16123,x16122)) % 19.23/19.06 [1613]~E(x16131,x16132)+E(f680(x16131,x16133),f680(x16132,x16133)) % 19.23/19.06 [1614]~E(x16141,x16142)+E(f680(x16143,x16141),f680(x16143,x16142)) % 19.23/19.06 [1615]~E(x16151,x16152)+E(f568(x16151),f568(x16152)) % 19.23/19.06 [1616]~E(x16161,x16162)+E(f462(x16161,x16163,x16164),f462(x16162,x16163,x16164)) % 19.23/19.06 [1617]~E(x16171,x16172)+E(f462(x16173,x16171,x16174),f462(x16173,x16172,x16174)) % 19.23/19.06 [1618]~E(x16181,x16182)+E(f462(x16183,x16184,x16181),f462(x16183,x16184,x16182)) % 19.23/19.06 [1619]~E(x16191,x16192)+E(f543(x16191,x16193,x16194,x16195),f543(x16192,x16193,x16194,x16195)) % 19.23/19.06 [1620]~E(x16201,x16202)+E(f543(x16203,x16201,x16204,x16205),f543(x16203,x16202,x16204,x16205)) % 19.23/19.06 [1621]~E(x16211,x16212)+E(f543(x16213,x16214,x16211,x16215),f543(x16213,x16214,x16212,x16215)) % 19.23/19.06 [1622]~E(x16221,x16222)+E(f543(x16223,x16224,x16225,x16221),f543(x16223,x16224,x16225,x16222)) % 19.23/19.06 [1623]~E(x16231,x16232)+E(f732(x16231,x16233),f732(x16232,x16233)) % 19.23/19.06 [1624]~E(x16241,x16242)+E(f732(x16243,x16241),f732(x16243,x16242)) % 19.23/19.06 [1625]~E(x16251,x16252)+E(f651(x16251,x16253),f651(x16252,x16253)) % 19.23/19.06 [1626]~E(x16261,x16262)+E(f651(x16263,x16261),f651(x16263,x16262)) % 19.23/19.06 [1627]~E(x16271,x16272)+E(f575(x16271,x16273,x16274,x16275,x16276),f575(x16272,x16273,x16274,x16275,x16276)) % 19.23/19.06 [1628]~E(x16281,x16282)+E(f575(x16283,x16281,x16284,x16285,x16286),f575(x16283,x16282,x16284,x16285,x16286)) % 19.23/19.06 [1629]~E(x16291,x16292)+E(f575(x16293,x16294,x16291,x16295,x16296),f575(x16293,x16294,x16292,x16295,x16296)) % 19.23/19.06 [1630]~E(x16301,x16302)+E(f575(x16303,x16304,x16305,x16301,x16306),f575(x16303,x16304,x16305,x16302,x16306)) % 19.23/19.06 [1631]~E(x16311,x16312)+E(f575(x16313,x16314,x16315,x16316,x16311),f575(x16313,x16314,x16315,x16316,x16312)) % 19.23/19.06 [1632]~E(x16321,x16322)+E(f494(x16321,x16323,x16324,x16325,x16326),f494(x16322,x16323,x16324,x16325,x16326)) % 19.23/19.06 [1633]~E(x16331,x16332)+E(f494(x16333,x16331,x16334,x16335,x16336),f494(x16333,x16332,x16334,x16335,x16336)) % 19.23/19.06 [1634]~E(x16341,x16342)+E(f494(x16343,x16344,x16341,x16345,x16346),f494(x16343,x16344,x16342,x16345,x16346)) % 19.23/19.06 [1635]~E(x16351,x16352)+E(f494(x16353,x16354,x16355,x16351,x16356),f494(x16353,x16354,x16355,x16352,x16356)) % 19.23/19.06 [1636]~E(x16361,x16362)+E(f494(x16363,x16364,x16365,x16366,x16361),f494(x16363,x16364,x16365,x16366,x16362)) % 19.23/19.06 [1637]~E(x16371,x16372)+E(f416(x16371,x16373,x16374,x16375,x16376),f416(x16372,x16373,x16374,x16375,x16376)) % 19.23/19.06 [1638]~E(x16381,x16382)+E(f416(x16383,x16381,x16384,x16385,x16386),f416(x16383,x16382,x16384,x16385,x16386)) % 19.23/19.06 [1639]~E(x16391,x16392)+E(f416(x16393,x16394,x16391,x16395,x16396),f416(x16393,x16394,x16392,x16395,x16396)) % 19.23/19.06 [1640]~E(x16401,x16402)+E(f416(x16403,x16404,x16405,x16401,x16406),f416(x16403,x16404,x16405,x16402,x16406)) % 19.23/19.06 [1641]~E(x16411,x16412)+E(f416(x16413,x16414,x16415,x16416,x16411),f416(x16413,x16414,x16415,x16416,x16412)) % 19.23/19.06 [1642]~E(x16421,x16422)+E(f420(x16421,x16423,x16424,x16425,x16426),f420(x16422,x16423,x16424,x16425,x16426)) % 19.23/19.06 [1643]~E(x16431,x16432)+E(f420(x16433,x16431,x16434,x16435,x16436),f420(x16433,x16432,x16434,x16435,x16436)) % 19.23/19.06 [1644]~E(x16441,x16442)+E(f420(x16443,x16444,x16441,x16445,x16446),f420(x16443,x16444,x16442,x16445,x16446)) % 19.23/19.06 [1645]~E(x16451,x16452)+E(f420(x16453,x16454,x16455,x16451,x16456),f420(x16453,x16454,x16455,x16452,x16456)) % 19.23/19.06 [1646]~E(x16461,x16462)+E(f420(x16463,x16464,x16465,x16466,x16461),f420(x16463,x16464,x16465,x16466,x16462)) % 19.23/19.06 [1647]~E(x16471,x16472)+E(f405(x16471,x16473,x16474,x16475,x16476),f405(x16472,x16473,x16474,x16475,x16476)) % 19.23/19.06 [1648]~E(x16481,x16482)+E(f405(x16483,x16481,x16484,x16485,x16486),f405(x16483,x16482,x16484,x16485,x16486)) % 19.23/19.06 [1649]~E(x16491,x16492)+E(f405(x16493,x16494,x16491,x16495,x16496),f405(x16493,x16494,x16492,x16495,x16496)) % 19.23/19.06 [1650]~E(x16501,x16502)+E(f405(x16503,x16504,x16505,x16501,x16506),f405(x16503,x16504,x16505,x16502,x16506)) % 19.23/19.06 [1651]~E(x16511,x16512)+E(f405(x16513,x16514,x16515,x16516,x16511),f405(x16513,x16514,x16515,x16516,x16512)) % 19.23/19.06 [1652]~E(x16521,x16522)+E(f816(x16521,x16523,x16524),f816(x16522,x16523,x16524)) % 19.23/19.06 [1653]~E(x16531,x16532)+E(f816(x16533,x16531,x16534),f816(x16533,x16532,x16534)) % 19.23/19.06 [1654]~E(x16541,x16542)+E(f816(x16543,x16544,x16541),f816(x16543,x16544,x16542)) % 19.23/19.06 [1655]~E(x16551,x16552)+E(f831(x16551,x16553,x16554),f831(x16552,x16553,x16554)) % 19.23/19.06 [1656]~E(x16561,x16562)+E(f831(x16563,x16561,x16564),f831(x16563,x16562,x16564)) % 19.23/19.06 [1657]~E(x16571,x16572)+E(f831(x16573,x16574,x16571),f831(x16573,x16574,x16572)) % 19.23/19.06 [1658]~E(x16581,x16582)+E(f524(x16581,x16583,x16584,x16585,x16586),f524(x16582,x16583,x16584,x16585,x16586)) % 19.23/19.06 [1659]~E(x16591,x16592)+E(f524(x16593,x16591,x16594,x16595,x16596),f524(x16593,x16592,x16594,x16595,x16596)) % 19.23/19.06 [1660]~E(x16601,x16602)+E(f524(x16603,x16604,x16601,x16605,x16606),f524(x16603,x16604,x16602,x16605,x16606)) % 19.23/19.06 [1661]~E(x16611,x16612)+E(f524(x16613,x16614,x16615,x16611,x16616),f524(x16613,x16614,x16615,x16612,x16616)) % 19.23/19.06 [1662]~E(x16621,x16622)+E(f524(x16623,x16624,x16625,x16626,x16621),f524(x16623,x16624,x16625,x16626,x16622)) % 19.23/19.06 [1663]~E(x16631,x16632)+E(f200(x16631,x16633,x16634,x16635),f200(x16632,x16633,x16634,x16635)) % 19.23/19.06 [1664]~E(x16641,x16642)+E(f200(x16643,x16641,x16644,x16645),f200(x16643,x16642,x16644,x16645)) % 19.23/19.06 [1665]~E(x16651,x16652)+E(f200(x16653,x16654,x16651,x16655),f200(x16653,x16654,x16652,x16655)) % 19.23/19.06 [1666]~E(x16661,x16662)+E(f200(x16663,x16664,x16665,x16661),f200(x16663,x16664,x16665,x16662)) % 19.23/19.06 [1667]~E(x16671,x16672)+E(f156(x16671,x16673),f156(x16672,x16673)) % 19.23/19.06 [1668]~E(x16681,x16682)+E(f156(x16683,x16681),f156(x16683,x16682)) % 19.23/19.06 [1669]~E(x16691,x16692)+E(f449(x16691,x16693,x16694,x16695,x16696),f449(x16692,x16693,x16694,x16695,x16696)) % 19.23/19.06 [1670]~E(x16701,x16702)+E(f449(x16703,x16701,x16704,x16705,x16706),f449(x16703,x16702,x16704,x16705,x16706)) % 19.23/19.06 [1671]~E(x16711,x16712)+E(f449(x16713,x16714,x16711,x16715,x16716),f449(x16713,x16714,x16712,x16715,x16716)) % 19.23/19.06 [1672]~E(x16721,x16722)+E(f449(x16723,x16724,x16725,x16721,x16726),f449(x16723,x16724,x16725,x16722,x16726)) % 19.23/19.06 [1673]~E(x16731,x16732)+E(f449(x16733,x16734,x16735,x16736,x16731),f449(x16733,x16734,x16735,x16736,x16732)) % 19.23/19.06 [1674]~E(x16741,x16742)+E(f559(x16741,x16743),f559(x16742,x16743)) % 19.23/19.06 [1675]~E(x16751,x16752)+E(f559(x16753,x16751),f559(x16753,x16752)) % 19.23/19.06 [1676]~E(x16761,x16762)+E(f401(x16761,x16763),f401(x16762,x16763)) % 19.23/19.06 [1677]~E(x16771,x16772)+E(f401(x16773,x16771),f401(x16773,x16772)) % 19.23/19.06 [1678]~E(x16781,x16782)+E(f208(x16781,x16783,x16784,x16785),f208(x16782,x16783,x16784,x16785)) % 19.23/19.06 [1679]~E(x16791,x16792)+E(f208(x16793,x16791,x16794,x16795),f208(x16793,x16792,x16794,x16795)) % 19.23/19.06 [1680]~E(x16801,x16802)+E(f208(x16803,x16804,x16801,x16805),f208(x16803,x16804,x16802,x16805)) % 19.23/19.06 [1681]~E(x16811,x16812)+E(f208(x16813,x16814,x16815,x16811),f208(x16813,x16814,x16815,x16812)) % 19.23/19.06 [1682]~E(x16821,x16822)+E(f592(x16821,x16823,x16824,x16825),f592(x16822,x16823,x16824,x16825)) % 19.23/19.06 [1683]~E(x16831,x16832)+E(f592(x16833,x16831,x16834,x16835),f592(x16833,x16832,x16834,x16835)) % 19.23/19.06 [1684]~E(x16841,x16842)+E(f592(x16843,x16844,x16841,x16845),f592(x16843,x16844,x16842,x16845)) % 19.23/19.06 [1685]~E(x16851,x16852)+E(f592(x16853,x16854,x16855,x16851),f592(x16853,x16854,x16855,x16852)) % 19.23/19.06 [1686]~E(x16861,x16862)+E(f482(x16861,x16863,x16864,x16865,x16866,x16867),f482(x16862,x16863,x16864,x16865,x16866,x16867)) % 19.23/19.06 [1687]~E(x16871,x16872)+E(f482(x16873,x16871,x16874,x16875,x16876,x16877),f482(x16873,x16872,x16874,x16875,x16876,x16877)) % 19.23/19.06 [1688]~E(x16881,x16882)+E(f482(x16883,x16884,x16881,x16885,x16886,x16887),f482(x16883,x16884,x16882,x16885,x16886,x16887)) % 19.23/19.06 [1689]~E(x16891,x16892)+E(f482(x16893,x16894,x16895,x16891,x16896,x16897),f482(x16893,x16894,x16895,x16892,x16896,x16897)) % 19.23/19.06 [1690]~E(x16901,x16902)+E(f482(x16903,x16904,x16905,x16906,x16901,x16907),f482(x16903,x16904,x16905,x16906,x16902,x16907)) % 19.23/19.06 [1691]~E(x16911,x16912)+E(f482(x16913,x16914,x16915,x16916,x16917,x16911),f482(x16913,x16914,x16915,x16916,x16917,x16912)) % 19.23/19.06 [1692]~E(x16921,x16922)+E(f469(x16921,x16923,x16924,x16925),f469(x16922,x16923,x16924,x16925)) % 19.23/19.06 [1693]~E(x16931,x16932)+E(f469(x16933,x16931,x16934,x16935),f469(x16933,x16932,x16934,x16935)) % 19.23/19.06 [1694]~E(x16941,x16942)+E(f469(x16943,x16944,x16941,x16945),f469(x16943,x16944,x16942,x16945)) % 19.23/19.06 [1695]~E(x16951,x16952)+E(f469(x16953,x16954,x16955,x16951),f469(x16953,x16954,x16955,x16952)) % 19.23/19.06 [1696]~E(x16961,x16962)+E(f621(x16961,x16963,x16964,x16965,x16966,x16967),f621(x16962,x16963,x16964,x16965,x16966,x16967)) % 19.23/19.06 [1697]~E(x16971,x16972)+E(f621(x16973,x16971,x16974,x16975,x16976,x16977),f621(x16973,x16972,x16974,x16975,x16976,x16977)) % 19.23/19.06 [1698]~E(x16981,x16982)+E(f621(x16983,x16984,x16981,x16985,x16986,x16987),f621(x16983,x16984,x16982,x16985,x16986,x16987)) % 19.23/19.06 [1699]~E(x16991,x16992)+E(f621(x16993,x16994,x16995,x16991,x16996,x16997),f621(x16993,x16994,x16995,x16992,x16996,x16997)) % 19.23/19.06 [1700]~E(x17001,x17002)+E(f621(x17003,x17004,x17005,x17006,x17001,x17007),f621(x17003,x17004,x17005,x17006,x17002,x17007)) % 19.23/19.06 [1701]~E(x17011,x17012)+E(f621(x17013,x17014,x17015,x17016,x17017,x17011),f621(x17013,x17014,x17015,x17016,x17017,x17012)) % 19.23/19.06 [1702]~E(x17021,x17022)+E(f632(x17021,x17023,x17024,x17025),f632(x17022,x17023,x17024,x17025)) % 19.23/19.06 [1703]~E(x17031,x17032)+E(f632(x17033,x17031,x17034,x17035),f632(x17033,x17032,x17034,x17035)) % 19.23/19.06 [1704]~E(x17041,x17042)+E(f632(x17043,x17044,x17041,x17045),f632(x17043,x17044,x17042,x17045)) % 19.23/19.06 [1705]~E(x17051,x17052)+E(f632(x17053,x17054,x17055,x17051),f632(x17053,x17054,x17055,x17052)) % 19.23/19.06 [1706]~E(x17061,x17062)+E(f682(x17061,x17063,x17064),f682(x17062,x17063,x17064)) % 19.23/19.06 [1707]~E(x17071,x17072)+E(f682(x17073,x17071,x17074),f682(x17073,x17072,x17074)) % 19.23/19.06 [1708]~E(x17081,x17082)+E(f682(x17083,x17084,x17081),f682(x17083,x17084,x17082)) % 19.23/19.06 [1709]~E(x17091,x17092)+E(f489(x17091,x17093,x17094,x17095),f489(x17092,x17093,x17094,x17095)) % 19.23/19.06 [1710]~E(x17101,x17102)+E(f489(x17103,x17101,x17104,x17105),f489(x17103,x17102,x17104,x17105)) % 19.23/19.06 [1711]~E(x17111,x17112)+E(f489(x17113,x17114,x17111,x17115),f489(x17113,x17114,x17112,x17115)) % 19.23/19.06 [1712]~E(x17121,x17122)+E(f489(x17123,x17124,x17125,x17121),f489(x17123,x17124,x17125,x17122)) % 19.23/19.06 [1713]~E(x17131,x17132)+E(f425(x17131,x17133,x17134,x17135,x17136),f425(x17132,x17133,x17134,x17135,x17136)) % 19.23/19.06 [1714]~E(x17141,x17142)+E(f425(x17143,x17141,x17144,x17145,x17146),f425(x17143,x17142,x17144,x17145,x17146)) % 19.23/19.06 [1715]~E(x17151,x17152)+E(f425(x17153,x17154,x17151,x17155,x17156),f425(x17153,x17154,x17152,x17155,x17156)) % 19.23/19.06 [1716]~E(x17161,x17162)+E(f425(x17163,x17164,x17165,x17161,x17166),f425(x17163,x17164,x17165,x17162,x17166)) % 19.23/19.06 [1717]~E(x17171,x17172)+E(f425(x17173,x17174,x17175,x17176,x17171),f425(x17173,x17174,x17175,x17176,x17172)) % 19.23/19.06 [1718]~E(x17181,x17182)+E(f566(x17181,x17183),f566(x17182,x17183)) % 19.23/19.06 [1719]~E(x17191,x17192)+E(f566(x17193,x17191),f566(x17193,x17192)) % 19.23/19.06 [1720]~E(x17201,x17202)+E(f827(x17201,x17203,x17204),f827(x17202,x17203,x17204)) % 19.23/19.06 [1721]~E(x17211,x17212)+E(f827(x17213,x17211,x17214),f827(x17213,x17212,x17214)) % 19.23/19.06 [1722]~E(x17221,x17222)+E(f827(x17223,x17224,x17221),f827(x17223,x17224,x17222)) % 19.23/19.06 [1723]~E(x17231,x17232)+E(f586(x17231,x17233),f586(x17232,x17233)) % 19.23/19.06 [1724]~E(x17241,x17242)+E(f586(x17243,x17241),f586(x17243,x17242)) % 19.23/19.06 [1725]~E(x17251,x17252)+E(f483(x17251,x17253),f483(x17252,x17253)) % 19.23/19.06 [1726]~E(x17261,x17262)+E(f483(x17263,x17261),f483(x17263,x17262)) % 19.23/19.06 [1727]~E(x17271,x17272)+E(f409(x17271,x17273,x17274,x17275),f409(x17272,x17273,x17274,x17275)) % 19.23/19.06 [1728]~E(x17281,x17282)+E(f409(x17283,x17281,x17284,x17285),f409(x17283,x17282,x17284,x17285)) % 19.23/19.06 [1729]~E(x17291,x17292)+E(f409(x17293,x17294,x17291,x17295),f409(x17293,x17294,x17292,x17295)) % 19.23/19.06 [1730]~E(x17301,x17302)+E(f409(x17303,x17304,x17305,x17301),f409(x17303,x17304,x17305,x17302)) % 19.23/19.06 [1731]~E(x17311,x17312)+E(f519(x17311,x17313,x17314,x17315,x17316),f519(x17312,x17313,x17314,x17315,x17316)) % 19.23/19.06 [1732]~E(x17321,x17322)+E(f519(x17323,x17321,x17324,x17325,x17326),f519(x17323,x17322,x17324,x17325,x17326)) % 19.23/19.06 [1733]~E(x17331,x17332)+E(f519(x17333,x17334,x17331,x17335,x17336),f519(x17333,x17334,x17332,x17335,x17336)) % 19.23/19.06 [1734]~E(x17341,x17342)+E(f519(x17343,x17344,x17345,x17341,x17346),f519(x17343,x17344,x17345,x17342,x17346)) % 19.23/19.06 [1735]~E(x17351,x17352)+E(f519(x17353,x17354,x17355,x17356,x17351),f519(x17353,x17354,x17355,x17356,x17352)) % 19.23/19.06 [1736]~E(x17361,x17362)+E(f434(x17361,x17363,x17364,x17365,x17366),f434(x17362,x17363,x17364,x17365,x17366)) % 19.23/19.06 [1737]~E(x17371,x17372)+E(f434(x17373,x17371,x17374,x17375,x17376),f434(x17373,x17372,x17374,x17375,x17376)) % 19.23/19.06 [1738]~E(x17381,x17382)+E(f434(x17383,x17384,x17381,x17385,x17386),f434(x17383,x17384,x17382,x17385,x17386)) % 19.23/19.06 [1739]~E(x17391,x17392)+E(f434(x17393,x17394,x17395,x17391,x17396),f434(x17393,x17394,x17395,x17392,x17396)) % 19.23/19.06 [1740]~E(x17401,x17402)+E(f434(x17403,x17404,x17405,x17406,x17401),f434(x17403,x17404,x17405,x17406,x17402)) % 19.23/19.06 [1741]~E(x17411,x17412)+E(f56(x17411),f56(x17412)) % 19.23/19.06 [1742]~E(x17421,x17422)+E(f496(x17421,x17423,x17424),f496(x17422,x17423,x17424)) % 19.23/19.06 [1743]~E(x17431,x17432)+E(f496(x17433,x17431,x17434),f496(x17433,x17432,x17434)) % 19.23/19.06 [1744]~E(x17441,x17442)+E(f496(x17443,x17444,x17441),f496(x17443,x17444,x17442)) % 19.23/19.06 [1745]~E(x17451,x17452)+E(f725(x17451,x17453,x17454,x17455,x17456),f725(x17452,x17453,x17454,x17455,x17456)) % 19.23/19.06 [1746]~E(x17461,x17462)+E(f725(x17463,x17461,x17464,x17465,x17466),f725(x17463,x17462,x17464,x17465,x17466)) % 19.23/19.06 [1747]~E(x17471,x17472)+E(f725(x17473,x17474,x17471,x17475,x17476),f725(x17473,x17474,x17472,x17475,x17476)) % 19.23/19.06 [1748]~E(x17481,x17482)+E(f725(x17483,x17484,x17485,x17481,x17486),f725(x17483,x17484,x17485,x17482,x17486)) % 19.23/19.06 [1749]~E(x17491,x17492)+E(f725(x17493,x17494,x17495,x17496,x17491),f725(x17493,x17494,x17495,x17496,x17492)) % 19.23/19.06 [1750]~E(x17501,x17502)+E(f799(x17501),f799(x17502)) % 19.23/19.06 [1751]~E(x17511,x17512)+E(f232(x17511,x17513,x17514),f232(x17512,x17513,x17514)) % 19.23/19.06 [1752]~E(x17521,x17522)+E(f232(x17523,x17521,x17524),f232(x17523,x17522,x17524)) % 19.23/19.06 [1753]~E(x17531,x17532)+E(f232(x17533,x17534,x17531),f232(x17533,x17534,x17532)) % 19.23/19.06 [1754]~E(x17541,x17542)+E(f397(x17541,x17543),f397(x17542,x17543)) % 19.23/19.06 [1755]~E(x17551,x17552)+E(f397(x17553,x17551),f397(x17553,x17552)) % 19.23/19.06 [1756]~E(x17561,x17562)+E(f840(x17561,x17563,x17564),f840(x17562,x17563,x17564)) % 19.23/19.06 [1757]~E(x17571,x17572)+E(f840(x17573,x17571,x17574),f840(x17573,x17572,x17574)) % 19.23/19.06 [1758]~E(x17581,x17582)+E(f840(x17583,x17584,x17581),f840(x17583,x17584,x17582)) % 19.23/19.06 [1759]~E(x17591,x17592)+E(f585(x17591,x17593,x17594,x17595,x17596,x17597),f585(x17592,x17593,x17594,x17595,x17596,x17597)) % 19.23/19.06 [1760]~E(x17601,x17602)+E(f585(x17603,x17601,x17604,x17605,x17606,x17607),f585(x17603,x17602,x17604,x17605,x17606,x17607)) % 19.23/19.06 [1761]~E(x17611,x17612)+E(f585(x17613,x17614,x17611,x17615,x17616,x17617),f585(x17613,x17614,x17612,x17615,x17616,x17617)) % 19.23/19.06 [1762]~E(x17621,x17622)+E(f585(x17623,x17624,x17625,x17621,x17626,x17627),f585(x17623,x17624,x17625,x17622,x17626,x17627)) % 19.23/19.06 [1763]~E(x17631,x17632)+E(f585(x17633,x17634,x17635,x17636,x17631,x17637),f585(x17633,x17634,x17635,x17636,x17632,x17637)) % 19.23/19.06 [1764]~E(x17641,x17642)+E(f585(x17643,x17644,x17645,x17646,x17647,x17641),f585(x17643,x17644,x17645,x17646,x17647,x17642)) % 19.23/19.06 [1765]~E(x17651,x17652)+E(f748(x17651,x17653,x17654,x17655),f748(x17652,x17653,x17654,x17655)) % 19.23/19.06 [1766]~E(x17661,x17662)+E(f748(x17663,x17661,x17664,x17665),f748(x17663,x17662,x17664,x17665)) % 19.23/19.06 [1767]~E(x17671,x17672)+E(f748(x17673,x17674,x17671,x17675),f748(x17673,x17674,x17672,x17675)) % 19.23/19.06 [1768]~E(x17681,x17682)+E(f748(x17683,x17684,x17685,x17681),f748(x17683,x17684,x17685,x17682)) % 19.23/19.06 [1769]~E(x17691,x17692)+E(f645(x17691),f645(x17692)) % 19.23/19.06 [1770]~E(x17701,x17702)+E(f741(x17701,x17703,x17704),f741(x17702,x17703,x17704)) % 19.23/19.06 [1771]~E(x17711,x17712)+E(f741(x17713,x17711,x17714),f741(x17713,x17712,x17714)) % 19.23/19.06 [1772]~E(x17721,x17722)+E(f741(x17723,x17724,x17721),f741(x17723,x17724,x17722)) % 19.23/19.06 [1773]~E(x17731,x17732)+E(f394(x17731,x17733),f394(x17732,x17733)) % 19.23/19.06 [1774]~E(x17741,x17742)+E(f394(x17743,x17741),f394(x17743,x17742)) % 19.23/19.06 [1775]~E(x17751,x17752)+E(f767(x17751,x17753,x17754),f767(x17752,x17753,x17754)) % 19.23/19.06 [1776]~E(x17761,x17762)+E(f767(x17763,x17761,x17764),f767(x17763,x17762,x17764)) % 19.23/19.06 [1777]~E(x17771,x17772)+E(f767(x17773,x17774,x17771),f767(x17773,x17774,x17772)) % 19.23/19.06 [1778]~E(x17781,x17782)+E(f583(x17781,x17783,x17784,x17785),f583(x17782,x17783,x17784,x17785)) % 19.23/19.06 [1779]~E(x17791,x17792)+E(f583(x17793,x17791,x17794,x17795),f583(x17793,x17792,x17794,x17795)) % 19.23/19.06 [1780]~E(x17801,x17802)+E(f583(x17803,x17804,x17801,x17805),f583(x17803,x17804,x17802,x17805)) % 19.23/19.06 [1781]~E(x17811,x17812)+E(f583(x17813,x17814,x17815,x17811),f583(x17813,x17814,x17815,x17812)) % 19.23/19.06 [1782]~E(x17821,x17822)+E(f456(x17821,x17823,x17824),f456(x17822,x17823,x17824)) % 19.23/19.06 [1783]~E(x17831,x17832)+E(f456(x17833,x17831,x17834),f456(x17833,x17832,x17834)) % 19.23/19.06 [1784]~E(x17841,x17842)+E(f456(x17843,x17844,x17841),f456(x17843,x17844,x17842)) % 19.23/19.06 [1785]~E(x17851,x17852)+E(f426(x17851,x17853,x17854,x17855,x17856,x17857,x17858),f426(x17852,x17853,x17854,x17855,x17856,x17857,x17858)) % 19.23/19.06 [1786]~E(x17861,x17862)+E(f426(x17863,x17861,x17864,x17865,x17866,x17867,x17868),f426(x17863,x17862,x17864,x17865,x17866,x17867,x17868)) % 19.23/19.06 [1787]~E(x17871,x17872)+E(f426(x17873,x17874,x17871,x17875,x17876,x17877,x17878),f426(x17873,x17874,x17872,x17875,x17876,x17877,x17878)) % 19.23/19.06 [1788]~E(x17881,x17882)+E(f426(x17883,x17884,x17885,x17881,x17886,x17887,x17888),f426(x17883,x17884,x17885,x17882,x17886,x17887,x17888)) % 19.23/19.06 [1789]~E(x17891,x17892)+E(f426(x17893,x17894,x17895,x17896,x17891,x17897,x17898),f426(x17893,x17894,x17895,x17896,x17892,x17897,x17898)) % 19.23/19.06 [1790]~E(x17901,x17902)+E(f426(x17903,x17904,x17905,x17906,x17907,x17901,x17908),f426(x17903,x17904,x17905,x17906,x17907,x17902,x17908)) % 19.23/19.06 [1791]~E(x17911,x17912)+E(f426(x17913,x17914,x17915,x17916,x17917,x17918,x17911),f426(x17913,x17914,x17915,x17916,x17917,x17918,x17912)) % 19.23/19.06 [1792]~E(x17921,x17922)+E(f21(x17921,x17923,x17924,x17925),f21(x17922,x17923,x17924,x17925)) % 19.23/19.06 [1793]~E(x17931,x17932)+E(f21(x17933,x17931,x17934,x17935),f21(x17933,x17932,x17934,x17935)) % 19.23/19.06 [1794]~E(x17941,x17942)+E(f21(x17943,x17944,x17941,x17945),f21(x17943,x17944,x17942,x17945)) % 19.23/19.06 [1795]~E(x17951,x17952)+E(f21(x17953,x17954,x17955,x17951),f21(x17953,x17954,x17955,x17952)) % 19.23/19.06 [1796]~E(x17961,x17962)+E(f126(x17961,x17963,x17964,x17965),f126(x17962,x17963,x17964,x17965)) % 19.23/19.06 [1797]~E(x17971,x17972)+E(f126(x17973,x17971,x17974,x17975),f126(x17973,x17972,x17974,x17975)) % 19.23/19.06 [1798]~E(x17981,x17982)+E(f126(x17983,x17984,x17981,x17985),f126(x17983,x17984,x17982,x17985)) % 19.23/19.06 [1799]~E(x17991,x17992)+E(f126(x17993,x17994,x17995,x17991),f126(x17993,x17994,x17995,x17992)) % 19.23/19.06 [1800]~E(x18001,x18002)+E(f206(x18001,x18003),f206(x18002,x18003)) % 19.23/19.06 [1801]~E(x18011,x18012)+E(f206(x18013,x18011),f206(x18013,x18012)) % 19.23/19.06 [1802]~E(x18021,x18022)+E(f354(x18021,x18023),f354(x18022,x18023)) % 19.23/19.06 [1803]~E(x18031,x18032)+E(f354(x18033,x18031),f354(x18033,x18032)) % 19.23/19.06 [1804]~E(x18041,x18042)+E(f557(x18041,x18043,x18044,x18045),f557(x18042,x18043,x18044,x18045)) % 19.23/19.06 [1805]~E(x18051,x18052)+E(f557(x18053,x18051,x18054,x18055),f557(x18053,x18052,x18054,x18055)) % 19.23/19.06 [1806]~E(x18061,x18062)+E(f557(x18063,x18064,x18061,x18065),f557(x18063,x18064,x18062,x18065)) % 19.23/19.06 [1807]~E(x18071,x18072)+E(f557(x18073,x18074,x18075,x18071),f557(x18073,x18074,x18075,x18072)) % 19.23/19.06 [1808]~E(x18081,x18082)+E(f535(x18081,x18083,x18084,x18085,x18086,x18087),f535(x18082,x18083,x18084,x18085,x18086,x18087)) % 19.23/19.06 [1809]~E(x18091,x18092)+E(f535(x18093,x18091,x18094,x18095,x18096,x18097),f535(x18093,x18092,x18094,x18095,x18096,x18097)) % 19.23/19.06 [1810]~E(x18101,x18102)+E(f535(x18103,x18104,x18101,x18105,x18106,x18107),f535(x18103,x18104,x18102,x18105,x18106,x18107)) % 19.23/19.06 [1811]~E(x18111,x18112)+E(f535(x18113,x18114,x18115,x18111,x18116,x18117),f535(x18113,x18114,x18115,x18112,x18116,x18117)) % 19.23/19.06 [1812]~E(x18121,x18122)+E(f535(x18123,x18124,x18125,x18126,x18121,x18127),f535(x18123,x18124,x18125,x18126,x18122,x18127)) % 19.23/19.06 [1813]~E(x18131,x18132)+E(f535(x18133,x18134,x18135,x18136,x18137,x18131),f535(x18133,x18134,x18135,x18136,x18137,x18132)) % 19.23/19.06 [1814]~E(x18141,x18142)+E(f142(x18141,x18143),f142(x18142,x18143)) % 19.23/19.06 [1815]~E(x18151,x18152)+E(f142(x18153,x18151),f142(x18153,x18152)) % 19.23/19.06 [1816]~E(x18161,x18162)+E(f569(x18161,x18163,x18164),f569(x18162,x18163,x18164)) % 19.23/19.06 [1817]~E(x18171,x18172)+E(f569(x18173,x18171,x18174),f569(x18173,x18172,x18174)) % 19.23/19.06 [1818]~E(x18181,x18182)+E(f569(x18183,x18184,x18181),f569(x18183,x18184,x18182)) % 19.23/19.06 [1819]~E(x18191,x18192)+E(f360(x18191,x18193,x18194,x18195,x18196,x18197,x18198),f360(x18192,x18193,x18194,x18195,x18196,x18197,x18198)) % 19.23/19.06 [1820]~E(x18201,x18202)+E(f360(x18203,x18201,x18204,x18205,x18206,x18207,x18208),f360(x18203,x18202,x18204,x18205,x18206,x18207,x18208)) % 19.23/19.06 [1821]~E(x18211,x18212)+E(f360(x18213,x18214,x18211,x18215,x18216,x18217,x18218),f360(x18213,x18214,x18212,x18215,x18216,x18217,x18218)) % 19.23/19.06 [1822]~E(x18221,x18222)+E(f360(x18223,x18224,x18225,x18221,x18226,x18227,x18228),f360(x18223,x18224,x18225,x18222,x18226,x18227,x18228)) % 19.23/19.06 [1823]~E(x18231,x18232)+E(f360(x18233,x18234,x18235,x18236,x18231,x18237,x18238),f360(x18233,x18234,x18235,x18236,x18232,x18237,x18238)) % 19.23/19.06 [1824]~E(x18241,x18242)+E(f360(x18243,x18244,x18245,x18246,x18247,x18241,x18248),f360(x18243,x18244,x18245,x18246,x18247,x18242,x18248)) % 19.23/19.06 [1825]~E(x18251,x18252)+E(f360(x18253,x18254,x18255,x18256,x18257,x18258,x18251),f360(x18253,x18254,x18255,x18256,x18257,x18258,x18252)) % 19.23/19.06 [1826]~E(x18261,x18262)+E(f766(x18261,x18263,x18264),f766(x18262,x18263,x18264)) % 19.23/19.06 [1827]~E(x18271,x18272)+E(f766(x18273,x18271,x18274),f766(x18273,x18272,x18274)) % 19.23/19.06 [1828]~E(x18281,x18282)+E(f766(x18283,x18284,x18281),f766(x18283,x18284,x18282)) % 19.23/19.06 [1829]~E(x18291,x18292)+E(f698(x18291,x18293,x18294,x18295,x18296,x18297,x18298),f698(x18292,x18293,x18294,x18295,x18296,x18297,x18298)) % 19.23/19.06 [1830]~E(x18301,x18302)+E(f698(x18303,x18301,x18304,x18305,x18306,x18307,x18308),f698(x18303,x18302,x18304,x18305,x18306,x18307,x18308)) % 19.23/19.06 [1831]~E(x18311,x18312)+E(f698(x18313,x18314,x18311,x18315,x18316,x18317,x18318),f698(x18313,x18314,x18312,x18315,x18316,x18317,x18318)) % 19.23/19.06 [1832]~E(x18321,x18322)+E(f698(x18323,x18324,x18325,x18321,x18326,x18327,x18328),f698(x18323,x18324,x18325,x18322,x18326,x18327,x18328)) % 19.23/19.06 [1833]~E(x18331,x18332)+E(f698(x18333,x18334,x18335,x18336,x18331,x18337,x18338),f698(x18333,x18334,x18335,x18336,x18332,x18337,x18338)) % 19.23/19.06 [1834]~E(x18341,x18342)+E(f698(x18343,x18344,x18345,x18346,x18347,x18341,x18348),f698(x18343,x18344,x18345,x18346,x18347,x18342,x18348)) % 19.23/19.06 [1835]~E(x18351,x18352)+E(f698(x18353,x18354,x18355,x18356,x18357,x18358,x18351),f698(x18353,x18354,x18355,x18356,x18357,x18358,x18352)) % 19.23/19.06 [1836]~E(x18361,x18362)+E(f326(x18361,x18363,x18364,x18365),f326(x18362,x18363,x18364,x18365)) % 19.23/19.06 [1837]~E(x18371,x18372)+E(f326(x18373,x18371,x18374,x18375),f326(x18373,x18372,x18374,x18375)) % 19.23/19.06 [1838]~E(x18381,x18382)+E(f326(x18383,x18384,x18381,x18385),f326(x18383,x18384,x18382,x18385)) % 19.23/19.06 [1839]~E(x18391,x18392)+E(f326(x18393,x18394,x18395,x18391),f326(x18393,x18394,x18395,x18392)) % 19.23/19.06 [1840]~E(x18401,x18402)+E(f45(x18401,x18403,x18404,x18405),f45(x18402,x18403,x18404,x18405)) % 19.23/19.06 [1841]~E(x18411,x18412)+E(f45(x18413,x18411,x18414,x18415),f45(x18413,x18412,x18414,x18415)) % 19.23/19.06 [1842]~E(x18421,x18422)+E(f45(x18423,x18424,x18421,x18425),f45(x18423,x18424,x18422,x18425)) % 19.23/19.06 [1843]~E(x18431,x18432)+E(f45(x18433,x18434,x18435,x18431),f45(x18433,x18434,x18435,x18432)) % 19.23/19.06 [1844]~E(x18441,x18442)+E(f673(x18441,x18443,x18444,x18445,x18446,x18447,x18448),f673(x18442,x18443,x18444,x18445,x18446,x18447,x18448)) % 19.23/19.06 [1845]~E(x18451,x18452)+E(f673(x18453,x18451,x18454,x18455,x18456,x18457,x18458),f673(x18453,x18452,x18454,x18455,x18456,x18457,x18458)) % 19.23/19.06 [1846]~E(x18461,x18462)+E(f673(x18463,x18464,x18461,x18465,x18466,x18467,x18468),f673(x18463,x18464,x18462,x18465,x18466,x18467,x18468)) % 19.23/19.06 [1847]~E(x18471,x18472)+E(f673(x18473,x18474,x18475,x18471,x18476,x18477,x18478),f673(x18473,x18474,x18475,x18472,x18476,x18477,x18478)) % 19.23/19.06 [1848]~E(x18481,x18482)+E(f673(x18483,x18484,x18485,x18486,x18481,x18487,x18488),f673(x18483,x18484,x18485,x18486,x18482,x18487,x18488)) % 19.23/19.06 [1849]~E(x18491,x18492)+E(f673(x18493,x18494,x18495,x18496,x18497,x18491,x18498),f673(x18493,x18494,x18495,x18496,x18497,x18492,x18498)) % 19.23/19.06 [1850]~E(x18501,x18502)+E(f673(x18503,x18504,x18505,x18506,x18507,x18508,x18501),f673(x18503,x18504,x18505,x18506,x18507,x18508,x18502)) % 19.23/19.06 [1851]~E(x18511,x18512)+E(f752(x18511,x18513,x18514,x18515),f752(x18512,x18513,x18514,x18515)) % 19.23/19.06 [1852]~E(x18521,x18522)+E(f752(x18523,x18521,x18524,x18525),f752(x18523,x18522,x18524,x18525)) % 19.23/19.06 [1853]~E(x18531,x18532)+E(f752(x18533,x18534,x18531,x18535),f752(x18533,x18534,x18532,x18535)) % 19.23/19.06 [1854]~E(x18541,x18542)+E(f752(x18543,x18544,x18545,x18541),f752(x18543,x18544,x18545,x18542)) % 19.23/19.06 [1855]~E(x18551,x18552)+E(f361(x18551,x18553,x18554,x18555),f361(x18552,x18553,x18554,x18555)) % 19.23/19.06 [1856]~E(x18561,x18562)+E(f361(x18563,x18561,x18564,x18565),f361(x18563,x18562,x18564,x18565)) % 19.23/19.06 [1857]~E(x18571,x18572)+E(f361(x18573,x18574,x18571,x18575),f361(x18573,x18574,x18572,x18575)) % 19.23/19.06 [1858]~E(x18581,x18582)+E(f361(x18583,x18584,x18585,x18581),f361(x18583,x18584,x18585,x18582)) % 19.23/19.06 [1859]~E(x18591,x18592)+E(f380(x18591,x18593,x18594),f380(x18592,x18593,x18594)) % 19.23/19.06 [1860]~E(x18601,x18602)+E(f380(x18603,x18601,x18604),f380(x18603,x18602,x18604)) % 19.23/19.06 [1861]~E(x18611,x18612)+E(f380(x18613,x18614,x18611),f380(x18613,x18614,x18612)) % 19.23/19.06 [1862]~E(x18621,x18622)+E(f515(x18621,x18623,x18624,x18625),f515(x18622,x18623,x18624,x18625)) % 19.23/19.06 [1863]~E(x18631,x18632)+E(f515(x18633,x18631,x18634,x18635),f515(x18633,x18632,x18634,x18635)) % 19.23/19.06 [1864]~E(x18641,x18642)+E(f515(x18643,x18644,x18641,x18645),f515(x18643,x18644,x18642,x18645)) % 19.23/19.06 [1865]~E(x18651,x18652)+E(f515(x18653,x18654,x18655,x18651),f515(x18653,x18654,x18655,x18652)) % 19.23/19.06 [1866]~E(x18661,x18662)+E(f591(x18661,x18663,x18664,x18665),f591(x18662,x18663,x18664,x18665)) % 19.23/19.06 [1867]~E(x18671,x18672)+E(f591(x18673,x18671,x18674,x18675),f591(x18673,x18672,x18674,x18675)) % 19.23/19.06 [1868]~E(x18681,x18682)+E(f591(x18683,x18684,x18681,x18685),f591(x18683,x18684,x18682,x18685)) % 19.23/19.06 [1869]~E(x18691,x18692)+E(f591(x18693,x18694,x18695,x18691),f591(x18693,x18694,x18695,x18692)) % 19.23/19.06 [1870]~E(x18701,x18702)+E(f439(x18701,x18703,x18704),f439(x18702,x18703,x18704)) % 19.23/19.06 [1871]~E(x18711,x18712)+E(f439(x18713,x18711,x18714),f439(x18713,x18712,x18714)) % 19.23/19.06 [1872]~E(x18721,x18722)+E(f439(x18723,x18724,x18721),f439(x18723,x18724,x18722)) % 19.23/19.06 [1873]~E(x18731,x18732)+E(f211(x18731),f211(x18732)) % 19.23/19.06 [1874]~E(x18741,x18742)+E(f207(x18741),f207(x18742)) % 19.23/19.06 [1875]~E(x18751,x18752)+E(f329(x18751,x18753,x18754,x18755,x18756,x18757),f329(x18752,x18753,x18754,x18755,x18756,x18757)) % 19.23/19.06 [1876]~E(x18761,x18762)+E(f329(x18763,x18761,x18764,x18765,x18766,x18767),f329(x18763,x18762,x18764,x18765,x18766,x18767)) % 19.23/19.06 [1877]~E(x18771,x18772)+E(f329(x18773,x18774,x18771,x18775,x18776,x18777),f329(x18773,x18774,x18772,x18775,x18776,x18777)) % 19.23/19.06 [1878]~E(x18781,x18782)+E(f329(x18783,x18784,x18785,x18781,x18786,x18787),f329(x18783,x18784,x18785,x18782,x18786,x18787)) % 19.23/19.06 [1879]~E(x18791,x18792)+E(f329(x18793,x18794,x18795,x18796,x18791,x18797),f329(x18793,x18794,x18795,x18796,x18792,x18797)) % 19.23/19.06 [1880]~E(x18801,x18802)+E(f329(x18803,x18804,x18805,x18806,x18807,x18801),f329(x18803,x18804,x18805,x18806,x18807,x18802)) % 19.23/19.06 [1881]~E(x18811,x18812)+E(f421(x18811,x18813,x18814,x18815,x18816),f421(x18812,x18813,x18814,x18815,x18816)) % 19.23/19.06 [1882]~E(x18821,x18822)+E(f421(x18823,x18821,x18824,x18825,x18826),f421(x18823,x18822,x18824,x18825,x18826)) % 19.23/19.06 [1883]~E(x18831,x18832)+E(f421(x18833,x18834,x18831,x18835,x18836),f421(x18833,x18834,x18832,x18835,x18836)) % 19.23/19.06 [1884]~E(x18841,x18842)+E(f421(x18843,x18844,x18845,x18841,x18846),f421(x18843,x18844,x18845,x18842,x18846)) % 19.23/19.06 [1885]~E(x18851,x18852)+E(f421(x18853,x18854,x18855,x18856,x18851),f421(x18853,x18854,x18855,x18856,x18852)) % 19.23/19.06 [1886]~E(x18861,x18862)+E(f821(x18861,x18863,x18864),f821(x18862,x18863,x18864)) % 19.23/19.06 [1887]~E(x18871,x18872)+E(f821(x18873,x18871,x18874),f821(x18873,x18872,x18874)) % 19.23/19.06 [1888]~E(x18881,x18882)+E(f821(x18883,x18884,x18881),f821(x18883,x18884,x18882)) % 19.23/19.06 [1889]~E(x18891,x18892)+E(f521(x18891,x18893,x18894,x18895,x18896,x18897),f521(x18892,x18893,x18894,x18895,x18896,x18897)) % 19.23/19.06 [1890]~E(x18901,x18902)+E(f521(x18903,x18901,x18904,x18905,x18906,x18907),f521(x18903,x18902,x18904,x18905,x18906,x18907)) % 19.23/19.06 [1891]~E(x18911,x18912)+E(f521(x18913,x18914,x18911,x18915,x18916,x18917),f521(x18913,x18914,x18912,x18915,x18916,x18917)) % 19.23/19.06 [1892]~E(x18921,x18922)+E(f521(x18923,x18924,x18925,x18921,x18926,x18927),f521(x18923,x18924,x18925,x18922,x18926,x18927)) % 19.23/19.06 [1893]~E(x18931,x18932)+E(f521(x18933,x18934,x18935,x18936,x18931,x18937),f521(x18933,x18934,x18935,x18936,x18932,x18937)) % 19.23/19.06 [1894]~E(x18941,x18942)+E(f521(x18943,x18944,x18945,x18946,x18947,x18941),f521(x18943,x18944,x18945,x18946,x18947,x18942)) % 19.23/19.06 [1895]~E(x18951,x18952)+E(f793(x18951,x18953,x18954,x18955),f793(x18952,x18953,x18954,x18955)) % 19.23/19.06 [1896]~E(x18961,x18962)+E(f793(x18963,x18961,x18964,x18965),f793(x18963,x18962,x18964,x18965)) % 19.23/19.06 [1897]~E(x18971,x18972)+E(f793(x18973,x18974,x18971,x18975),f793(x18973,x18974,x18972,x18975)) % 19.23/19.06 [1898]~E(x18981,x18982)+E(f793(x18983,x18984,x18985,x18981),f793(x18983,x18984,x18985,x18982)) % 19.23/19.06 [1899]~E(x18991,x18992)+E(f700(x18991,x18993,x18994,x18995),f700(x18992,x18993,x18994,x18995)) % 19.23/19.06 [1900]~E(x19001,x19002)+E(f700(x19003,x19001,x19004,x19005),f700(x19003,x19002,x19004,x19005)) % 19.23/19.06 [1901]~E(x19011,x19012)+E(f700(x19013,x19014,x19011,x19015),f700(x19013,x19014,x19012,x19015)) % 19.23/19.06 [1902]~E(x19021,x19022)+E(f700(x19023,x19024,x19025,x19021),f700(x19023,x19024,x19025,x19022)) % 19.23/19.06 [1903]~E(x19031,x19032)+E(f705(x19031,x19033,x19034),f705(x19032,x19033,x19034)) % 19.23/19.06 [1904]~E(x19041,x19042)+E(f705(x19043,x19041,x19044),f705(x19043,x19042,x19044)) % 19.23/19.06 [1905]~E(x19051,x19052)+E(f705(x19053,x19054,x19051),f705(x19053,x19054,x19052)) % 19.23/19.06 [1906]~E(x19061,x19062)+E(f488(x19061,x19063,x19064,x19065),f488(x19062,x19063,x19064,x19065)) % 19.23/19.06 [1907]~E(x19071,x19072)+E(f488(x19073,x19071,x19074,x19075),f488(x19073,x19072,x19074,x19075)) % 19.23/19.06 [1908]~E(x19081,x19082)+E(f488(x19083,x19084,x19081,x19085),f488(x19083,x19084,x19082,x19085)) % 19.23/19.06 [1909]~E(x19091,x19092)+E(f488(x19093,x19094,x19095,x19091),f488(x19093,x19094,x19095,x19092)) % 19.23/19.06 [1910]~E(x19101,x19102)+E(f379(x19101),f379(x19102)) % 19.23/19.06 [1911]~E(x19111,x19112)+E(f689(x19111,x19113,x19114,x19115,x19116,x19117,x19118,x19119),f689(x19112,x19113,x19114,x19115,x19116,x19117,x19118,x19119)) % 19.23/19.06 [1912]~E(x19121,x19122)+E(f689(x19123,x19121,x19124,x19125,x19126,x19127,x19128,x19129),f689(x19123,x19122,x19124,x19125,x19126,x19127,x19128,x19129)) % 19.23/19.06 [1913]~E(x19131,x19132)+E(f689(x19133,x19134,x19131,x19135,x19136,x19137,x19138,x19139),f689(x19133,x19134,x19132,x19135,x19136,x19137,x19138,x19139)) % 19.23/19.06 [1914]~E(x19141,x19142)+E(f689(x19143,x19144,x19145,x19141,x19146,x19147,x19148,x19149),f689(x19143,x19144,x19145,x19142,x19146,x19147,x19148,x19149)) % 19.23/19.06 [1915]~E(x19151,x19152)+E(f689(x19153,x19154,x19155,x19156,x19151,x19157,x19158,x19159),f689(x19153,x19154,x19155,x19156,x19152,x19157,x19158,x19159)) % 19.23/19.06 [1916]~E(x19161,x19162)+E(f689(x19163,x19164,x19165,x19166,x19167,x19161,x19168,x19169),f689(x19163,x19164,x19165,x19166,x19167,x19162,x19168,x19169)) % 19.23/19.06 [1917]~E(x19171,x19172)+E(f689(x19173,x19174,x19175,x19176,x19177,x19178,x19171,x19179),f689(x19173,x19174,x19175,x19176,x19177,x19178,x19172,x19179)) % 19.23/19.06 [1918]~E(x19181,x19182)+E(f689(x19183,x19184,x19185,x19186,x19187,x19188,x19189,x19181),f689(x19183,x19184,x19185,x19186,x19187,x19188,x19189,x19182)) % 19.23/19.06 [1919]~E(x19191,x19192)+E(f273(x19191),f273(x19192)) % 19.23/19.06 [1920]~E(x19201,x19202)+E(f637(x19201,x19203,x19204,x19205,x19206,x19207),f637(x19202,x19203,x19204,x19205,x19206,x19207)) % 19.23/19.06 [1921]~E(x19211,x19212)+E(f637(x19213,x19211,x19214,x19215,x19216,x19217),f637(x19213,x19212,x19214,x19215,x19216,x19217)) % 19.23/19.06 [1922]~E(x19221,x19222)+E(f637(x19223,x19224,x19221,x19225,x19226,x19227),f637(x19223,x19224,x19222,x19225,x19226,x19227)) % 19.23/19.06 [1923]~E(x19231,x19232)+E(f637(x19233,x19234,x19235,x19231,x19236,x19237),f637(x19233,x19234,x19235,x19232,x19236,x19237)) % 19.23/19.06 [1924]~E(x19241,x19242)+E(f637(x19243,x19244,x19245,x19246,x19241,x19247),f637(x19243,x19244,x19245,x19246,x19242,x19247)) % 19.23/19.06 [1925]~E(x19251,x19252)+E(f637(x19253,x19254,x19255,x19256,x19257,x19251),f637(x19253,x19254,x19255,x19256,x19257,x19252)) % 19.23/19.06 [1926]~E(x19261,x19262)+E(f782(x19261,x19263,x19264),f782(x19262,x19263,x19264)) % 19.23/19.06 [1927]~E(x19271,x19272)+E(f782(x19273,x19271,x19274),f782(x19273,x19272,x19274)) % 19.23/19.06 [1928]~E(x19281,x19282)+E(f782(x19283,x19284,x19281),f782(x19283,x19284,x19282)) % 19.23/19.06 [1929]~E(x19291,x19292)+E(f742(x19291,x19293,x19294,x19295),f742(x19292,x19293,x19294,x19295)) % 19.23/19.06 [1930]~E(x19301,x19302)+E(f742(x19303,x19301,x19304,x19305),f742(x19303,x19302,x19304,x19305)) % 19.23/19.06 [1931]~E(x19311,x19312)+E(f742(x19313,x19314,x19311,x19315),f742(x19313,x19314,x19312,x19315)) % 19.23/19.06 [1932]~E(x19321,x19322)+E(f742(x19323,x19324,x19325,x19321),f742(x19323,x19324,x19325,x19322)) % 19.23/19.06 [1933]~E(x19331,x19332)+E(f277(x19331,x19333,x19334,x19335),f277(x19332,x19333,x19334,x19335)) % 19.23/19.06 [1934]~E(x19341,x19342)+E(f277(x19343,x19341,x19344,x19345),f277(x19343,x19342,x19344,x19345)) % 19.23/19.06 [1935]~E(x19351,x19352)+E(f277(x19353,x19354,x19351,x19355),f277(x19353,x19354,x19352,x19355)) % 19.23/19.06 [1936]~E(x19361,x19362)+E(f277(x19363,x19364,x19365,x19361),f277(x19363,x19364,x19365,x19362)) % 19.23/19.06 [1937]~E(x19371,x19372)+E(f498(x19371,x19373),f498(x19372,x19373)) % 19.23/19.06 [1938]~E(x19381,x19382)+E(f498(x19383,x19381),f498(x19383,x19382)) % 19.23/19.06 [1939]~E(x19391,x19392)+E(f418(x19391,x19393,x19394,x19395,x19396),f418(x19392,x19393,x19394,x19395,x19396)) % 19.23/19.06 [1940]~E(x19401,x19402)+E(f418(x19403,x19401,x19404,x19405,x19406),f418(x19403,x19402,x19404,x19405,x19406)) % 19.23/19.06 [1941]~E(x19411,x19412)+E(f418(x19413,x19414,x19411,x19415,x19416),f418(x19413,x19414,x19412,x19415,x19416)) % 19.23/19.06 [1942]~E(x19421,x19422)+E(f418(x19423,x19424,x19425,x19421,x19426),f418(x19423,x19424,x19425,x19422,x19426)) % 19.23/19.06 [1943]~E(x19431,x19432)+E(f418(x19433,x19434,x19435,x19436,x19431),f418(x19433,x19434,x19435,x19436,x19432)) % 19.23/19.06 [1944]~E(x19441,x19442)+E(f318(x19441,x19443,x19444),f318(x19442,x19443,x19444)) % 19.23/19.06 [1945]~E(x19451,x19452)+E(f318(x19453,x19451,x19454),f318(x19453,x19452,x19454)) % 19.23/19.06 [1946]~E(x19461,x19462)+E(f318(x19463,x19464,x19461),f318(x19463,x19464,x19462)) % 19.23/19.06 [1947]~E(x19471,x19472)+E(f349(x19471,x19473),f349(x19472,x19473)) % 19.23/19.06 [1948]~E(x19481,x19482)+E(f349(x19483,x19481),f349(x19483,x19482)) % 19.23/19.06 [1949]~E(x19491,x19492)+E(f139(x19491,x19493),f139(x19492,x19493)) % 19.23/19.06 [1950]~E(x19501,x19502)+E(f139(x19503,x19501),f139(x19503,x19502)) % 19.23/19.06 [1951]~E(x19511,x19512)+E(f753(x19511,x19513,x19514,x19515),f753(x19512,x19513,x19514,x19515)) % 19.23/19.06 [1952]~E(x19521,x19522)+E(f753(x19523,x19521,x19524,x19525),f753(x19523,x19522,x19524,x19525)) % 19.23/19.06 [1953]~E(x19531,x19532)+E(f753(x19533,x19534,x19531,x19535),f753(x19533,x19534,x19532,x19535)) % 19.23/19.06 [1954]~E(x19541,x19542)+E(f753(x19543,x19544,x19545,x19541),f753(x19543,x19544,x19545,x19542)) % 19.23/19.06 [1955]~E(x19551,x19552)+E(f692(x19551,x19553,x19554),f692(x19552,x19553,x19554)) % 19.23/19.06 [1956]~E(x19561,x19562)+E(f692(x19563,x19561,x19564),f692(x19563,x19562,x19564)) % 19.23/19.06 [1957]~E(x19571,x19572)+E(f692(x19573,x19574,x19571),f692(x19573,x19574,x19572)) % 19.23/19.06 [1958]~E(x19581,x19582)+E(f187(x19581,x19583,x19584,x19585),f187(x19582,x19583,x19584,x19585)) % 19.23/19.06 [1959]~E(x19591,x19592)+E(f187(x19593,x19591,x19594,x19595),f187(x19593,x19592,x19594,x19595)) % 19.23/19.06 [1960]~E(x19601,x19602)+E(f187(x19603,x19604,x19601,x19605),f187(x19603,x19604,x19602,x19605)) % 19.23/19.06 [1961]~E(x19611,x19612)+E(f187(x19613,x19614,x19615,x19611),f187(x19613,x19614,x19615,x19612)) % 19.23/19.06 [1962]~E(x19621,x19622)+E(f675(x19621,x19623,x19624,x19625,x19626),f675(x19622,x19623,x19624,x19625,x19626)) % 19.23/19.06 [1963]~E(x19631,x19632)+E(f675(x19633,x19631,x19634,x19635,x19636),f675(x19633,x19632,x19634,x19635,x19636)) % 19.23/19.06 [1964]~E(x19641,x19642)+E(f675(x19643,x19644,x19641,x19645,x19646),f675(x19643,x19644,x19642,x19645,x19646)) % 19.23/19.06 [1965]~E(x19651,x19652)+E(f675(x19653,x19654,x19655,x19651,x19656),f675(x19653,x19654,x19655,x19652,x19656)) % 19.23/19.06 [1966]~E(x19661,x19662)+E(f675(x19663,x19664,x19665,x19666,x19661),f675(x19663,x19664,x19665,x19666,x19662)) % 19.23/19.06 [1967]~E(x19671,x19672)+E(f263(x19671,x19673,x19674,x19675,x19676),f263(x19672,x19673,x19674,x19675,x19676)) % 19.23/19.06 [1968]~E(x19681,x19682)+E(f263(x19683,x19681,x19684,x19685,x19686),f263(x19683,x19682,x19684,x19685,x19686)) % 19.23/19.06 [1969]~E(x19691,x19692)+E(f263(x19693,x19694,x19691,x19695,x19696),f263(x19693,x19694,x19692,x19695,x19696)) % 19.23/19.06 [1970]~E(x19701,x19702)+E(f263(x19703,x19704,x19705,x19701,x19706),f263(x19703,x19704,x19705,x19702,x19706)) % 19.23/19.06 [1971]~E(x19711,x19712)+E(f263(x19713,x19714,x19715,x19716,x19711),f263(x19713,x19714,x19715,x19716,x19712)) % 19.23/19.06 [1972]~E(x19721,x19722)+E(f487(x19721,x19723,x19724,x19725),f487(x19722,x19723,x19724,x19725)) % 19.23/19.06 [1973]~E(x19731,x19732)+E(f487(x19733,x19731,x19734,x19735),f487(x19733,x19732,x19734,x19735)) % 19.23/19.06 [1974]~E(x19741,x19742)+E(f487(x19743,x19744,x19741,x19745),f487(x19743,x19744,x19742,x19745)) % 19.23/19.06 [1975]~E(x19751,x19752)+E(f487(x19753,x19754,x19755,x19751),f487(x19753,x19754,x19755,x19752)) % 19.23/19.06 [1976]~E(x19761,x19762)+E(f203(x19761),f203(x19762)) % 19.23/19.06 [1977]~E(x19771,x19772)+E(f558(x19771,x19773,x19774,x19775,x19776,x19777),f558(x19772,x19773,x19774,x19775,x19776,x19777)) % 19.23/19.06 [1978]~E(x19781,x19782)+E(f558(x19783,x19781,x19784,x19785,x19786,x19787),f558(x19783,x19782,x19784,x19785,x19786,x19787)) % 19.23/19.06 [1979]~E(x19791,x19792)+E(f558(x19793,x19794,x19791,x19795,x19796,x19797),f558(x19793,x19794,x19792,x19795,x19796,x19797)) % 19.23/19.06 [1980]~E(x19801,x19802)+E(f558(x19803,x19804,x19805,x19801,x19806,x19807),f558(x19803,x19804,x19805,x19802,x19806,x19807)) % 19.23/19.06 [1981]~E(x19811,x19812)+E(f558(x19813,x19814,x19815,x19816,x19811,x19817),f558(x19813,x19814,x19815,x19816,x19812,x19817)) % 19.23/19.06 [1982]~E(x19821,x19822)+E(f558(x19823,x19824,x19825,x19826,x19827,x19821),f558(x19823,x19824,x19825,x19826,x19827,x19822)) % 19.23/19.06 [1983]~E(x19831,x19832)+E(f843(x19831,x19833,x19834),f843(x19832,x19833,x19834)) % 19.23/19.06 [1984]~E(x19841,x19842)+E(f843(x19843,x19841,x19844),f843(x19843,x19842,x19844)) % 19.23/19.06 [1985]~E(x19851,x19852)+E(f843(x19853,x19854,x19851),f843(x19853,x19854,x19852)) % 19.23/19.06 [1986]~E(x19861,x19862)+E(f784(x19861,x19863),f784(x19862,x19863)) % 19.23/19.06 [1987]~E(x19871,x19872)+E(f784(x19873,x19871),f784(x19873,x19872)) % 19.23/19.06 [1988]~E(x19881,x19882)+E(f491(x19881,x19883),f491(x19882,x19883)) % 19.23/19.06 [1989]~E(x19891,x19892)+E(f491(x19893,x19891),f491(x19893,x19892)) % 19.23/19.06 [1990]~E(x19901,x19902)+E(f284(x19901,x19903,x19904,x19905),f284(x19902,x19903,x19904,x19905)) % 19.23/19.06 [1991]~E(x19911,x19912)+E(f284(x19913,x19911,x19914,x19915),f284(x19913,x19912,x19914,x19915)) % 19.23/19.06 [1992]~E(x19921,x19922)+E(f284(x19923,x19924,x19921,x19925),f284(x19923,x19924,x19922,x19925)) % 19.23/19.06 [1993]~E(x19931,x19932)+E(f284(x19933,x19934,x19935,x19931),f284(x19933,x19934,x19935,x19932)) % 19.23/19.06 [1994]~E(x19941,x19942)+E(f570(x19941,x19943,x19944,x19945),f570(x19942,x19943,x19944,x19945)) % 19.23/19.06 [1995]~E(x19951,x19952)+E(f570(x19953,x19951,x19954,x19955),f570(x19953,x19952,x19954,x19955)) % 19.23/19.06 [1996]~E(x19961,x19962)+E(f570(x19963,x19964,x19961,x19965),f570(x19963,x19964,x19962,x19965)) % 19.23/19.06 [1997]~E(x19971,x19972)+E(f570(x19973,x19974,x19975,x19971),f570(x19973,x19974,x19975,x19972)) % 19.23/19.06 [1998]~E(x19981,x19982)+E(f325(x19981,x19983,x19984,x19985),f325(x19982,x19983,x19984,x19985)) % 19.23/19.06 [1999]~E(x19991,x19992)+E(f325(x19993,x19991,x19994,x19995),f325(x19993,x19992,x19994,x19995)) % 19.23/19.06 [2000]~E(x20001,x20002)+E(f325(x20003,x20004,x20001,x20005),f325(x20003,x20004,x20002,x20005)) % 19.23/19.06 [2001]~E(x20011,x20012)+E(f325(x20013,x20014,x20015,x20011),f325(x20013,x20014,x20015,x20012)) % 19.23/19.06 [2002]~E(x20021,x20022)+E(f729(x20021,x20023,x20024,x20025,x20026),f729(x20022,x20023,x20024,x20025,x20026)) % 19.23/19.06 [2003]~E(x20031,x20032)+E(f729(x20033,x20031,x20034,x20035,x20036),f729(x20033,x20032,x20034,x20035,x20036)) % 19.23/19.06 [2004]~E(x20041,x20042)+E(f729(x20043,x20044,x20041,x20045,x20046),f729(x20043,x20044,x20042,x20045,x20046)) % 19.23/19.06 [2005]~E(x20051,x20052)+E(f729(x20053,x20054,x20055,x20051,x20056),f729(x20053,x20054,x20055,x20052,x20056)) % 19.23/19.06 [2006]~E(x20061,x20062)+E(f729(x20063,x20064,x20065,x20066,x20061),f729(x20063,x20064,x20065,x20066,x20062)) % 19.23/19.06 [2007]~E(x20071,x20072)+E(f388(x20071,x20073),f388(x20072,x20073)) % 19.23/19.06 [2008]~E(x20081,x20082)+E(f388(x20083,x20081),f388(x20083,x20082)) % 19.23/19.06 [2009]~E(x20091,x20092)+E(f696(x20091,x20093,x20094,x20095),f696(x20092,x20093,x20094,x20095)) % 19.23/19.06 [2010]~E(x20101,x20102)+E(f696(x20103,x20101,x20104,x20105),f696(x20103,x20102,x20104,x20105)) % 19.23/19.06 [2011]~E(x20111,x20112)+E(f696(x20113,x20114,x20111,x20115),f696(x20113,x20114,x20112,x20115)) % 19.23/19.06 [2012]~E(x20121,x20122)+E(f696(x20123,x20124,x20125,x20121),f696(x20123,x20124,x20125,x20122)) % 19.23/19.06 [2013]~E(x20131,x20132)+E(f493(x20131,x20133),f493(x20132,x20133)) % 19.23/19.06 [2014]~E(x20141,x20142)+E(f493(x20143,x20141),f493(x20143,x20142)) % 19.23/19.06 [2015]~E(x20151,x20152)+E(f528(x20151,x20153,x20154,x20155,x20156),f528(x20152,x20153,x20154,x20155,x20156)) % 19.23/19.06 [2016]~E(x20161,x20162)+E(f528(x20163,x20161,x20164,x20165,x20166),f528(x20163,x20162,x20164,x20165,x20166)) % 19.23/19.06 [2017]~E(x20171,x20172)+E(f528(x20173,x20174,x20171,x20175,x20176),f528(x20173,x20174,x20172,x20175,x20176)) % 19.23/19.06 [2018]~E(x20181,x20182)+E(f528(x20183,x20184,x20185,x20181,x20186),f528(x20183,x20184,x20185,x20182,x20186)) % 19.23/19.06 [2019]~E(x20191,x20192)+E(f528(x20193,x20194,x20195,x20196,x20191),f528(x20193,x20194,x20195,x20196,x20192)) % 19.23/19.06 [2020]~E(x20201,x20202)+E(f826(x20201,x20203,x20204),f826(x20202,x20203,x20204)) % 19.23/19.06 [2021]~E(x20211,x20212)+E(f826(x20213,x20211,x20214),f826(x20213,x20212,x20214)) % 19.23/19.06 [2022]~E(x20221,x20222)+E(f826(x20223,x20224,x20221),f826(x20223,x20224,x20222)) % 19.23/19.06 [2023]~E(x20231,x20232)+E(f324(x20231,x20233,x20234),f324(x20232,x20233,x20234)) % 19.23/19.06 [2024]~E(x20241,x20242)+E(f324(x20243,x20241,x20244),f324(x20243,x20242,x20244)) % 19.23/19.06 [2025]~E(x20251,x20252)+E(f324(x20253,x20254,x20251),f324(x20253,x20254,x20252)) % 19.23/19.06 [2026]~E(x20261,x20262)+E(f213(x20261,x20263,x20264,x20265),f213(x20262,x20263,x20264,x20265)) % 19.23/19.06 [2027]~E(x20271,x20272)+E(f213(x20273,x20271,x20274,x20275),f213(x20273,x20272,x20274,x20275)) % 19.23/19.06 [2028]~E(x20281,x20282)+E(f213(x20283,x20284,x20281,x20285),f213(x20283,x20284,x20282,x20285)) % 19.23/19.06 [2029]~E(x20291,x20292)+E(f213(x20293,x20294,x20295,x20291),f213(x20293,x20294,x20295,x20292)) % 19.23/19.06 [2030]~E(x20301,x20302)+E(f46(x20301,x20303,x20304,x20305),f46(x20302,x20303,x20304,x20305)) % 19.23/19.06 [2031]~E(x20311,x20312)+E(f46(x20313,x20311,x20314,x20315),f46(x20313,x20312,x20314,x20315)) % 19.23/19.06 [2032]~E(x20321,x20322)+E(f46(x20323,x20324,x20321,x20325),f46(x20323,x20324,x20322,x20325)) % 19.23/19.06 [2033]~E(x20331,x20332)+E(f46(x20333,x20334,x20335,x20331),f46(x20333,x20334,x20335,x20332)) % 19.23/19.06 [2034]~E(x20341,x20342)+E(f573(x20341,x20343,x20344),f573(x20342,x20343,x20344)) % 19.23/19.06 [2035]~E(x20351,x20352)+E(f573(x20353,x20351,x20354),f573(x20353,x20352,x20354)) % 19.23/19.06 [2036]~E(x20361,x20362)+E(f573(x20363,x20364,x20361),f573(x20363,x20364,x20362)) % 19.23/19.06 [2037]~E(x20371,x20372)+E(f562(x20371,x20373,x20374),f562(x20372,x20373,x20374)) % 19.23/19.06 [2038]~E(x20381,x20382)+E(f562(x20383,x20381,x20384),f562(x20383,x20382,x20384)) % 19.23/19.06 [2039]~E(x20391,x20392)+E(f562(x20393,x20394,x20391),f562(x20393,x20394,x20392)) % 19.23/19.06 [2040]~E(x20401,x20402)+E(f281(x20401,x20403,x20404,x20405),f281(x20402,x20403,x20404,x20405)) % 19.23/19.06 [2041]~E(x20411,x20412)+E(f281(x20413,x20411,x20414,x20415),f281(x20413,x20412,x20414,x20415)) % 19.23/19.06 [2042]~E(x20421,x20422)+E(f281(x20423,x20424,x20421,x20425),f281(x20423,x20424,x20422,x20425)) % 19.23/19.06 [2043]~E(x20431,x20432)+E(f281(x20433,x20434,x20435,x20431),f281(x20433,x20434,x20435,x20432)) % 19.23/19.06 [2044]~E(x20441,x20442)+E(f709(x20441,x20443,x20444,x20445),f709(x20442,x20443,x20444,x20445)) % 19.23/19.06 [2045]~E(x20451,x20452)+E(f709(x20453,x20451,x20454,x20455),f709(x20453,x20452,x20454,x20455)) % 19.23/19.06 [2046]~E(x20461,x20462)+E(f709(x20463,x20464,x20461,x20465),f709(x20463,x20464,x20462,x20465)) % 19.23/19.06 [2047]~E(x20471,x20472)+E(f709(x20473,x20474,x20475,x20471),f709(x20473,x20474,x20475,x20472)) % 19.23/19.06 [2048]~E(x20481,x20482)+E(f620(x20481,x20483,x20484,x20485,x20486,x20487),f620(x20482,x20483,x20484,x20485,x20486,x20487)) % 19.23/19.06 [2049]~E(x20491,x20492)+E(f620(x20493,x20491,x20494,x20495,x20496,x20497),f620(x20493,x20492,x20494,x20495,x20496,x20497)) % 19.23/19.06 [2050]~E(x20501,x20502)+E(f620(x20503,x20504,x20501,x20505,x20506,x20507),f620(x20503,x20504,x20502,x20505,x20506,x20507)) % 19.23/19.06 [2051]~E(x20511,x20512)+E(f620(x20513,x20514,x20515,x20511,x20516,x20517),f620(x20513,x20514,x20515,x20512,x20516,x20517)) % 19.23/19.06 [2052]~E(x20521,x20522)+E(f620(x20523,x20524,x20525,x20526,x20521,x20527),f620(x20523,x20524,x20525,x20526,x20522,x20527)) % 19.23/19.06 [2053]~E(x20531,x20532)+E(f620(x20533,x20534,x20535,x20536,x20537,x20531),f620(x20533,x20534,x20535,x20536,x20537,x20532)) % 19.23/19.06 [2054]~E(x20541,x20542)+E(f722(x20541,x20543,x20544),f722(x20542,x20543,x20544)) % 19.23/19.06 [2055]~E(x20551,x20552)+E(f722(x20553,x20551,x20554),f722(x20553,x20552,x20554)) % 19.23/19.06 [2056]~E(x20561,x20562)+E(f722(x20563,x20564,x20561),f722(x20563,x20564,x20562)) % 19.23/19.06 [2057]~E(x20571,x20572)+E(f761(x20571,x20573,x20574),f761(x20572,x20573,x20574)) % 19.23/19.06 [2058]~E(x20581,x20582)+E(f761(x20583,x20581,x20584),f761(x20583,x20582,x20584)) % 19.23/19.06 [2059]~E(x20591,x20592)+E(f761(x20593,x20594,x20591),f761(x20593,x20594,x20592)) % 19.23/19.06 [2060]~E(x20601,x20602)+E(f520(x20601,x20603,x20604,x20605,x20606),f520(x20602,x20603,x20604,x20605,x20606)) % 19.23/19.06 [2061]~E(x20611,x20612)+E(f520(x20613,x20611,x20614,x20615,x20616),f520(x20613,x20612,x20614,x20615,x20616)) % 19.23/19.06 [2062]~E(x20621,x20622)+E(f520(x20623,x20624,x20621,x20625,x20626),f520(x20623,x20624,x20622,x20625,x20626)) % 19.23/19.06 [2063]~E(x20631,x20632)+E(f520(x20633,x20634,x20635,x20631,x20636),f520(x20633,x20634,x20635,x20632,x20636)) % 19.23/19.06 [2064]~E(x20641,x20642)+E(f520(x20643,x20644,x20645,x20646,x20641),f520(x20643,x20644,x20645,x20646,x20642)) % 19.23/19.06 [2065]~E(x20651,x20652)+E(f497(x20651,x20653,x20654),f497(x20652,x20653,x20654)) % 19.23/19.06 [2066]~E(x20661,x20662)+E(f497(x20663,x20661,x20664),f497(x20663,x20662,x20664)) % 19.23/19.06 [2067]~E(x20671,x20672)+E(f497(x20673,x20674,x20671),f497(x20673,x20674,x20672)) % 19.23/19.06 [2068]~E(x20681,x20682)+E(f737(x20681,x20683),f737(x20682,x20683)) % 19.23/19.06 [2069]~E(x20691,x20692)+E(f737(x20693,x20691),f737(x20693,x20692)) % 19.23/19.06 [2070]~E(x20701,x20702)+E(f674(x20701,x20703,x20704,x20705),f674(x20702,x20703,x20704,x20705)) % 19.23/19.06 [2071]~E(x20711,x20712)+E(f674(x20713,x20711,x20714,x20715),f674(x20713,x20712,x20714,x20715)) % 19.23/19.06 [2072]~E(x20721,x20722)+E(f674(x20723,x20724,x20721,x20725),f674(x20723,x20724,x20722,x20725)) % 19.23/19.06 [2073]~E(x20731,x20732)+E(f674(x20733,x20734,x20735,x20731),f674(x20733,x20734,x20735,x20732)) % 19.23/19.06 [2074]~E(x20741,x20742)+E(f59(x20741),f59(x20742)) % 19.23/19.06 [2075]~E(x20751,x20752)+E(f812(x20751,x20753,x20754),f812(x20752,x20753,x20754)) % 19.23/19.06 [2076]~E(x20761,x20762)+E(f812(x20763,x20761,x20764),f812(x20763,x20762,x20764)) % 19.23/19.06 [2077]~E(x20771,x20772)+E(f812(x20773,x20774,x20771),f812(x20773,x20774,x20772)) % 19.23/19.06 [2078]~E(x20781,x20782)+E(f657(x20781,x20783,x20784),f657(x20782,x20783,x20784)) % 19.23/19.06 [2079]~E(x20791,x20792)+E(f657(x20793,x20791,x20794),f657(x20793,x20792,x20794)) % 19.23/19.06 [2080]~E(x20801,x20802)+E(f657(x20803,x20804,x20801),f657(x20803,x20804,x20802)) % 19.23/19.06 [2081]~E(x20811,x20812)+E(f131(x20811),f131(x20812)) % 19.23/19.06 [2082]~E(x20821,x20822)+E(f618(x20821,x20823,x20824,x20825,x20826,x20827),f618(x20822,x20823,x20824,x20825,x20826,x20827)) % 19.23/19.06 [2083]~E(x20831,x20832)+E(f618(x20833,x20831,x20834,x20835,x20836,x20837),f618(x20833,x20832,x20834,x20835,x20836,x20837)) % 19.23/19.06 [2084]~E(x20841,x20842)+E(f618(x20843,x20844,x20841,x20845,x20846,x20847),f618(x20843,x20844,x20842,x20845,x20846,x20847)) % 19.23/19.06 [2085]~E(x20851,x20852)+E(f618(x20853,x20854,x20855,x20851,x20856,x20857),f618(x20853,x20854,x20855,x20852,x20856,x20857)) % 19.23/19.06 [2086]~E(x20861,x20862)+E(f618(x20863,x20864,x20865,x20866,x20861,x20867),f618(x20863,x20864,x20865,x20866,x20862,x20867)) % 19.23/19.06 [2087]~E(x20871,x20872)+E(f618(x20873,x20874,x20875,x20876,x20877,x20871),f618(x20873,x20874,x20875,x20876,x20877,x20872)) % 19.23/19.06 [2088]~E(x20881,x20882)+E(f355(x20881,x20883,x20884),f355(x20882,x20883,x20884)) % 19.23/19.06 [2089]~E(x20891,x20892)+E(f355(x20893,x20891,x20894),f355(x20893,x20892,x20894)) % 19.23/19.06 [2090]~E(x20901,x20902)+E(f355(x20903,x20904,x20901),f355(x20903,x20904,x20902)) % 19.23/19.06 [2091]~E(x20911,x20912)+E(f671(x20911,x20913,x20914,x20915),f671(x20912,x20913,x20914,x20915)) % 19.23/19.06 [2092]~E(x20921,x20922)+E(f671(x20923,x20921,x20924,x20925),f671(x20923,x20922,x20924,x20925)) % 19.23/19.06 [2093]~E(x20931,x20932)+E(f671(x20933,x20934,x20931,x20935),f671(x20933,x20934,x20932,x20935)) % 19.23/19.06 [2094]~E(x20941,x20942)+E(f671(x20943,x20944,x20945,x20941),f671(x20943,x20944,x20945,x20942)) % 19.23/19.06 [2095]~E(x20951,x20952)+E(f833(x20951,x20953,x20954),f833(x20952,x20953,x20954)) % 19.23/19.06 [2096]~E(x20961,x20962)+E(f833(x20963,x20961,x20964),f833(x20963,x20962,x20964)) % 19.23/19.06 [2097]~E(x20971,x20972)+E(f833(x20973,x20974,x20971),f833(x20973,x20974,x20972)) % 19.23/19.06 [2098]~E(x20981,x20982)+E(f283(x20981,x20983,x20984,x20985),f283(x20982,x20983,x20984,x20985)) % 19.23/19.06 [2099]~E(x20991,x20992)+E(f283(x20993,x20991,x20994,x20995),f283(x20993,x20992,x20994,x20995)) % 19.23/19.06 [2100]~E(x21001,x21002)+E(f283(x21003,x21004,x21001,x21005),f283(x21003,x21004,x21002,x21005)) % 19.23/19.06 [2101]~E(x21011,x21012)+E(f283(x21013,x21014,x21015,x21011),f283(x21013,x21014,x21015,x21012)) % 19.23/19.06 [2102]~E(x21021,x21022)+E(f381(x21021,x21023,x21024,x21025),f381(x21022,x21023,x21024,x21025)) % 19.23/19.06 [2103]~E(x21031,x21032)+E(f381(x21033,x21031,x21034,x21035),f381(x21033,x21032,x21034,x21035)) % 19.23/19.06 [2104]~E(x21041,x21042)+E(f381(x21043,x21044,x21041,x21045),f381(x21043,x21044,x21042,x21045)) % 19.23/19.06 [2105]~E(x21051,x21052)+E(f381(x21053,x21054,x21055,x21051),f381(x21053,x21054,x21055,x21052)) % 19.23/19.06 [2106]~E(x21061,x21062)+E(f787(x21061,x21063,x21064),f787(x21062,x21063,x21064)) % 19.23/19.06 [2107]~E(x21071,x21072)+E(f787(x21073,x21071,x21074),f787(x21073,x21072,x21074)) % 19.23/19.06 [2108]~E(x21081,x21082)+E(f787(x21083,x21084,x21081),f787(x21083,x21084,x21082)) % 19.23/19.06 [2109]~E(x21091,x21092)+E(f803(x21091,x21093),f803(x21092,x21093)) % 19.23/19.06 [2110]~E(x21101,x21102)+E(f803(x21103,x21101),f803(x21103,x21102)) % 19.23/19.06 [2111]~E(x21111,x21112)+E(f726(x21111,x21113,x21114,x21115),f726(x21112,x21113,x21114,x21115)) % 19.23/19.06 [2112]~E(x21121,x21122)+E(f726(x21123,x21121,x21124,x21125),f726(x21123,x21122,x21124,x21125)) % 19.23/19.06 [2113]~E(x21131,x21132)+E(f726(x21133,x21134,x21131,x21135),f726(x21133,x21134,x21132,x21135)) % 19.23/19.06 [2114]~E(x21141,x21142)+E(f726(x21143,x21144,x21145,x21141),f726(x21143,x21144,x21145,x21142)) % 19.23/19.06 [2115]~E(x21151,x21152)+E(f669(x21151,x21153),f669(x21152,x21153)) % 19.23/19.06 [2116]~E(x21161,x21162)+E(f669(x21163,x21161),f669(x21163,x21162)) % 19.23/19.06 [2117]~E(x21171,x21172)+E(f459(x21171,x21173),f459(x21172,x21173)) % 19.23/19.06 [2118]~E(x21181,x21182)+E(f459(x21183,x21181),f459(x21183,x21182)) % 19.23/19.06 [2119]~E(x21191,x21192)+E(f634(x21191,x21193,x21194,x21195,x21196,x21197),f634(x21192,x21193,x21194,x21195,x21196,x21197)) % 19.23/19.06 [2120]~E(x21201,x21202)+E(f634(x21203,x21201,x21204,x21205,x21206,x21207),f634(x21203,x21202,x21204,x21205,x21206,x21207)) % 19.23/19.06 [2121]~E(x21211,x21212)+E(f634(x21213,x21214,x21211,x21215,x21216,x21217),f634(x21213,x21214,x21212,x21215,x21216,x21217)) % 19.23/19.06 [2122]~E(x21221,x21222)+E(f634(x21223,x21224,x21225,x21221,x21226,x21227),f634(x21223,x21224,x21225,x21222,x21226,x21227)) % 19.23/19.06 [2123]~E(x21231,x21232)+E(f634(x21233,x21234,x21235,x21236,x21231,x21237),f634(x21233,x21234,x21235,x21236,x21232,x21237)) % 19.23/19.06 [2124]~E(x21241,x21242)+E(f634(x21243,x21244,x21245,x21246,x21247,x21241),f634(x21243,x21244,x21245,x21246,x21247,x21242)) % 19.23/19.06 [2125]~E(x21251,x21252)+E(f365(x21251,x21253,x21254,x21255),f365(x21252,x21253,x21254,x21255)) % 19.23/19.06 [2126]~E(x21261,x21262)+E(f365(x21263,x21261,x21264,x21265),f365(x21263,x21262,x21264,x21265)) % 19.23/19.06 [2127]~E(x21271,x21272)+E(f365(x21273,x21274,x21271,x21275),f365(x21273,x21274,x21272,x21275)) % 19.23/19.06 [2128]~E(x21281,x21282)+E(f365(x21283,x21284,x21285,x21281),f365(x21283,x21284,x21285,x21282)) % 19.23/19.06 [2129]~E(x21291,x21292)+E(f372(x21291,x21293,x21294,x21295,x21296),f372(x21292,x21293,x21294,x21295,x21296)) % 19.23/19.06 [2130]~E(x21301,x21302)+E(f372(x21303,x21301,x21304,x21305,x21306),f372(x21303,x21302,x21304,x21305,x21306)) % 19.23/19.06 [2131]~E(x21311,x21312)+E(f372(x21313,x21314,x21311,x21315,x21316),f372(x21313,x21314,x21312,x21315,x21316)) % 19.23/19.06 [2132]~E(x21321,x21322)+E(f372(x21323,x21324,x21325,x21321,x21326),f372(x21323,x21324,x21325,x21322,x21326)) % 19.23/19.06 [2133]~E(x21331,x21332)+E(f372(x21333,x21334,x21335,x21336,x21331),f372(x21333,x21334,x21335,x21336,x21332)) % 19.23/19.06 [2134]~E(x21341,x21342)+E(f624(x21341),f624(x21342)) % 19.23/19.06 [2135]~E(x21351,x21352)+E(f422(x21351,x21353,x21354,x21355,x21356),f422(x21352,x21353,x21354,x21355,x21356)) % 19.23/19.06 [2136]~E(x21361,x21362)+E(f422(x21363,x21361,x21364,x21365,x21366),f422(x21363,x21362,x21364,x21365,x21366)) % 19.23/19.06 [2137]~E(x21371,x21372)+E(f422(x21373,x21374,x21371,x21375,x21376),f422(x21373,x21374,x21372,x21375,x21376)) % 19.23/19.06 [2138]~E(x21381,x21382)+E(f422(x21383,x21384,x21385,x21381,x21386),f422(x21383,x21384,x21385,x21382,x21386)) % 19.23/19.06 [2139]~E(x21391,x21392)+E(f422(x21393,x21394,x21395,x21396,x21391),f422(x21393,x21394,x21395,x21396,x21392)) % 19.23/19.06 [2140]~E(x21401,x21402)+E(f231(x21401,x21403,x21404,x21405),f231(x21402,x21403,x21404,x21405)) % 19.23/19.06 [2141]~E(x21411,x21412)+E(f231(x21413,x21411,x21414,x21415),f231(x21413,x21412,x21414,x21415)) % 19.23/19.06 [2142]~E(x21421,x21422)+E(f231(x21423,x21424,x21421,x21425),f231(x21423,x21424,x21422,x21425)) % 19.23/19.06 [2143]~E(x21431,x21432)+E(f231(x21433,x21434,x21435,x21431),f231(x21433,x21434,x21435,x21432)) % 19.23/19.06 [2144]~E(x21441,x21442)+E(f386(x21441,x21443),f386(x21442,x21443)) % 19.23/19.06 [2145]~E(x21451,x21452)+E(f386(x21453,x21451),f386(x21453,x21452)) % 19.23/19.06 [2146]~E(x21461,x21462)+E(f102(x21461,x21463,x21464),f102(x21462,x21463,x21464)) % 19.23/19.06 [2147]~E(x21471,x21472)+E(f102(x21473,x21471,x21474),f102(x21473,x21472,x21474)) % 19.23/19.06 [2148]~E(x21481,x21482)+E(f102(x21483,x21484,x21481),f102(x21483,x21484,x21482)) % 19.23/19.06 [2149]~E(x21491,x21492)+E(f824(x21491,x21493,x21494),f824(x21492,x21493,x21494)) % 19.23/19.06 [2150]~E(x21501,x21502)+E(f824(x21503,x21501,x21504),f824(x21503,x21502,x21504)) % 19.23/19.06 [2151]~E(x21511,x21512)+E(f824(x21513,x21514,x21511),f824(x21513,x21514,x21512)) % 19.23/19.06 [2152]~E(x21521,x21522)+E(f701(x21521,x21523),f701(x21522,x21523)) % 19.23/19.06 [2153]~E(x21531,x21532)+E(f701(x21533,x21531),f701(x21533,x21532)) % 19.23/19.06 [2154]~E(x21541,x21542)+E(f417(x21541,x21543,x21544,x21545,x21546,x21547),f417(x21542,x21543,x21544,x21545,x21546,x21547)) % 19.23/19.06 [2155]~E(x21551,x21552)+E(f417(x21553,x21551,x21554,x21555,x21556,x21557),f417(x21553,x21552,x21554,x21555,x21556,x21557)) % 19.23/19.06 [2156]~E(x21561,x21562)+E(f417(x21563,x21564,x21561,x21565,x21566,x21567),f417(x21563,x21564,x21562,x21565,x21566,x21567)) % 19.23/19.06 [2157]~E(x21571,x21572)+E(f417(x21573,x21574,x21575,x21571,x21576,x21577),f417(x21573,x21574,x21575,x21572,x21576,x21577)) % 19.23/19.06 [2158]~E(x21581,x21582)+E(f417(x21583,x21584,x21585,x21586,x21581,x21587),f417(x21583,x21584,x21585,x21586,x21582,x21587)) % 19.23/19.06 [2159]~E(x21591,x21592)+E(f417(x21593,x21594,x21595,x21596,x21597,x21591),f417(x21593,x21594,x21595,x21596,x21597,x21592)) % 19.23/19.06 [2160]~E(x21601,x21602)+E(f479(x21601,x21603,x21604,x21605),f479(x21602,x21603,x21604,x21605)) % 19.23/19.06 [2161]~E(x21611,x21612)+E(f479(x21613,x21611,x21614,x21615),f479(x21613,x21612,x21614,x21615)) % 19.23/19.06 [2162]~E(x21621,x21622)+E(f479(x21623,x21624,x21621,x21625),f479(x21623,x21624,x21622,x21625)) % 19.23/19.06 [2163]~E(x21631,x21632)+E(f479(x21633,x21634,x21635,x21631),f479(x21633,x21634,x21635,x21632)) % 19.23/19.06 [2164]~E(x21641,x21642)+E(f554(x21641,x21643,x21644,x21645,x21646,x21647),f554(x21642,x21643,x21644,x21645,x21646,x21647)) % 19.23/19.06 [2165]~E(x21651,x21652)+E(f554(x21653,x21651,x21654,x21655,x21656,x21657),f554(x21653,x21652,x21654,x21655,x21656,x21657)) % 19.23/19.06 [2166]~E(x21661,x21662)+E(f554(x21663,x21664,x21661,x21665,x21666,x21667),f554(x21663,x21664,x21662,x21665,x21666,x21667)) % 19.23/19.06 [2167]~E(x21671,x21672)+E(f554(x21673,x21674,x21675,x21671,x21676,x21677),f554(x21673,x21674,x21675,x21672,x21676,x21677)) % 19.23/19.06 [2168]~E(x21681,x21682)+E(f554(x21683,x21684,x21685,x21686,x21681,x21687),f554(x21683,x21684,x21685,x21686,x21682,x21687)) % 19.23/19.06 [2169]~E(x21691,x21692)+E(f554(x21693,x21694,x21695,x21696,x21697,x21691),f554(x21693,x21694,x21695,x21696,x21697,x21692)) % 19.23/19.06 [2170]~E(x21701,x21702)+E(f704(x21701,x21703),f704(x21702,x21703)) % 19.23/19.06 [2171]~E(x21711,x21712)+E(f704(x21713,x21711),f704(x21713,x21712)) % 19.23/19.06 [2172]~E(x21721,x21722)+E(f809(x21721,x21723,x21724),f809(x21722,x21723,x21724)) % 19.23/19.06 [2173]~E(x21731,x21732)+E(f809(x21733,x21731,x21734),f809(x21733,x21732,x21734)) % 19.23/19.06 [2174]~E(x21741,x21742)+E(f809(x21743,x21744,x21741),f809(x21743,x21744,x21742)) % 19.23/19.06 [2175]~E(x21751,x21752)+E(f683(x21751,x21753,x21754),f683(x21752,x21753,x21754)) % 19.23/19.06 [2176]~E(x21761,x21762)+E(f683(x21763,x21761,x21764),f683(x21763,x21762,x21764)) % 19.23/19.06 [2177]~E(x21771,x21772)+E(f683(x21773,x21774,x21771),f683(x21773,x21774,x21772)) % 19.23/19.06 [2178]~E(x21781,x21782)+E(f387(x21781,x21783),f387(x21782,x21783)) % 19.23/19.06 [2179]~E(x21791,x21792)+E(f387(x21793,x21791),f387(x21793,x21792)) % 19.23/19.06 [2180]~E(x21801,x21802)+E(f582(x21801,x21803),f582(x21802,x21803)) % 19.23/19.06 [2181]~E(x21811,x21812)+E(f582(x21813,x21811),f582(x21813,x21812)) % 19.23/19.06 [2182]~E(x21821,x21822)+E(f605(x21821,x21823),f605(x21822,x21823)) % 19.23/19.06 [2183]~E(x21831,x21832)+E(f605(x21833,x21831),f605(x21833,x21832)) % 19.23/19.06 [2184]~E(x21841,x21842)+E(f815(x21841,x21843),f815(x21842,x21843)) % 19.23/19.06 [2185]~E(x21851,x21852)+E(f815(x21853,x21851),f815(x21853,x21852)) % 19.23/19.06 [2186]~E(x21861,x21862)+E(f560(x21861,x21863),f560(x21862,x21863)) % 19.23/19.06 [2187]~E(x21871,x21872)+E(f560(x21873,x21871),f560(x21873,x21872)) % 19.23/19.06 [2188]~E(x21881,x21882)+E(f684(x21881,x21883,x21884,x21885),f684(x21882,x21883,x21884,x21885)) % 19.23/19.06 [2189]~E(x21891,x21892)+E(f684(x21893,x21891,x21894,x21895),f684(x21893,x21892,x21894,x21895)) % 19.23/19.06 [2190]~E(x21901,x21902)+E(f684(x21903,x21904,x21901,x21905),f684(x21903,x21904,x21902,x21905)) % 19.23/19.06 [2191]~E(x21911,x21912)+E(f684(x21913,x21914,x21915,x21911),f684(x21913,x21914,x21915,x21912)) % 19.23/19.06 [2192]~E(x21921,x21922)+E(f635(x21921,x21923,x21924),f635(x21922,x21923,x21924)) % 19.23/19.06 [2193]~E(x21931,x21932)+E(f635(x21933,x21931,x21934),f635(x21933,x21932,x21934)) % 19.23/19.06 [2194]~E(x21941,x21942)+E(f635(x21943,x21944,x21941),f635(x21943,x21944,x21942)) % 19.23/19.06 [2195]~E(x21951,x21952)+E(f198(x21951,x21953,x21954,x21955),f198(x21952,x21953,x21954,x21955)) % 19.23/19.06 [2196]~E(x21961,x21962)+E(f198(x21963,x21961,x21964,x21965),f198(x21963,x21962,x21964,x21965)) % 19.23/19.06 [2197]~E(x21971,x21972)+E(f198(x21973,x21974,x21971,x21975),f198(x21973,x21974,x21972,x21975)) % 19.23/19.06 [2198]~E(x21981,x21982)+E(f198(x21983,x21984,x21985,x21981),f198(x21983,x21984,x21985,x21982)) % 19.23/19.06 [2199]~E(x21991,x21992)+E(f445(x21991,x21993,x21994),f445(x21992,x21993,x21994)) % 19.23/19.06 [2200]~E(x22001,x22002)+E(f445(x22003,x22001,x22004),f445(x22003,x22002,x22004)) % 19.23/19.06 [2201]~E(x22011,x22012)+E(f445(x22013,x22014,x22011),f445(x22013,x22014,x22012)) % 19.23/19.06 [2202]~E(x22021,x22022)+E(f415(x22021,x22023,x22024,x22025,x22026),f415(x22022,x22023,x22024,x22025,x22026)) % 19.23/19.06 [2203]~E(x22031,x22032)+E(f415(x22033,x22031,x22034,x22035,x22036),f415(x22033,x22032,x22034,x22035,x22036)) % 19.23/19.06 [2204]~E(x22041,x22042)+E(f415(x22043,x22044,x22041,x22045,x22046),f415(x22043,x22044,x22042,x22045,x22046)) % 19.23/19.06 [2205]~E(x22051,x22052)+E(f415(x22053,x22054,x22055,x22051,x22056),f415(x22053,x22054,x22055,x22052,x22056)) % 19.23/19.06 [2206]~E(x22061,x22062)+E(f415(x22063,x22064,x22065,x22066,x22061),f415(x22063,x22064,x22065,x22066,x22062)) % 19.23/19.06 [2207]~E(x22071,x22072)+E(f460(x22071,x22073,x22074),f460(x22072,x22073,x22074)) % 19.23/19.06 [2208]~E(x22081,x22082)+E(f460(x22083,x22081,x22084),f460(x22083,x22082,x22084)) % 19.23/19.06 [2209]~E(x22091,x22092)+E(f460(x22093,x22094,x22091),f460(x22093,x22094,x22092)) % 19.23/19.06 [2210]~E(x22101,x22102)+E(f374(x22101,x22103,x22104),f374(x22102,x22103,x22104)) % 19.23/19.06 [2211]~E(x22111,x22112)+E(f374(x22113,x22111,x22114),f374(x22113,x22112,x22114)) % 19.23/19.06 [2212]~E(x22121,x22122)+E(f374(x22123,x22124,x22121),f374(x22123,x22124,x22122)) % 19.23/19.06 [2213]~E(x22131,x22132)+E(f244(x22131,x22133),f244(x22132,x22133)) % 19.23/19.06 [2214]~E(x22141,x22142)+E(f244(x22143,x22141),f244(x22143,x22142)) % 19.23/19.06 [2215]~E(x22151,x22152)+E(f615(x22151,x22153,x22154),f615(x22152,x22153,x22154)) % 19.23/19.06 [2216]~E(x22161,x22162)+E(f615(x22163,x22161,x22164),f615(x22163,x22162,x22164)) % 19.23/19.06 [2217]~E(x22171,x22172)+E(f615(x22173,x22174,x22171),f615(x22173,x22174,x22172)) % 19.23/19.06 [2218]~E(x22181,x22182)+E(f862(x22181,x22183),f862(x22182,x22183)) % 19.23/19.06 [2219]~E(x22191,x22192)+E(f862(x22193,x22191),f862(x22193,x22192)) % 19.23/19.06 [2220]~E(x22201,x22202)+E(f550(x22201,x22203,x22204),f550(x22202,x22203,x22204)) % 19.23/19.06 [2221]~E(x22211,x22212)+E(f550(x22213,x22211,x22214),f550(x22213,x22212,x22214)) % 19.23/19.06 [2222]~E(x22221,x22222)+E(f550(x22223,x22224,x22221),f550(x22223,x22224,x22222)) % 19.23/19.06 [2223]~E(x22231,x22232)+E(f631(x22231,x22233,x22234,x22235),f631(x22232,x22233,x22234,x22235)) % 19.23/19.06 [2224]~E(x22241,x22242)+E(f631(x22243,x22241,x22244,x22245),f631(x22243,x22242,x22244,x22245)) % 19.23/19.06 [2225]~E(x22251,x22252)+E(f631(x22253,x22254,x22251,x22255),f631(x22253,x22254,x22252,x22255)) % 19.23/19.06 [2226]~E(x22261,x22262)+E(f631(x22263,x22264,x22265,x22261),f631(x22263,x22264,x22265,x22262)) % 19.23/19.06 [2227]~E(x22271,x22272)+E(f759(x22271,x22273,x22274),f759(x22272,x22273,x22274)) % 19.23/19.06 [2228]~E(x22281,x22282)+E(f759(x22283,x22281,x22284),f759(x22283,x22282,x22284)) % 19.23/19.06 [2229]~E(x22291,x22292)+E(f759(x22293,x22294,x22291),f759(x22293,x22294,x22292)) % 19.23/19.06 [2230]~E(x22301,x22302)+E(f541(x22301,x22303,x22304),f541(x22302,x22303,x22304)) % 19.23/19.06 [2231]~E(x22311,x22312)+E(f541(x22313,x22311,x22314),f541(x22313,x22312,x22314)) % 19.23/19.06 [2232]~E(x22321,x22322)+E(f541(x22323,x22324,x22321),f541(x22323,x22324,x22322)) % 19.23/19.06 [2233]~E(x22331,x22332)+E(f629(x22331,x22333,x22334,x22335,x22336,x22337),f629(x22332,x22333,x22334,x22335,x22336,x22337)) % 19.23/19.06 [2234]~E(x22341,x22342)+E(f629(x22343,x22341,x22344,x22345,x22346,x22347),f629(x22343,x22342,x22344,x22345,x22346,x22347)) % 19.23/19.06 [2235]~E(x22351,x22352)+E(f629(x22353,x22354,x22351,x22355,x22356,x22357),f629(x22353,x22354,x22352,x22355,x22356,x22357)) % 19.23/19.06 [2236]~E(x22361,x22362)+E(f629(x22363,x22364,x22365,x22361,x22366,x22367),f629(x22363,x22364,x22365,x22362,x22366,x22367)) % 19.23/19.06 [2237]~E(x22371,x22372)+E(f629(x22373,x22374,x22375,x22376,x22371,x22377),f629(x22373,x22374,x22375,x22376,x22372,x22377)) % 19.23/19.06 [2238]~E(x22381,x22382)+E(f629(x22383,x22384,x22385,x22386,x22387,x22381),f629(x22383,x22384,x22385,x22386,x22387,x22382)) % 19.23/19.06 [2239]~E(x22391,x22392)+E(f527(x22391,x22393,x22394,x22395),f527(x22392,x22393,x22394,x22395)) % 19.23/19.06 [2240]~E(x22401,x22402)+E(f527(x22403,x22401,x22404,x22405),f527(x22403,x22402,x22404,x22405)) % 19.23/19.06 [2241]~E(x22411,x22412)+E(f527(x22413,x22414,x22411,x22415),f527(x22413,x22414,x22412,x22415)) % 19.23/19.06 [2242]~E(x22421,x22422)+E(f527(x22423,x22424,x22425,x22421),f527(x22423,x22424,x22425,x22422)) % 19.23/19.06 [2243]~E(x22431,x22432)+E(f427(x22431,x22433,x22434),f427(x22432,x22433,x22434)) % 19.23/19.06 [2244]~E(x22441,x22442)+E(f427(x22443,x22441,x22444),f427(x22443,x22442,x22444)) % 19.23/19.06 [2245]~E(x22451,x22452)+E(f427(x22453,x22454,x22451),f427(x22453,x22454,x22452)) % 19.23/19.06 [2246]~E(x22461,x22462)+E(f395(x22461,x22463),f395(x22462,x22463)) % 19.23/19.06 [2247]~E(x22471,x22472)+E(f395(x22473,x22471),f395(x22473,x22472)) % 19.23/19.06 [2248]~E(x22481,x22482)+E(f626(x22481,x22483),f626(x22482,x22483)) % 19.23/19.06 [2249]~E(x22491,x22492)+E(f626(x22493,x22491),f626(x22493,x22492)) % 19.23/19.06 [2250]~E(x22501,x22502)+E(f227(x22501,x22503,x22504,x22505,x22506),f227(x22502,x22503,x22504,x22505,x22506)) % 19.23/19.06 [2251]~E(x22511,x22512)+E(f227(x22513,x22511,x22514,x22515,x22516),f227(x22513,x22512,x22514,x22515,x22516)) % 19.23/19.06 [2252]~E(x22521,x22522)+E(f227(x22523,x22524,x22521,x22525,x22526),f227(x22523,x22524,x22522,x22525,x22526)) % 19.23/19.06 [2253]~E(x22531,x22532)+E(f227(x22533,x22534,x22535,x22531,x22536),f227(x22533,x22534,x22535,x22532,x22536)) % 19.23/19.06 [2254]~E(x22541,x22542)+E(f227(x22543,x22544,x22545,x22546,x22541),f227(x22543,x22544,x22545,x22546,x22542)) % 19.23/19.06 [2255]~E(x22551,x22552)+E(f473(x22551,x22553,x22554,x22555),f473(x22552,x22553,x22554,x22555)) % 19.23/19.06 [2256]~E(x22561,x22562)+E(f473(x22563,x22561,x22564,x22565),f473(x22563,x22562,x22564,x22565)) % 19.23/19.06 [2257]~E(x22571,x22572)+E(f473(x22573,x22574,x22571,x22575),f473(x22573,x22574,x22572,x22575)) % 19.23/19.06 [2258]~E(x22581,x22582)+E(f473(x22583,x22584,x22585,x22581),f473(x22583,x22584,x22585,x22582)) % 19.23/19.06 [2259]~E(x22591,x22592)+E(f230(x22591,x22593,x22594),f230(x22592,x22593,x22594)) % 19.23/19.06 [2260]~E(x22601,x22602)+E(f230(x22603,x22601,x22604),f230(x22603,x22602,x22604)) % 19.23/19.06 [2261]~E(x22611,x22612)+E(f230(x22613,x22614,x22611),f230(x22613,x22614,x22612)) % 19.23/19.06 [2262]~E(x22621,x22622)+E(f751(x22621,x22623,x22624,x22625,x22626),f751(x22622,x22623,x22624,x22625,x22626)) % 19.23/19.06 [2263]~E(x22631,x22632)+E(f751(x22633,x22631,x22634,x22635,x22636),f751(x22633,x22632,x22634,x22635,x22636)) % 19.23/19.06 [2264]~E(x22641,x22642)+E(f751(x22643,x22644,x22641,x22645,x22646),f751(x22643,x22644,x22642,x22645,x22646)) % 19.23/19.06 [2265]~E(x22651,x22652)+E(f751(x22653,x22654,x22655,x22651,x22656),f751(x22653,x22654,x22655,x22652,x22656)) % 19.23/19.06 [2266]~E(x22661,x22662)+E(f751(x22663,x22664,x22665,x22666,x22661),f751(x22663,x22664,x22665,x22666,x22662)) % 19.23/19.06 [2267]~E(x22671,x22672)+E(f373(x22671,x22673),f373(x22672,x22673)) % 19.23/19.06 [2268]~E(x22681,x22682)+E(f373(x22683,x22681),f373(x22683,x22682)) % 19.23/19.06 [2269]~E(x22691,x22692)+E(f424(x22691,x22693,x22694,x22695),f424(x22692,x22693,x22694,x22695)) % 19.23/19.06 [2270]~E(x22701,x22702)+E(f424(x22703,x22701,x22704,x22705),f424(x22703,x22702,x22704,x22705)) % 19.23/19.06 [2271]~E(x22711,x22712)+E(f424(x22713,x22714,x22711,x22715),f424(x22713,x22714,x22712,x22715)) % 19.23/19.06 [2272]~E(x22721,x22722)+E(f424(x22723,x22724,x22725,x22721),f424(x22723,x22724,x22725,x22722)) % 19.23/19.06 [2273]~E(x22731,x22732)+E(f600(x22731,x22733,x22734),f600(x22732,x22733,x22734)) % 19.23/19.06 [2274]~E(x22741,x22742)+E(f600(x22743,x22741,x22744),f600(x22743,x22742,x22744)) % 19.23/19.06 [2275]~E(x22751,x22752)+E(f600(x22753,x22754,x22751),f600(x22753,x22754,x22752)) % 19.23/19.06 [2276]~E(x22761,x22762)+E(f819(x22761,x22763,x22764),f819(x22762,x22763,x22764)) % 19.23/19.06 [2277]~E(x22771,x22772)+E(f819(x22773,x22771,x22774),f819(x22773,x22772,x22774)) % 19.23/19.06 [2278]~E(x22781,x22782)+E(f819(x22783,x22784,x22781),f819(x22783,x22784,x22782)) % 19.23/19.06 [2279]~E(x22791,x22792)+E(f619(x22791,x22793,x22794,x22795,x22796,x22797),f619(x22792,x22793,x22794,x22795,x22796,x22797)) % 19.23/19.06 [2280]~E(x22801,x22802)+E(f619(x22803,x22801,x22804,x22805,x22806,x22807),f619(x22803,x22802,x22804,x22805,x22806,x22807)) % 19.23/19.06 [2281]~E(x22811,x22812)+E(f619(x22813,x22814,x22811,x22815,x22816,x22817),f619(x22813,x22814,x22812,x22815,x22816,x22817)) % 19.23/19.06 [2282]~E(x22821,x22822)+E(f619(x22823,x22824,x22825,x22821,x22826,x22827),f619(x22823,x22824,x22825,x22822,x22826,x22827)) % 19.23/19.06 [2283]~E(x22831,x22832)+E(f619(x22833,x22834,x22835,x22836,x22831,x22837),f619(x22833,x22834,x22835,x22836,x22832,x22837)) % 19.23/19.06 [2284]~E(x22841,x22842)+E(f619(x22843,x22844,x22845,x22846,x22847,x22841),f619(x22843,x22844,x22845,x22846,x22847,x22842)) % 19.23/19.06 [2285]~E(x22851,x22852)+E(f572(x22851,x22853,x22854,x22855,x22856,x22857,x22858,x22859),f572(x22852,x22853,x22854,x22855,x22856,x22857,x22858,x22859)) % 19.23/19.06 [2286]~E(x22861,x22862)+E(f572(x22863,x22861,x22864,x22865,x22866,x22867,x22868,x22869),f572(x22863,x22862,x22864,x22865,x22866,x22867,x22868,x22869)) % 19.23/19.06 [2287]~E(x22871,x22872)+E(f572(x22873,x22874,x22871,x22875,x22876,x22877,x22878,x22879),f572(x22873,x22874,x22872,x22875,x22876,x22877,x22878,x22879)) % 19.23/19.06 [2288]~E(x22881,x22882)+E(f572(x22883,x22884,x22885,x22881,x22886,x22887,x22888,x22889),f572(x22883,x22884,x22885,x22882,x22886,x22887,x22888,x22889)) % 19.23/19.06 [2289]~E(x22891,x22892)+E(f572(x22893,x22894,x22895,x22896,x22891,x22897,x22898,x22899),f572(x22893,x22894,x22895,x22896,x22892,x22897,x22898,x22899)) % 19.23/19.06 [2290]~E(x22901,x22902)+E(f572(x22903,x22904,x22905,x22906,x22907,x22901,x22908,x22909),f572(x22903,x22904,x22905,x22906,x22907,x22902,x22908,x22909)) % 19.23/19.06 [2291]~E(x22911,x22912)+E(f572(x22913,x22914,x22915,x22916,x22917,x22918,x22911,x22919),f572(x22913,x22914,x22915,x22916,x22917,x22918,x22912,x22919)) % 19.23/19.06 [2292]~E(x22921,x22922)+E(f572(x22923,x22924,x22925,x22926,x22927,x22928,x22929,x22921),f572(x22923,x22924,x22925,x22926,x22927,x22928,x22929,x22922)) % 19.23/19.06 [2293]~E(x22931,x22932)+E(f786(x22931,x22933,x22934),f786(x22932,x22933,x22934)) % 19.23/19.06 [2294]~E(x22941,x22942)+E(f786(x22943,x22941,x22944),f786(x22943,x22942,x22944)) % 19.23/19.06 [2295]~E(x22951,x22952)+E(f786(x22953,x22954,x22951),f786(x22953,x22954,x22952)) % 19.23/19.06 [2296]~E(x22961,x22962)+E(f652(x22961,x22963),f652(x22962,x22963)) % 19.23/19.06 [2297]~E(x22971,x22972)+E(f652(x22973,x22971),f652(x22973,x22972)) % 19.23/19.06 [2298]~E(x22981,x22982)+E(f533(x22981,x22983,x22984,x22985,x22986),f533(x22982,x22983,x22984,x22985,x22986)) % 19.23/19.06 [2299]~E(x22991,x22992)+E(f533(x22993,x22991,x22994,x22995,x22996),f533(x22993,x22992,x22994,x22995,x22996)) % 19.23/19.06 [2300]~E(x23001,x23002)+E(f533(x23003,x23004,x23001,x23005,x23006),f533(x23003,x23004,x23002,x23005,x23006)) % 19.23/19.06 [2301]~E(x23011,x23012)+E(f533(x23013,x23014,x23015,x23011,x23016),f533(x23013,x23014,x23015,x23012,x23016)) % 19.23/19.06 [2302]~E(x23021,x23022)+E(f533(x23023,x23024,x23025,x23026,x23021),f533(x23023,x23024,x23025,x23026,x23022)) % 19.23/19.06 [2303]~E(x23031,x23032)+E(f639(x23031,x23033),f639(x23032,x23033)) % 19.23/19.06 [2304]~E(x23041,x23042)+E(f639(x23043,x23041),f639(x23043,x23042)) % 19.23/19.06 [2305]~E(x23051,x23052)+E(f451(x23051,x23053,x23054,x23055),f451(x23052,x23053,x23054,x23055)) % 19.23/19.06 [2306]~E(x23061,x23062)+E(f451(x23063,x23061,x23064,x23065),f451(x23063,x23062,x23064,x23065)) % 19.23/19.06 [2307]~E(x23071,x23072)+E(f451(x23073,x23074,x23071,x23075),f451(x23073,x23074,x23072,x23075)) % 19.23/19.06 [2308]~E(x23081,x23082)+E(f451(x23083,x23084,x23085,x23081),f451(x23083,x23084,x23085,x23082)) % 19.23/19.06 [2309]~E(x23091,x23092)+E(f485(x23091,x23093),f485(x23092,x23093)) % 19.23/19.06 [2310]~E(x23101,x23102)+E(f485(x23103,x23101),f485(x23103,x23102)) % 19.23/19.06 [2311]~E(x23111,x23112)+E(f414(x23111,x23113,x23114,x23115),f414(x23112,x23113,x23114,x23115)) % 19.23/19.06 [2312]~E(x23121,x23122)+E(f414(x23123,x23121,x23124,x23125),f414(x23123,x23122,x23124,x23125)) % 19.23/19.06 [2313]~E(x23131,x23132)+E(f414(x23133,x23134,x23131,x23135),f414(x23133,x23134,x23132,x23135)) % 19.23/19.06 [2314]~E(x23141,x23142)+E(f414(x23143,x23144,x23145,x23141),f414(x23143,x23144,x23145,x23142)) % 19.23/19.06 [2315]~E(x23151,x23152)+E(f389(x23151,x23153),f389(x23152,x23153)) % 19.23/19.06 [2316]~E(x23161,x23162)+E(f389(x23163,x23161),f389(x23163,x23162)) % 19.23/19.06 [2317]~E(x23171,x23172)+E(f571(x23171,x23173,x23174),f571(x23172,x23173,x23174)) % 19.23/19.06 [2318]~E(x23181,x23182)+E(f571(x23183,x23181,x23184),f571(x23183,x23182,x23184)) % 19.23/19.06 [2319]~E(x23191,x23192)+E(f571(x23193,x23194,x23191),f571(x23193,x23194,x23192)) % 19.23/19.06 [2320]~E(x23201,x23202)+E(f663(x23201,x23203,x23204,x23205,x23206),f663(x23202,x23203,x23204,x23205,x23206)) % 19.23/19.06 [2321]~E(x23211,x23212)+E(f663(x23213,x23211,x23214,x23215,x23216),f663(x23213,x23212,x23214,x23215,x23216)) % 19.23/19.06 [2322]~E(x23221,x23222)+E(f663(x23223,x23224,x23221,x23225,x23226),f663(x23223,x23224,x23222,x23225,x23226)) % 19.23/19.06 [2323]~E(x23231,x23232)+E(f663(x23233,x23234,x23235,x23231,x23236),f663(x23233,x23234,x23235,x23232,x23236)) % 19.23/19.06 [2324]~E(x23241,x23242)+E(f663(x23243,x23244,x23245,x23246,x23241),f663(x23243,x23244,x23245,x23246,x23242)) % 19.23/19.06 [2325]~E(x23251,x23252)+E(f599(x23251,x23253,x23254,x23255),f599(x23252,x23253,x23254,x23255)) % 19.23/19.06 [2326]~E(x23261,x23262)+E(f599(x23263,x23261,x23264,x23265),f599(x23263,x23262,x23264,x23265)) % 19.23/19.06 [2327]~E(x23271,x23272)+E(f599(x23273,x23274,x23271,x23275),f599(x23273,x23274,x23272,x23275)) % 19.23/19.06 [2328]~E(x23281,x23282)+E(f599(x23283,x23284,x23285,x23281),f599(x23283,x23284,x23285,x23282)) % 19.23/19.06 [2329]~E(x23291,x23292)+E(f731(x23291,x23293),f731(x23292,x23293)) % 19.23/19.06 [2330]~E(x23301,x23302)+E(f731(x23303,x23301),f731(x23303,x23302)) % 19.23/19.06 [2331]~E(x23311,x23312)+E(f391(x23311,x23313),f391(x23312,x23313)) % 19.23/19.06 [2332]~E(x23321,x23322)+E(f391(x23323,x23321),f391(x23323,x23322)) % 19.23/19.06 [2333]~E(x23331,x23332)+E(f810(x23331,x23333,x23334),f810(x23332,x23333,x23334)) % 19.23/19.06 [2334]~E(x23341,x23342)+E(f810(x23343,x23341,x23344),f810(x23343,x23342,x23344)) % 19.23/19.06 [2335]~E(x23351,x23352)+E(f810(x23353,x23354,x23351),f810(x23353,x23354,x23352)) % 19.23/19.06 [2336]~E(x23361,x23362)+E(f217(x23361,x23363),f217(x23362,x23363)) % 19.23/19.06 [2337]~E(x23371,x23372)+E(f217(x23373,x23371),f217(x23373,x23372)) % 19.23/19.06 [2338]~E(x23381,x23382)+E(f802(x23381,x23383),f802(x23382,x23383)) % 19.23/19.06 [2339]~E(x23391,x23392)+E(f802(x23393,x23391),f802(x23393,x23392)) % 19.23/19.06 [2340]~E(x23401,x23402)+E(f437(x23401,x23403,x23404),f437(x23402,x23403,x23404)) % 19.23/19.06 [2341]~E(x23411,x23412)+E(f437(x23413,x23411,x23414),f437(x23413,x23412,x23414)) % 19.23/19.06 [2342]~E(x23421,x23422)+E(f437(x23423,x23424,x23421),f437(x23423,x23424,x23422)) % 19.23/19.06 [2343]~E(x23431,x23432)+E(f382(x23431,x23433,x23434),f382(x23432,x23433,x23434)) % 19.23/19.06 [2344]~E(x23441,x23442)+E(f382(x23443,x23441,x23444),f382(x23443,x23442,x23444)) % 19.23/19.06 [2345]~E(x23451,x23452)+E(f382(x23453,x23454,x23451),f382(x23453,x23454,x23452)) % 19.23/19.06 [2346]~E(x23461,x23462)+E(f377(x23461,x23463,x23464),f377(x23462,x23463,x23464)) % 19.23/19.06 [2347]~E(x23471,x23472)+E(f377(x23473,x23471,x23474),f377(x23473,x23472,x23474)) % 19.23/19.06 [2348]~E(x23481,x23482)+E(f377(x23483,x23484,x23481),f377(x23483,x23484,x23482)) % 19.23/19.06 [2349]~E(x23491,x23492)+E(f264(x23491,x23493,x23494,x23495,x23496),f264(x23492,x23493,x23494,x23495,x23496)) % 19.23/19.06 [2350]~E(x23501,x23502)+E(f264(x23503,x23501,x23504,x23505,x23506),f264(x23503,x23502,x23504,x23505,x23506)) % 19.23/19.06 [2351]~E(x23511,x23512)+E(f264(x23513,x23514,x23511,x23515,x23516),f264(x23513,x23514,x23512,x23515,x23516)) % 19.23/19.06 [2352]~E(x23521,x23522)+E(f264(x23523,x23524,x23525,x23521,x23526),f264(x23523,x23524,x23525,x23522,x23526)) % 19.23/19.06 [2353]~E(x23531,x23532)+E(f264(x23533,x23534,x23535,x23536,x23531),f264(x23533,x23534,x23535,x23536,x23532)) % 19.23/19.06 [2354]~E(x23541,x23542)+E(f778(x23541,x23543,x23544),f778(x23542,x23543,x23544)) % 19.23/19.06 [2355]~E(x23551,x23552)+E(f778(x23553,x23551,x23554),f778(x23553,x23552,x23554)) % 19.23/19.06 [2356]~E(x23561,x23562)+E(f778(x23563,x23564,x23561),f778(x23563,x23564,x23562)) % 19.23/19.06 [2357]~E(x23571,x23572)+E(f710(x23571,x23573,x23574,x23575),f710(x23572,x23573,x23574,x23575)) % 19.23/19.06 [2358]~E(x23581,x23582)+E(f710(x23583,x23581,x23584,x23585),f710(x23583,x23582,x23584,x23585)) % 19.23/19.06 [2359]~E(x23591,x23592)+E(f710(x23593,x23594,x23591,x23595),f710(x23593,x23594,x23592,x23595)) % 19.23/19.06 [2360]~E(x23601,x23602)+E(f710(x23603,x23604,x23605,x23601),f710(x23603,x23604,x23605,x23602)) % 19.23/19.06 [2361]~E(x23611,x23612)+E(f760(x23611,x23613,x23614),f760(x23612,x23613,x23614)) % 19.23/19.06 [2362]~E(x23621,x23622)+E(f760(x23623,x23621,x23624),f760(x23623,x23622,x23624)) % 19.23/19.06 [2363]~E(x23631,x23632)+E(f760(x23633,x23634,x23631),f760(x23633,x23634,x23632)) % 19.23/19.06 [2364]~E(x23641,x23642)+E(f523(x23641,x23643,x23644,x23645),f523(x23642,x23643,x23644,x23645)) % 19.23/19.06 [2365]~E(x23651,x23652)+E(f523(x23653,x23651,x23654,x23655),f523(x23653,x23652,x23654,x23655)) % 19.23/19.06 [2366]~E(x23661,x23662)+E(f523(x23663,x23664,x23661,x23665),f523(x23663,x23664,x23662,x23665)) % 19.23/19.06 [2367]~E(x23671,x23672)+E(f523(x23673,x23674,x23675,x23671),f523(x23673,x23674,x23675,x23672)) % 19.23/19.06 [2368]~E(x23681,x23682)+E(f659(x23681,x23683,x23684,x23685,x23686),f659(x23682,x23683,x23684,x23685,x23686)) % 19.23/19.06 [2369]~E(x23691,x23692)+E(f659(x23693,x23691,x23694,x23695,x23696),f659(x23693,x23692,x23694,x23695,x23696)) % 19.23/19.06 [2370]~E(x23701,x23702)+E(f659(x23703,x23704,x23701,x23705,x23706),f659(x23703,x23704,x23702,x23705,x23706)) % 19.23/19.06 [2371]~E(x23711,x23712)+E(f659(x23713,x23714,x23715,x23711,x23716),f659(x23713,x23714,x23715,x23712,x23716)) % 19.23/19.06 [2372]~E(x23721,x23722)+E(f659(x23723,x23724,x23725,x23726,x23721),f659(x23723,x23724,x23725,x23726,x23722)) % 19.23/19.06 [2373]~E(x23731,x23732)+E(f754(x23731,x23733,x23734,x23735),f754(x23732,x23733,x23734,x23735)) % 19.23/19.06 [2374]~E(x23741,x23742)+E(f754(x23743,x23741,x23744,x23745),f754(x23743,x23742,x23744,x23745)) % 19.23/19.06 [2375]~E(x23751,x23752)+E(f754(x23753,x23754,x23751,x23755),f754(x23753,x23754,x23752,x23755)) % 19.23/19.06 [2376]~E(x23761,x23762)+E(f754(x23763,x23764,x23765,x23761),f754(x23763,x23764,x23765,x23762)) % 19.23/19.06 [2377]~E(x23771,x23772)+E(f501(x23771,x23773,x23774,x23775,x23776),f501(x23772,x23773,x23774,x23775,x23776)) % 19.23/19.06 [2378]~E(x23781,x23782)+E(f501(x23783,x23781,x23784,x23785,x23786),f501(x23783,x23782,x23784,x23785,x23786)) % 19.23/19.06 [2379]~E(x23791,x23792)+E(f501(x23793,x23794,x23791,x23795,x23796),f501(x23793,x23794,x23792,x23795,x23796)) % 19.23/19.06 [2380]~E(x23801,x23802)+E(f501(x23803,x23804,x23805,x23801,x23806),f501(x23803,x23804,x23805,x23802,x23806)) % 19.23/19.06 [2381]~E(x23811,x23812)+E(f501(x23813,x23814,x23815,x23816,x23811),f501(x23813,x23814,x23815,x23816,x23812)) % 19.23/19.06 [2382]~E(x23821,x23822)+E(f352(x23821,x23823),f352(x23822,x23823)) % 19.23/19.06 [2383]~E(x23831,x23832)+E(f352(x23833,x23831),f352(x23833,x23832)) % 19.23/19.06 [2384]~E(x23841,x23842)+E(f838(x23841,x23843,x23844,x23845,x23846),f838(x23842,x23843,x23844,x23845,x23846)) % 19.23/19.06 [2385]~E(x23851,x23852)+E(f838(x23853,x23851,x23854,x23855,x23856),f838(x23853,x23852,x23854,x23855,x23856)) % 19.23/19.06 [2386]~E(x23861,x23862)+E(f838(x23863,x23864,x23861,x23865,x23866),f838(x23863,x23864,x23862,x23865,x23866)) % 19.23/19.06 [2387]~E(x23871,x23872)+E(f838(x23873,x23874,x23875,x23871,x23876),f838(x23873,x23874,x23875,x23872,x23876)) % 19.23/19.06 [2388]~E(x23881,x23882)+E(f838(x23883,x23884,x23885,x23886,x23881),f838(x23883,x23884,x23885,x23886,x23882)) % 19.23/19.06 [2389]~E(x23891,x23892)+E(f846(x23891,x23893,x23894,x23895,x23896,x23897,x23898),f846(x23892,x23893,x23894,x23895,x23896,x23897,x23898)) % 19.23/19.06 [2390]~E(x23901,x23902)+E(f846(x23903,x23901,x23904,x23905,x23906,x23907,x23908),f846(x23903,x23902,x23904,x23905,x23906,x23907,x23908)) % 19.23/19.06 [2391]~E(x23911,x23912)+E(f846(x23913,x23914,x23911,x23915,x23916,x23917,x23918),f846(x23913,x23914,x23912,x23915,x23916,x23917,x23918)) % 19.23/19.06 [2392]~E(x23921,x23922)+E(f846(x23923,x23924,x23925,x23921,x23926,x23927,x23928),f846(x23923,x23924,x23925,x23922,x23926,x23927,x23928)) % 19.23/19.06 [2393]~E(x23931,x23932)+E(f846(x23933,x23934,x23935,x23936,x23931,x23937,x23938),f846(x23933,x23934,x23935,x23936,x23932,x23937,x23938)) % 19.23/19.06 [2394]~E(x23941,x23942)+E(f846(x23943,x23944,x23945,x23946,x23947,x23941,x23948),f846(x23943,x23944,x23945,x23946,x23947,x23942,x23948)) % 19.23/19.06 [2395]~E(x23951,x23952)+E(f846(x23953,x23954,x23955,x23956,x23957,x23958,x23951),f846(x23953,x23954,x23955,x23956,x23957,x23958,x23952)) % 19.23/19.06 [2396]~E(x23961,x23962)+E(f581(x23961,x23963),f581(x23962,x23963)) % 19.23/19.06 [2397]~E(x23971,x23972)+E(f581(x23973,x23971),f581(x23973,x23972)) % 19.23/19.06 [2398]~E(x23981,x23982)+E(f801(x23981),f801(x23982)) % 19.23/19.06 [2399]~E(x23991,x23992)+E(f371(x23991),f371(x23992)) % 19.23/19.06 [2400]~E(x24001,x24002)+E(f574(x24001,x24003,x24004,x24005,x24006),f574(x24002,x24003,x24004,x24005,x24006)) % 19.23/19.06 [2401]~E(x24011,x24012)+E(f574(x24013,x24011,x24014,x24015,x24016),f574(x24013,x24012,x24014,x24015,x24016)) % 19.23/19.06 [2402]~E(x24021,x24022)+E(f574(x24023,x24024,x24021,x24025,x24026),f574(x24023,x24024,x24022,x24025,x24026)) % 19.23/19.06 [2403]~E(x24031,x24032)+E(f574(x24033,x24034,x24035,x24031,x24036),f574(x24033,x24034,x24035,x24032,x24036)) % 19.23/19.06 [2404]~E(x24041,x24042)+E(f574(x24043,x24044,x24045,x24046,x24041),f574(x24043,x24044,x24045,x24046,x24042)) % 19.23/19.06 [2405]~E(x24051,x24052)+E(f57(x24051),f57(x24052)) % 19.23/19.06 [2406]~E(x24061,x24062)+E(f383(x24061,x24063,x24064),f383(x24062,x24063,x24064)) % 19.23/19.06 [2407]~E(x24071,x24072)+E(f383(x24073,x24071,x24074),f383(x24073,x24072,x24074)) % 19.23/19.06 [2408]~E(x24081,x24082)+E(f383(x24083,x24084,x24081),f383(x24083,x24084,x24082)) % 19.23/19.06 [2409]~E(x24091,x24092)+E(f739(x24091),f739(x24092)) % 19.23/19.06 [2410]~E(x24101,x24102)+E(f530(x24101,x24103,x24104,x24105,x24106,x24107),f530(x24102,x24103,x24104,x24105,x24106,x24107)) % 19.23/19.06 [2411]~E(x24111,x24112)+E(f530(x24113,x24111,x24114,x24115,x24116,x24117),f530(x24113,x24112,x24114,x24115,x24116,x24117)) % 19.23/19.06 [2412]~E(x24121,x24122)+E(f530(x24123,x24124,x24121,x24125,x24126,x24127),f530(x24123,x24124,x24122,x24125,x24126,x24127)) % 19.23/19.06 [2413]~E(x24131,x24132)+E(f530(x24133,x24134,x24135,x24131,x24136,x24137),f530(x24133,x24134,x24135,x24132,x24136,x24137)) % 19.23/19.06 [2414]~E(x24141,x24142)+E(f530(x24143,x24144,x24145,x24146,x24141,x24147),f530(x24143,x24144,x24145,x24146,x24142,x24147)) % 19.23/19.06 [2415]~E(x24151,x24152)+E(f530(x24153,x24154,x24155,x24156,x24157,x24151),f530(x24153,x24154,x24155,x24156,x24157,x24152)) % 19.23/19.06 [2416]~E(x24161,x24162)+E(f282(x24161),f282(x24162)) % 19.23/19.06 [2417]~E(x24171,x24172)+E(f212(x24171,x24173,x24174,x24175),f212(x24172,x24173,x24174,x24175)) % 19.23/19.06 [2418]~E(x24181,x24182)+E(f212(x24183,x24181,x24184,x24185),f212(x24183,x24182,x24184,x24185)) % 19.23/19.06 [2419]~E(x24191,x24192)+E(f212(x24193,x24194,x24191,x24195),f212(x24193,x24194,x24192,x24195)) % 19.23/19.06 [2420]~E(x24201,x24202)+E(f212(x24203,x24204,x24205,x24201),f212(x24203,x24204,x24205,x24202)) % 19.23/19.06 [2421]~E(x24211,x24212)+E(f24(x24211,x24213),f24(x24212,x24213)) % 19.23/19.06 [2422]~E(x24221,x24222)+E(f24(x24223,x24221),f24(x24223,x24222)) % 19.23/19.06 [2423]~E(x24231,x24232)+E(f774(x24231,x24233),f774(x24232,x24233)) % 19.23/19.06 [2424]~E(x24241,x24242)+E(f774(x24243,x24241),f774(x24243,x24242)) % 19.23/19.06 [2425]~E(x24251,x24252)+E(f617(x24251,x24253,x24254,x24255),f617(x24252,x24253,x24254,x24255)) % 19.23/19.06 [2426]~E(x24261,x24262)+E(f617(x24263,x24261,x24264,x24265),f617(x24263,x24262,x24264,x24265)) % 19.23/19.06 [2427]~E(x24271,x24272)+E(f617(x24273,x24274,x24271,x24275),f617(x24273,x24274,x24272,x24275)) % 19.23/19.06 [2428]~E(x24281,x24282)+E(f617(x24283,x24284,x24285,x24281),f617(x24283,x24284,x24285,x24282)) % 19.23/19.06 [2429]~E(x24291,x24292)+E(f356(x24291,x24293),f356(x24292,x24293)) % 19.23/19.06 [2430]~E(x24301,x24302)+E(f356(x24303,x24301),f356(x24303,x24302)) % 19.23/19.06 [2431]~E(x24311,x24312)+E(f435(x24311,x24313,x24314),f435(x24312,x24313,x24314)) % 19.23/19.06 [2432]~E(x24321,x24322)+E(f435(x24323,x24321,x24324),f435(x24323,x24322,x24324)) % 19.23/19.06 [2433]~E(x24331,x24332)+E(f435(x24333,x24334,x24331),f435(x24333,x24334,x24332)) % 19.23/19.06 [2434]~E(x24341,x24342)+E(f410(x24341,x24343,x24344),f410(x24342,x24343,x24344)) % 19.23/19.06 [2435]~E(x24351,x24352)+E(f410(x24353,x24351,x24354),f410(x24353,x24352,x24354)) % 19.23/19.06 [2436]~E(x24361,x24362)+E(f410(x24363,x24364,x24361),f410(x24363,x24364,x24362)) % 19.23/19.06 [2437]~E(x24371,x24372)+E(f433(x24371,x24373,x24374),f433(x24372,x24373,x24374)) % 19.23/19.06 [2438]~E(x24381,x24382)+E(f433(x24383,x24381,x24384),f433(x24383,x24382,x24384)) % 19.23/19.06 [2439]~E(x24391,x24392)+E(f433(x24393,x24394,x24391),f433(x24393,x24394,x24392)) % 19.23/19.06 [2440]~E(x24401,x24402)+E(f584(x24401,x24403,x24404,x24405,x24406,x24407),f584(x24402,x24403,x24404,x24405,x24406,x24407)) % 19.23/19.06 [2441]~E(x24411,x24412)+E(f584(x24413,x24411,x24414,x24415,x24416,x24417),f584(x24413,x24412,x24414,x24415,x24416,x24417)) % 19.23/19.06 [2442]~E(x24421,x24422)+E(f584(x24423,x24424,x24421,x24425,x24426,x24427),f584(x24423,x24424,x24422,x24425,x24426,x24427)) % 19.23/19.06 [2443]~E(x24431,x24432)+E(f584(x24433,x24434,x24435,x24431,x24436,x24437),f584(x24433,x24434,x24435,x24432,x24436,x24437)) % 19.23/19.06 [2444]~E(x24441,x24442)+E(f584(x24443,x24444,x24445,x24446,x24441,x24447),f584(x24443,x24444,x24445,x24446,x24442,x24447)) % 19.23/19.06 [2445]~E(x24451,x24452)+E(f584(x24453,x24454,x24455,x24456,x24457,x24451),f584(x24453,x24454,x24455,x24456,x24457,x24452)) % 19.23/19.06 [2446]~E(x24461,x24462)+E(f504(x24461,x24463,x24464,x24465,x24466),f504(x24462,x24463,x24464,x24465,x24466)) % 19.23/19.06 [2447]~E(x24471,x24472)+E(f504(x24473,x24471,x24474,x24475,x24476),f504(x24473,x24472,x24474,x24475,x24476)) % 19.23/19.06 [2448]~E(x24481,x24482)+E(f504(x24483,x24484,x24481,x24485,x24486),f504(x24483,x24484,x24482,x24485,x24486)) % 19.23/19.06 [2449]~E(x24491,x24492)+E(f504(x24493,x24494,x24495,x24491,x24496),f504(x24493,x24494,x24495,x24492,x24496)) % 19.23/19.06 [2450]~E(x24501,x24502)+E(f504(x24503,x24504,x24505,x24506,x24501),f504(x24503,x24504,x24505,x24506,x24502)) % 19.23/19.06 [2451]~E(x24511,x24512)+E(f587(x24511,x24513,x24514,x24515),f587(x24512,x24513,x24514,x24515)) % 19.23/19.06 [2452]~E(x24521,x24522)+E(f587(x24523,x24521,x24524,x24525),f587(x24523,x24522,x24524,x24525)) % 19.23/19.06 [2453]~E(x24531,x24532)+E(f587(x24533,x24534,x24531,x24535),f587(x24533,x24534,x24532,x24535)) % 19.23/19.06 [2454]~E(x24541,x24542)+E(f587(x24543,x24544,x24545,x24541),f587(x24543,x24544,x24545,x24542)) % 19.23/19.06 [2455]~E(x24551,x24552)+E(f457(x24551),f457(x24552)) % 19.23/19.06 [2456]~E(x24561,x24562)+E(f225(x24561,x24563,x24564),f225(x24562,x24563,x24564)) % 19.23/19.06 [2457]~E(x24571,x24572)+E(f225(x24573,x24571,x24574),f225(x24573,x24572,x24574)) % 19.23/19.06 [2458]~E(x24581,x24582)+E(f225(x24583,x24584,x24581),f225(x24583,x24584,x24582)) % 19.23/19.06 [2459]~E(x24591,x24592)+E(f805(x24591,x24593),f805(x24592,x24593)) % 19.23/19.06 [2460]~E(x24601,x24602)+E(f805(x24603,x24601),f805(x24603,x24602)) % 19.23/19.06 [2461]~E(x24611,x24612)+E(f481(x24611,x24613,x24614,x24615),f481(x24612,x24613,x24614,x24615)) % 19.23/19.06 [2462]~E(x24621,x24622)+E(f481(x24623,x24621,x24624,x24625),f481(x24623,x24622,x24624,x24625)) % 19.23/19.06 [2463]~E(x24631,x24632)+E(f481(x24633,x24634,x24631,x24635),f481(x24633,x24634,x24632,x24635)) % 19.23/19.06 [2464]~E(x24641,x24642)+E(f481(x24643,x24644,x24645,x24641),f481(x24643,x24644,x24645,x24642)) % 19.23/19.06 [2465]~E(x24651,x24652)+E(f210(x24651,x24653,x24654,x24655,x24656,x24657,x24658),f210(x24652,x24653,x24654,x24655,x24656,x24657,x24658)) % 19.23/19.06 [2466]~E(x24661,x24662)+E(f210(x24663,x24661,x24664,x24665,x24666,x24667,x24668),f210(x24663,x24662,x24664,x24665,x24666,x24667,x24668)) % 19.23/19.06 [2467]~E(x24671,x24672)+E(f210(x24673,x24674,x24671,x24675,x24676,x24677,x24678),f210(x24673,x24674,x24672,x24675,x24676,x24677,x24678)) % 19.23/19.06 [2468]~E(x24681,x24682)+E(f210(x24683,x24684,x24685,x24681,x24686,x24687,x24688),f210(x24683,x24684,x24685,x24682,x24686,x24687,x24688)) % 19.23/19.06 [2469]~E(x24691,x24692)+E(f210(x24693,x24694,x24695,x24696,x24691,x24697,x24698),f210(x24693,x24694,x24695,x24696,x24692,x24697,x24698)) % 19.23/19.06 [2470]~E(x24701,x24702)+E(f210(x24703,x24704,x24705,x24706,x24707,x24701,x24708),f210(x24703,x24704,x24705,x24706,x24707,x24702,x24708)) % 19.23/19.06 [2471]~E(x24711,x24712)+E(f210(x24713,x24714,x24715,x24716,x24717,x24718,x24711),f210(x24713,x24714,x24715,x24716,x24717,x24718,x24712)) % 19.23/19.06 [2472]~E(x24721,x24722)+E(f661(x24721,x24723),f661(x24722,x24723)) % 19.23/19.06 [2473]~E(x24731,x24732)+E(f661(x24733,x24731),f661(x24733,x24732)) % 19.23/19.06 [2474]~E(x24741,x24742)+E(f503(x24741,x24743,x24744,x24745,x24746),f503(x24742,x24743,x24744,x24745,x24746)) % 19.23/19.06 [2475]~E(x24751,x24752)+E(f503(x24753,x24751,x24754,x24755,x24756),f503(x24753,x24752,x24754,x24755,x24756)) % 19.23/19.06 [2476]~E(x24761,x24762)+E(f503(x24763,x24764,x24761,x24765,x24766),f503(x24763,x24764,x24762,x24765,x24766)) % 19.23/19.06 [2477]~E(x24771,x24772)+E(f503(x24773,x24774,x24775,x24771,x24776),f503(x24773,x24774,x24775,x24772,x24776)) % 19.23/19.06 [2478]~E(x24781,x24782)+E(f503(x24783,x24784,x24785,x24786,x24781),f503(x24783,x24784,x24785,x24786,x24782)) % 19.23/19.06 [2479]~E(x24791,x24792)+E(f608(x24791,x24793,x24794),f608(x24792,x24793,x24794)) % 19.23/19.06 [2480]~E(x24801,x24802)+E(f608(x24803,x24801,x24804),f608(x24803,x24802,x24804)) % 19.23/19.06 [2481]~E(x24811,x24812)+E(f608(x24813,x24814,x24811),f608(x24813,x24814,x24812)) % 19.23/19.06 [2482]~E(x24821,x24822)+E(f321(x24821,x24823,x24824),f321(x24822,x24823,x24824)) % 19.23/19.06 [2483]~E(x24831,x24832)+E(f321(x24833,x24831,x24834),f321(x24833,x24832,x24834)) % 19.23/19.06 [2484]~E(x24841,x24842)+E(f321(x24843,x24844,x24841),f321(x24843,x24844,x24842)) % 19.23/19.06 [2485]~E(x24851,x24852)+E(f366(x24851,x24853,x24854,x24855,x24856),f366(x24852,x24853,x24854,x24855,x24856)) % 19.23/19.06 [2486]~E(x24861,x24862)+E(f366(x24863,x24861,x24864,x24865,x24866),f366(x24863,x24862,x24864,x24865,x24866)) % 19.23/19.06 [2487]~E(x24871,x24872)+E(f366(x24873,x24874,x24871,x24875,x24876),f366(x24873,x24874,x24872,x24875,x24876)) % 19.23/19.06 [2488]~E(x24881,x24882)+E(f366(x24883,x24884,x24885,x24881,x24886),f366(x24883,x24884,x24885,x24882,x24886)) % 19.23/19.06 [2489]~E(x24891,x24892)+E(f366(x24893,x24894,x24895,x24896,x24891),f366(x24893,x24894,x24895,x24896,x24892)) % 19.23/19.06 [2490]~E(x24901,x24902)+E(f452(x24901,x24903,x24904,x24905),f452(x24902,x24903,x24904,x24905)) % 19.23/19.06 [2491]~E(x24911,x24912)+E(f452(x24913,x24911,x24914,x24915),f452(x24913,x24912,x24914,x24915)) % 19.23/19.06 [2492]~E(x24921,x24922)+E(f452(x24923,x24924,x24921,x24925),f452(x24923,x24924,x24922,x24925)) % 19.23/19.06 [2493]~E(x24931,x24932)+E(f452(x24933,x24934,x24935,x24931),f452(x24933,x24934,x24935,x24932)) % 19.23/19.06 [2494]~E(x24941,x24942)+E(f716(x24941,x24943,x24944,x24945),f716(x24942,x24943,x24944,x24945)) % 19.23/19.06 [2495]~E(x24951,x24952)+E(f716(x24953,x24951,x24954,x24955),f716(x24953,x24952,x24954,x24955)) % 19.23/19.06 [2496]~E(x24961,x24962)+E(f716(x24963,x24964,x24961,x24965),f716(x24963,x24964,x24962,x24965)) % 19.23/19.06 [2497]~E(x24971,x24972)+E(f716(x24973,x24974,x24975,x24971),f716(x24973,x24974,x24975,x24972)) % 19.23/19.06 [2498]~E(x24981,x24982)+E(f580(x24981,x24983),f580(x24982,x24983)) % 19.23/19.06 [2499]~E(x24991,x24992)+E(f580(x24993,x24991),f580(x24993,x24992)) % 19.23/19.06 [2500]~E(x25001,x25002)+E(f773(x25001),f773(x25002)) % 19.23/19.06 [2501]~E(x25011,x25012)+E(f280(x25011,x25013,x25014,x25015),f280(x25012,x25013,x25014,x25015)) % 19.23/19.06 [2502]~E(x25021,x25022)+E(f280(x25023,x25021,x25024,x25025),f280(x25023,x25022,x25024,x25025)) % 19.23/19.06 [2503]~E(x25031,x25032)+E(f280(x25033,x25034,x25031,x25035),f280(x25033,x25034,x25032,x25035)) % 19.23/19.06 [2504]~E(x25041,x25042)+E(f280(x25043,x25044,x25045,x25041),f280(x25043,x25044,x25045,x25042)) % 19.23/19.06 [2505]~E(x25051,x25052)+E(f756(x25051),f756(x25052)) % 19.23/19.06 [2506]~E(x25061,x25062)+E(f822(x25061,x25063,x25064),f822(x25062,x25063,x25064)) % 19.23/19.06 [2507]~E(x25071,x25072)+E(f822(x25073,x25071,x25074),f822(x25073,x25072,x25074)) % 19.23/19.06 [2508]~E(x25081,x25082)+E(f822(x25083,x25084,x25081),f822(x25083,x25084,x25082)) % 19.23/19.06 [2509]~E(x25091,x25092)+E(f385(x25091,x25093,x25094,x25095),f385(x25092,x25093,x25094,x25095)) % 19.23/19.06 [2510]~E(x25101,x25102)+E(f385(x25103,x25101,x25104,x25105),f385(x25103,x25102,x25104,x25105)) % 19.23/19.06 [2511]~E(x25111,x25112)+E(f385(x25113,x25114,x25111,x25115),f385(x25113,x25114,x25112,x25115)) % 19.23/19.06 [2512]~E(x25121,x25122)+E(f385(x25123,x25124,x25125,x25121),f385(x25123,x25124,x25125,x25122)) % 19.23/19.06 [2513]~E(x25131,x25132)+E(f392(x25131,x25133),f392(x25132,x25133)) % 19.23/19.06 [2514]~E(x25141,x25142)+E(f392(x25143,x25141),f392(x25143,x25142)) % 19.23/19.06 [2515]~E(x25151,x25152)+E(f553(x25151),f553(x25152)) % 19.23/19.06 [2516]~E(x25161,x25162)+E(f393(x25161,x25163,x25164),f393(x25162,x25163,x25164)) % 19.23/19.06 [2517]~E(x25171,x25172)+E(f393(x25173,x25171,x25174),f393(x25173,x25172,x25174)) % 19.23/19.06 [2518]~E(x25181,x25182)+E(f393(x25183,x25184,x25181),f393(x25183,x25184,x25182)) % 19.23/19.06 [2519]~E(x25191,x25192)+E(f499(x25191,x25193,x25194,x25195,x25196),f499(x25192,x25193,x25194,x25195,x25196)) % 19.23/19.06 [2520]~E(x25201,x25202)+E(f499(x25203,x25201,x25204,x25205,x25206),f499(x25203,x25202,x25204,x25205,x25206)) % 19.23/19.06 [2521]~E(x25211,x25212)+E(f499(x25213,x25214,x25211,x25215,x25216),f499(x25213,x25214,x25212,x25215,x25216)) % 19.23/19.06 [2522]~E(x25221,x25222)+E(f499(x25223,x25224,x25225,x25221,x25226),f499(x25223,x25224,x25225,x25222,x25226)) % 19.23/19.06 [2523]~E(x25231,x25232)+E(f499(x25233,x25234,x25235,x25236,x25231),f499(x25233,x25234,x25235,x25236,x25232)) % 19.23/19.06 [2524]~E(x25241,x25242)+E(f713(x25241,x25243,x25244,x25245,x25246),f713(x25242,x25243,x25244,x25245,x25246)) % 19.23/19.06 [2525]~E(x25251,x25252)+E(f713(x25253,x25251,x25254,x25255,x25256),f713(x25253,x25252,x25254,x25255,x25256)) % 19.23/19.06 [2526]~E(x25261,x25262)+E(f713(x25263,x25264,x25261,x25265,x25266),f713(x25263,x25264,x25262,x25265,x25266)) % 19.23/19.06 [2527]~E(x25271,x25272)+E(f713(x25273,x25274,x25275,x25271,x25276),f713(x25273,x25274,x25275,x25272,x25276)) % 19.23/19.06 [2528]~E(x25281,x25282)+E(f713(x25283,x25284,x25285,x25286,x25281),f713(x25283,x25284,x25285,x25286,x25282)) % 19.23/19.06 [2529]~E(x25291,x25292)+E(f228(x25291,x25293,x25294,x25295,x25296),f228(x25292,x25293,x25294,x25295,x25296)) % 19.23/19.06 [2530]~E(x25301,x25302)+E(f228(x25303,x25301,x25304,x25305,x25306),f228(x25303,x25302,x25304,x25305,x25306)) % 19.23/19.06 [2531]~E(x25311,x25312)+E(f228(x25313,x25314,x25311,x25315,x25316),f228(x25313,x25314,x25312,x25315,x25316)) % 19.23/19.06 [2532]~E(x25321,x25322)+E(f228(x25323,x25324,x25325,x25321,x25326),f228(x25323,x25324,x25325,x25322,x25326)) % 19.23/19.06 [2533]~E(x25331,x25332)+E(f228(x25333,x25334,x25335,x25336,x25331),f228(x25333,x25334,x25335,x25336,x25332)) % 19.23/19.06 [2534]~E(x25341,x25342)+E(f607(x25341,x25343),f607(x25342,x25343)) % 19.23/19.06 [2535]~E(x25351,x25352)+E(f607(x25353,x25351),f607(x25353,x25352)) % 19.23/19.06 [2536]~E(x25361,x25362)+E(f104(x25361,x25363,x25364,x25365),f104(x25362,x25363,x25364,x25365)) % 19.23/19.06 [2537]~E(x25371,x25372)+E(f104(x25373,x25371,x25374,x25375),f104(x25373,x25372,x25374,x25375)) % 19.23/19.06 [2538]~E(x25381,x25382)+E(f104(x25383,x25384,x25381,x25385),f104(x25383,x25384,x25382,x25385)) % 19.23/19.06 [2539]~E(x25391,x25392)+E(f104(x25393,x25394,x25395,x25391),f104(x25393,x25394,x25395,x25392)) % 19.23/19.06 [2540]~E(x25401,x25402)+E(f579(x25401,x25403),f579(x25402,x25403)) % 19.23/19.06 [2541]~E(x25411,x25412)+E(f579(x25413,x25411),f579(x25413,x25412)) % 19.23/19.06 [2542]~E(x25421,x25422)+E(f771(x25421),f771(x25422)) % 19.23/19.06 [2543]~E(x25431,x25432)+E(f567(x25431),f567(x25432)) % 19.23/19.06 [2544]~E(x25441,x25442)+E(f839(x25441,x25443,x25444),f839(x25442,x25443,x25444)) % 19.23/19.06 [2545]~E(x25451,x25452)+E(f839(x25453,x25451,x25454),f839(x25453,x25452,x25454)) % 19.23/19.06 [2546]~E(x25461,x25462)+E(f839(x25463,x25464,x25461),f839(x25463,x25464,x25462)) % 19.23/19.06 [2547]~E(x25471,x25472)+E(f348(x25471,x25473),f348(x25472,x25473)) % 19.23/19.06 [2548]~E(x25481,x25482)+E(f348(x25483,x25481),f348(x25483,x25482)) % 19.23/19.06 [2549]~E(x25491,x25492)+E(f226(x25491,x25493,x25494,x25495,x25496),f226(x25492,x25493,x25494,x25495,x25496)) % 19.23/19.06 [2550]~E(x25501,x25502)+E(f226(x25503,x25501,x25504,x25505,x25506),f226(x25503,x25502,x25504,x25505,x25506)) % 19.23/19.06 [2551]~E(x25511,x25512)+E(f226(x25513,x25514,x25511,x25515,x25516),f226(x25513,x25514,x25512,x25515,x25516)) % 19.23/19.06 [2552]~E(x25521,x25522)+E(f226(x25523,x25524,x25525,x25521,x25526),f226(x25523,x25524,x25525,x25522,x25526)) % 19.23/19.06 [2553]~E(x25531,x25532)+E(f226(x25533,x25534,x25535,x25536,x25531),f226(x25533,x25534,x25535,x25536,x25532)) % 19.23/19.06 [2554]~E(x25541,x25542)+E(f576(x25541,x25543),f576(x25542,x25543)) % 19.23/19.06 [2555]~E(x25551,x25552)+E(f576(x25553,x25551),f576(x25553,x25552)) % 19.23/19.06 [2556]~E(x25561,x25562)+E(f347(x25561,x25563),f347(x25562,x25563)) % 19.23/19.06 [2557]~E(x25571,x25572)+E(f347(x25573,x25571),f347(x25573,x25572)) % 19.23/19.06 [2558]~P1(x25581)+P1(x25582)+~E(x25581,x25582) % 19.23/19.06 [2559]~P85(x25591)+P85(x25592)+~E(x25591,x25592) % 19.23/19.06 [2560]P14(x25602,x25603,x25604,x25605,x25606,x25607)+~E(x25601,x25602)+~P14(x25601,x25603,x25604,x25605,x25606,x25607) % 19.23/19.06 [2561]P14(x25613,x25612,x25614,x25615,x25616,x25617)+~E(x25611,x25612)+~P14(x25613,x25611,x25614,x25615,x25616,x25617) % 19.23/19.06 [2562]P14(x25623,x25624,x25622,x25625,x25626,x25627)+~E(x25621,x25622)+~P14(x25623,x25624,x25621,x25625,x25626,x25627) % 19.23/19.06 [2563]P14(x25633,x25634,x25635,x25632,x25636,x25637)+~E(x25631,x25632)+~P14(x25633,x25634,x25635,x25631,x25636,x25637) % 19.23/19.06 [2564]P14(x25643,x25644,x25645,x25646,x25642,x25647)+~E(x25641,x25642)+~P14(x25643,x25644,x25645,x25646,x25641,x25647) % 19.23/19.06 [2565]P14(x25653,x25654,x25655,x25656,x25657,x25652)+~E(x25651,x25652)+~P14(x25653,x25654,x25655,x25656,x25657,x25651) % 19.23/19.06 [2566]P9(x25662,x25663,x25664)+~E(x25661,x25662)+~P9(x25661,x25663,x25664) % 19.23/19.06 [2567]P9(x25673,x25672,x25674)+~E(x25671,x25672)+~P9(x25673,x25671,x25674) % 19.23/19.06 [2568]P9(x25683,x25684,x25682)+~E(x25681,x25682)+~P9(x25683,x25684,x25681) % 19.23/19.06 [2569]~P2(x25691)+P2(x25692)+~E(x25691,x25692) % 19.23/19.06 [2570]~P101(x25701)+P101(x25702)+~E(x25701,x25702) % 19.23/19.06 [2571]~P112(x25711)+P112(x25712)+~E(x25711,x25712) % 19.23/19.06 [2572]~P63(x25721)+P63(x25722)+~E(x25721,x25722) % 19.23/19.06 [2573]~P10(x25731)+P10(x25732)+~E(x25731,x25732) % 19.23/19.06 [2574]~P103(x25741)+P103(x25742)+~E(x25741,x25742) % 19.23/19.06 [2575]~P64(x25751)+P64(x25752)+~E(x25751,x25752) % 19.23/19.06 [2576]~P98(x25761)+P98(x25762)+~E(x25761,x25762) % 19.23/19.06 [2577]~P120(x25771)+P120(x25772)+~E(x25771,x25772) % 19.23/19.06 [2578]~P67(x25781)+P67(x25782)+~E(x25781,x25782) % 19.23/19.06 [2579]~P68(x25791)+P68(x25792)+~E(x25791,x25792) % 19.23/19.06 [2580]~P69(x25801)+P69(x25802)+~E(x25801,x25802) % 19.23/19.06 [2581]~P4(x25811)+P4(x25812)+~E(x25811,x25812) % 19.23/19.06 [2582]P38(x25822,x25823,x25824,x25825)+~E(x25821,x25822)+~P38(x25821,x25823,x25824,x25825) % 19.23/19.06 [2583]P38(x25833,x25832,x25834,x25835)+~E(x25831,x25832)+~P38(x25833,x25831,x25834,x25835) % 19.23/19.06 [2584]P38(x25843,x25844,x25842,x25845)+~E(x25841,x25842)+~P38(x25843,x25844,x25841,x25845) % 19.23/19.06 [2585]P38(x25853,x25854,x25855,x25852)+~E(x25851,x25852)+~P38(x25853,x25854,x25855,x25851) % 19.23/19.06 [2586]~P122(x25861)+P122(x25862)+~E(x25861,x25862) % 19.23/19.06 [2587]~P74(x25871)+P74(x25872)+~E(x25871,x25872) % 19.23/19.06 [2588]~P86(x25881)+P86(x25882)+~E(x25881,x25882) % 19.23/19.06 [2589]P35(x25892,x25893)+~E(x25891,x25892)+~P35(x25891,x25893) % 19.23/19.06 [2590]P35(x25903,x25902)+~E(x25901,x25902)+~P35(x25903,x25901) % 19.23/19.06 [2591]~P125(x25911)+P125(x25912)+~E(x25911,x25912) % 19.23/19.06 [2592]~P111(x25921)+P111(x25922)+~E(x25921,x25922) % 19.23/19.06 [2593]~P61(x25931)+P61(x25932)+~E(x25931,x25932) % 19.23/19.06 [2594]~P104(x25941)+P104(x25942)+~E(x25941,x25942) % 19.23/19.06 [2595]~P81(x25951)+P81(x25952)+~E(x25951,x25952) % 19.23/19.06 [2596]~P62(x25961)+P62(x25962)+~E(x25961,x25962) % 19.23/19.06 [2597]P142(x25972,x25973,x25974)+~E(x25971,x25972)+~P142(x25971,x25973,x25974) % 19.23/19.06 [2598]P142(x25983,x25982,x25984)+~E(x25981,x25982)+~P142(x25983,x25981,x25984) % 19.23/19.06 [2599]P142(x25993,x25994,x25992)+~E(x25991,x25992)+~P142(x25993,x25994,x25991) % 19.23/19.06 [2600]~P77(x26001)+P77(x26002)+~E(x26001,x26002) % 19.23/19.06 [2601]~P99(x26011)+P99(x26012)+~E(x26011,x26012) % 19.23/19.06 [2602]~P80(x26021)+P80(x26022)+~E(x26021,x26022) % 19.23/19.06 [2603]P143(x26032,x26033,x26034)+~E(x26031,x26032)+~P143(x26031,x26033,x26034) % 19.23/19.06 [2604]P143(x26043,x26042,x26044)+~E(x26041,x26042)+~P143(x26043,x26041,x26044) % 19.23/19.06 [2605]P143(x26053,x26054,x26052)+~E(x26051,x26052)+~P143(x26053,x26054,x26051) % 19.23/19.06 [2606]P33(x26062,x26063,x26064,x26065)+~E(x26061,x26062)+~P33(x26061,x26063,x26064,x26065) % 19.23/19.06 [2607]P33(x26073,x26072,x26074,x26075)+~E(x26071,x26072)+~P33(x26073,x26071,x26074,x26075) % 19.23/19.06 [2608]P33(x26083,x26084,x26082,x26085)+~E(x26081,x26082)+~P33(x26083,x26084,x26081,x26085) % 19.23/19.06 [2609]P33(x26093,x26094,x26095,x26092)+~E(x26091,x26092)+~P33(x26093,x26094,x26095,x26091) % 19.23/19.06 [2610]~P89(x26101)+P89(x26102)+~E(x26101,x26102) % 19.23/19.06 [2611]~P113(x26111)+P113(x26112)+~E(x26111,x26112) % 19.23/19.06 [2612]P26(x26122,x26123,x26124,x26125)+~E(x26121,x26122)+~P26(x26121,x26123,x26124,x26125) % 19.23/19.06 [2613]P26(x26133,x26132,x26134,x26135)+~E(x26131,x26132)+~P26(x26133,x26131,x26134,x26135) % 19.23/19.06 [2614]P26(x26143,x26144,x26142,x26145)+~E(x26141,x26142)+~P26(x26143,x26144,x26141,x26145) % 19.23/19.06 [2615]P26(x26153,x26154,x26155,x26152)+~E(x26151,x26152)+~P26(x26153,x26154,x26155,x26151) % 19.23/19.06 [2616]~P90(x26161)+P90(x26162)+~E(x26161,x26162) % 19.23/19.06 [2617]~P59(x26171)+P59(x26172)+~E(x26171,x26172) % 19.23/19.06 [2618]~P130(x26181)+P130(x26182)+~E(x26181,x26182) % 19.23/19.06 [2619]~P71(x26191)+P71(x26192)+~E(x26191,x26192) % 19.23/19.06 [2620]~P87(x26201)+P87(x26202)+~E(x26201,x26202) % 19.23/19.06 [2621]~P115(x26211)+P115(x26212)+~E(x26211,x26212) % 19.23/19.06 [2622]~P109(x26221)+P109(x26222)+~E(x26221,x26222) % 19.23/19.06 [2623]~P100(x26231)+P100(x26232)+~E(x26231,x26232) % 19.23/19.06 [2624]~P95(x26241)+P95(x26242)+~E(x26241,x26242) % 19.23/19.06 [2625]P19(x26252,x26253,x26254)+~E(x26251,x26252)+~P19(x26251,x26253,x26254) % 19.23/19.06 [2626]P19(x26263,x26262,x26264)+~E(x26261,x26262)+~P19(x26263,x26261,x26264) % 19.23/19.06 [2627]P19(x26273,x26274,x26272)+~E(x26271,x26272)+~P19(x26273,x26274,x26271) % 19.23/19.06 [2628]P15(x26282,x26283)+~E(x26281,x26282)+~P15(x26281,x26283) % 19.23/19.06 [2629]P15(x26293,x26292)+~E(x26291,x26292)+~P15(x26293,x26291) % 19.23/19.06 [2630]~P139(x26301)+P139(x26302)+~E(x26301,x26302) % 19.23/19.06 [2631]P41(x26312,x26313)+~E(x26311,x26312)+~P41(x26311,x26313) % 19.23/19.06 [2632]P41(x26323,x26322)+~E(x26321,x26322)+~P41(x26323,x26321) % 19.23/19.06 [2633]P8(x26332,x26333)+~E(x26331,x26332)+~P8(x26331,x26333) % 19.23/19.06 [2634]P8(x26343,x26342)+~E(x26341,x26342)+~P8(x26343,x26341) % 19.23/19.06 [2635]~P6(x26351)+P6(x26352)+~E(x26351,x26352) % 19.23/19.06 [2636]~P127(x26361)+P127(x26362)+~E(x26361,x26362) % 19.23/19.06 [2637]P47(x26372,x26373)+~E(x26371,x26372)+~P47(x26371,x26373) % 19.23/19.06 [2638]P47(x26383,x26382)+~E(x26381,x26382)+~P47(x26383,x26381) % 19.23/19.06 [2639]~P79(x26391)+P79(x26392)+~E(x26391,x26392) % 19.23/19.06 [2640]P43(x26402,x26403)+~E(x26401,x26402)+~P43(x26401,x26403) % 19.23/19.06 [2641]P43(x26413,x26412)+~E(x26411,x26412)+~P43(x26413,x26411) % 19.23/19.06 [2642]~P37(x26421)+P37(x26422)+~E(x26421,x26422) % 19.23/19.06 [2643]~P70(x26431)+P70(x26432)+~E(x26431,x26432) % 19.23/19.06 [2644]~P135(x26441)+P135(x26442)+~E(x26441,x26442) % 19.23/19.06 [2645]~P123(x26451)+P123(x26452)+~E(x26451,x26452) % 19.23/19.06 [2646]P44(x26462,x26463,x26464)+~E(x26461,x26462)+~P44(x26461,x26463,x26464) % 19.23/19.06 [2647]P44(x26473,x26472,x26474)+~E(x26471,x26472)+~P44(x26473,x26471,x26474) % 19.23/19.06 [2648]P44(x26483,x26484,x26482)+~E(x26481,x26482)+~P44(x26483,x26484,x26481) % 19.23/19.06 [2649]~P114(x26491)+P114(x26492)+~E(x26491,x26492) % 19.23/19.06 [2650]~P136(x26501)+P136(x26502)+~E(x26501,x26502) % 19.23/19.06 [2651]~P105(x26511)+P105(x26512)+~E(x26511,x26512) % 19.23/19.06 [2652]~P88(x26521)+P88(x26522)+~E(x26521,x26522) % 19.23/19.06 [2653]~P60(x26531)+P60(x26532)+~E(x26531,x26532) % 19.23/19.06 [2654]~P75(x26541)+P75(x26542)+~E(x26541,x26542) % 19.23/19.06 [2655]~P7(x26551)+P7(x26552)+~E(x26551,x26552) % 19.23/19.06 [2656]P57(x26562,x26563)+~E(x26561,x26562)+~P57(x26561,x26563) % 19.23/19.06 [2657]P57(x26573,x26572)+~E(x26571,x26572)+~P57(x26573,x26571) % 19.23/19.06 [2658]~P72(x26581)+P72(x26582)+~E(x26581,x26582) % 19.23/19.06 [2659]P27(x26592,x26593)+~E(x26591,x26592)+~P27(x26591,x26593) % 19.23/19.06 [2660]P27(x26603,x26602)+~E(x26601,x26602)+~P27(x26603,x26601) % 19.23/19.06 [2661]P16(x26612,x26613,x26614)+~E(x26611,x26612)+~P16(x26611,x26613,x26614) % 19.23/19.06 [2662]P16(x26623,x26622,x26624)+~E(x26621,x26622)+~P16(x26623,x26621,x26624) % 19.23/19.06 [2663]P16(x26633,x26634,x26632)+~E(x26631,x26632)+~P16(x26633,x26634,x26631) % 19.23/19.06 [2664]~P76(x26641)+P76(x26642)+~E(x26641,x26642) % 19.23/19.06 [2665]P52(x26652,x26653,x26654)+~E(x26651,x26652)+~P52(x26651,x26653,x26654) % 19.23/19.06 [2666]P52(x26663,x26662,x26664)+~E(x26661,x26662)+~P52(x26663,x26661,x26664) % 19.23/19.06 [2667]P52(x26673,x26674,x26672)+~E(x26671,x26672)+~P52(x26673,x26674,x26671) % 19.23/19.06 [2668]P17(x26682,x26683,x26684)+~E(x26681,x26682)+~P17(x26681,x26683,x26684) % 19.23/19.06 [2669]P17(x26693,x26692,x26694)+~E(x26691,x26692)+~P17(x26693,x26691,x26694) % 19.23/19.06 [2670]P17(x26703,x26704,x26702)+~E(x26701,x26702)+~P17(x26703,x26704,x26701) % 19.23/19.06 [2671]~P65(x26711)+P65(x26712)+~E(x26711,x26712) % 19.23/19.06 [2672]~P110(x26721)+P110(x26722)+~E(x26721,x26722) % 19.23/19.06 [2673]P55(x26732,x26733)+~E(x26731,x26732)+~P55(x26731,x26733) % 19.23/19.06 [2674]P55(x26743,x26742)+~E(x26741,x26742)+~P55(x26743,x26741) % 19.23/19.06 [2675]~P117(x26751)+P117(x26752)+~E(x26751,x26752) % 19.23/19.06 [2676]~P3(x26761)+P3(x26762)+~E(x26761,x26762) % 19.23/19.06 [2677]~P124(x26771)+P124(x26772)+~E(x26771,x26772) % 19.23/19.06 [2678]~P78(x26781)+P78(x26782)+~E(x26781,x26782) % 19.23/19.06 [2679]P18(x26792,x26793,x26794)+~E(x26791,x26792)+~P18(x26791,x26793,x26794) % 19.23/19.06 [2680]P18(x26803,x26802,x26804)+~E(x26801,x26802)+~P18(x26803,x26801,x26804) % 19.23/19.06 [2681]P18(x26813,x26814,x26812)+~E(x26811,x26812)+~P18(x26813,x26814,x26811) % 19.23/19.06 [2682]~P137(x26821)+P137(x26822)+~E(x26821,x26822) % 19.23/19.06 [2683]~P129(x26831)+P129(x26832)+~E(x26831,x26832) % 19.23/19.06 [2684]~P91(x26841)+P91(x26842)+~E(x26841,x26842) % 19.23/19.06 [2685]P32(x26852,x26853)+~E(x26851,x26852)+~P32(x26851,x26853) % 19.23/19.06 [2686]P32(x26863,x26862)+~E(x26861,x26862)+~P32(x26863,x26861) % 19.23/19.06 [2687]~P140(x26871)+P140(x26872)+~E(x26871,x26872) % 19.23/19.06 [2688]P28(x26882,x26883,x26884)+~E(x26881,x26882)+~P28(x26881,x26883,x26884) % 19.23/19.06 [2689]P28(x26893,x26892,x26894)+~E(x26891,x26892)+~P28(x26893,x26891,x26894) % 19.23/19.06 [2690]P28(x26903,x26904,x26902)+~E(x26901,x26902)+~P28(x26903,x26904,x26901) % 19.23/19.06 [2691]P48(x26912,x26913)+~E(x26911,x26912)+~P48(x26911,x26913) % 19.23/19.06 [2692]P48(x26923,x26922)+~E(x26921,x26922)+~P48(x26923,x26921) % 19.23/19.06 [2693]~P138(x26931)+P138(x26932)+~E(x26931,x26932) % 19.23/19.06 [2694]P25(x26942,x26943,x26944)+~E(x26941,x26942)+~P25(x26941,x26943,x26944) % 19.23/19.06 [2695]P25(x26953,x26952,x26954)+~E(x26951,x26952)+~P25(x26953,x26951,x26954) % 19.23/19.06 [2696]P25(x26963,x26964,x26962)+~E(x26961,x26962)+~P25(x26963,x26964,x26961) % 19.23/19.06 [2697]P46(x26972,x26973,x26974)+~E(x26971,x26972)+~P46(x26971,x26973,x26974) % 19.23/19.06 [2698]P46(x26983,x26982,x26984)+~E(x26981,x26982)+~P46(x26983,x26981,x26984) % 19.23/19.06 [2699]P46(x26993,x26994,x26992)+~E(x26991,x26992)+~P46(x26993,x26994,x26991) % 19.23/19.06 [2700]P30(x27002,x27003,x27004)+~E(x27001,x27002)+~P30(x27001,x27003,x27004) % 19.23/19.06 [2701]P30(x27013,x27012,x27014)+~E(x27011,x27012)+~P30(x27013,x27011,x27014) % 19.23/19.06 [2702]P30(x27023,x27024,x27022)+~E(x27021,x27022)+~P30(x27023,x27024,x27021) % 19.23/19.06 [2703]~P116(x27031)+P116(x27032)+~E(x27031,x27032) % 19.23/19.06 [2704]~P58(x27041)+P58(x27042)+~E(x27041,x27042) % 19.23/19.06 [2705]~P121(x27051)+P121(x27052)+~E(x27051,x27052) % 19.23/19.06 [2706]~P106(x27061)+P106(x27062)+~E(x27061,x27062) % 19.23/19.06 [2707]~P96(x27071)+P96(x27072)+~E(x27071,x27072) % 19.23/19.06 [2708]P21(x27082,x27083,x27084,x27085)+~E(x27081,x27082)+~P21(x27081,x27083,x27084,x27085) % 19.23/19.06 [2709]P21(x27093,x27092,x27094,x27095)+~E(x27091,x27092)+~P21(x27093,x27091,x27094,x27095) % 19.23/19.06 [2710]P21(x27103,x27104,x27102,x27105)+~E(x27101,x27102)+~P21(x27103,x27104,x27101,x27105) % 19.23/19.06 [2711]P21(x27113,x27114,x27115,x27112)+~E(x27111,x27112)+~P21(x27113,x27114,x27115,x27111) % 19.23/19.06 [2712]P49(x27122,x27123,x27124,x27125)+~E(x27121,x27122)+~P49(x27121,x27123,x27124,x27125) % 19.23/19.06 [2713]P49(x27133,x27132,x27134,x27135)+~E(x27131,x27132)+~P49(x27133,x27131,x27134,x27135) % 19.23/19.06 [2714]P49(x27143,x27144,x27142,x27145)+~E(x27141,x27142)+~P49(x27143,x27144,x27141,x27145) % 19.23/19.06 [2715]P49(x27153,x27154,x27155,x27152)+~E(x27151,x27152)+~P49(x27153,x27154,x27155,x27151) % 19.23/19.06 [2716]~P118(x27161)+P118(x27162)+~E(x27161,x27162) % 19.23/19.06 [2717]~P92(x27171)+P92(x27172)+~E(x27171,x27172) % 19.23/19.06 [2718]P40(x27182,x27183,x27184,x27185,x27186,x27187)+~E(x27181,x27182)+~P40(x27181,x27183,x27184,x27185,x27186,x27187) % 19.23/19.06 [2719]P40(x27193,x27192,x27194,x27195,x27196,x27197)+~E(x27191,x27192)+~P40(x27193,x27191,x27194,x27195,x27196,x27197) % 19.23/19.06 [2720]P40(x27203,x27204,x27202,x27205,x27206,x27207)+~E(x27201,x27202)+~P40(x27203,x27204,x27201,x27205,x27206,x27207) % 19.23/19.06 [2721]P40(x27213,x27214,x27215,x27212,x27216,x27217)+~E(x27211,x27212)+~P40(x27213,x27214,x27215,x27211,x27216,x27217) % 19.23/19.06 [2722]P40(x27223,x27224,x27225,x27226,x27222,x27227)+~E(x27221,x27222)+~P40(x27223,x27224,x27225,x27226,x27221,x27227) % 19.23/19.06 [2723]P40(x27233,x27234,x27235,x27236,x27237,x27232)+~E(x27231,x27232)+~P40(x27233,x27234,x27235,x27236,x27237,x27231) % 19.23/19.06 [2724]~P82(x27241)+P82(x27242)+~E(x27241,x27242) % 19.23/19.06 [2725]~P126(x27251)+P126(x27252)+~E(x27251,x27252) % 19.23/19.06 [2726]P31(x27262,x27263,x27264)+~E(x27261,x27262)+~P31(x27261,x27263,x27264) % 19.23/19.06 [2727]P31(x27273,x27272,x27274)+~E(x27271,x27272)+~P31(x27273,x27271,x27274) % 19.23/19.06 [2728]P31(x27283,x27284,x27282)+~E(x27281,x27282)+~P31(x27283,x27284,x27281) % 19.23/19.06 [2729]~P131(x27291)+P131(x27292)+~E(x27291,x27292) % 19.23/19.06 [2730]~P5(x27301)+P5(x27302)+~E(x27301,x27302) % 19.23/19.06 [2731]P50(x27312,x27313,x27314,x27315,x27316,x27317,x27318)+~E(x27311,x27312)+~P50(x27311,x27313,x27314,x27315,x27316,x27317,x27318) % 19.23/19.06 [2732]P50(x27323,x27322,x27324,x27325,x27326,x27327,x27328)+~E(x27321,x27322)+~P50(x27323,x27321,x27324,x27325,x27326,x27327,x27328) % 19.23/19.06 [2733]P50(x27333,x27334,x27332,x27335,x27336,x27337,x27338)+~E(x27331,x27332)+~P50(x27333,x27334,x27331,x27335,x27336,x27337,x27338) % 19.23/19.06 [2734]P50(x27343,x27344,x27345,x27342,x27346,x27347,x27348)+~E(x27341,x27342)+~P50(x27343,x27344,x27345,x27341,x27346,x27347,x27348) % 19.23/19.06 [2735]P50(x27353,x27354,x27355,x27356,x27352,x27357,x27358)+~E(x27351,x27352)+~P50(x27353,x27354,x27355,x27356,x27351,x27357,x27358) % 19.23/19.06 [2736]P50(x27363,x27364,x27365,x27366,x27367,x27362,x27368)+~E(x27361,x27362)+~P50(x27363,x27364,x27365,x27366,x27367,x27361,x27368) % 19.23/19.06 [2737]P50(x27373,x27374,x27375,x27376,x27377,x27378,x27372)+~E(x27371,x27372)+~P50(x27373,x27374,x27375,x27376,x27377,x27378,x27371) % 19.23/19.06 [2738]P12(x27382,x27383,x27384,x27385,x27386)+~E(x27381,x27382)+~P12(x27381,x27383,x27384,x27385,x27386) % 19.23/19.06 [2739]P12(x27393,x27392,x27394,x27395,x27396)+~E(x27391,x27392)+~P12(x27393,x27391,x27394,x27395,x27396) % 19.23/19.06 [2740]P12(x27403,x27404,x27402,x27405,x27406)+~E(x27401,x27402)+~P12(x27403,x27404,x27401,x27405,x27406) % 19.23/19.06 [2741]P12(x27413,x27414,x27415,x27412,x27416)+~E(x27411,x27412)+~P12(x27413,x27414,x27415,x27411,x27416) % 19.23/19.06 [2742]P12(x27423,x27424,x27425,x27426,x27422)+~E(x27421,x27422)+~P12(x27423,x27424,x27425,x27426,x27421) % 19.23/19.06 [2743]P20(x27432,x27433,x27434,x27435)+~E(x27431,x27432)+~P20(x27431,x27433,x27434,x27435) % 19.23/19.06 [2744]P20(x27443,x27442,x27444,x27445)+~E(x27441,x27442)+~P20(x27443,x27441,x27444,x27445) % 19.23/19.06 [2745]P20(x27453,x27454,x27452,x27455)+~E(x27451,x27452)+~P20(x27453,x27454,x27451,x27455) % 19.23/19.06 [2746]P20(x27463,x27464,x27465,x27462)+~E(x27461,x27462)+~P20(x27463,x27464,x27465,x27461) % 19.23/19.06 [2747]P56(x27472,x27473,x27474,x27475)+~E(x27471,x27472)+~P56(x27471,x27473,x27474,x27475) % 19.23/19.06 [2748]P56(x27483,x27482,x27484,x27485)+~E(x27481,x27482)+~P56(x27483,x27481,x27484,x27485) % 19.23/19.06 [2749]P56(x27493,x27494,x27492,x27495)+~E(x27491,x27492)+~P56(x27493,x27494,x27491,x27495) % 19.23/19.06 [2750]P56(x27503,x27504,x27505,x27502)+~E(x27501,x27502)+~P56(x27503,x27504,x27505,x27501) % 19.23/19.06 [2751]~P133(x27511)+P133(x27512)+~E(x27511,x27512) % 19.23/19.06 [2752]P54(x27522,x27523,x27524,x27525,x27526)+~E(x27521,x27522)+~P54(x27521,x27523,x27524,x27525,x27526) % 19.23/19.06 [2753]P54(x27533,x27532,x27534,x27535,x27536)+~E(x27531,x27532)+~P54(x27533,x27531,x27534,x27535,x27536) % 19.23/19.06 [2754]P54(x27543,x27544,x27542,x27545,x27546)+~E(x27541,x27542)+~P54(x27543,x27544,x27541,x27545,x27546) % 19.23/19.06 [2755]P54(x27553,x27554,x27555,x27552,x27556)+~E(x27551,x27552)+~P54(x27553,x27554,x27555,x27551,x27556) % 19.23/19.06 [2756]P54(x27563,x27564,x27565,x27566,x27562)+~E(x27561,x27562)+~P54(x27563,x27564,x27565,x27566,x27561) % 19.23/19.06 [2757]P13(x27572,x27573,x27574,x27575)+~E(x27571,x27572)+~P13(x27571,x27573,x27574,x27575) % 19.23/19.06 [2758]P13(x27583,x27582,x27584,x27585)+~E(x27581,x27582)+~P13(x27583,x27581,x27584,x27585) % 19.23/19.06 [2759]P13(x27593,x27594,x27592,x27595)+~E(x27591,x27592)+~P13(x27593,x27594,x27591,x27595) % 19.23/19.06 [2760]P13(x27603,x27604,x27605,x27602)+~E(x27601,x27602)+~P13(x27603,x27604,x27605,x27601) % 19.23/19.06 [2761]~P132(x27611)+P132(x27612)+~E(x27611,x27612) % 19.23/19.06 [2762]~P119(x27621)+P119(x27622)+~E(x27621,x27622) % 19.23/19.06 [2763]~P93(x27631)+P93(x27632)+~E(x27631,x27632) % 19.23/19.06 [2764]P29(x27642,x27643)+~E(x27641,x27642)+~P29(x27641,x27643) % 19.23/19.06 [2765]P29(x27653,x27652)+~E(x27651,x27652)+~P29(x27653,x27651) % 19.23/19.06 [2766]~P134(x27661)+P134(x27662)+~E(x27661,x27662) % 19.23/19.06 [2767]P45(x27672,x27673,x27674)+~E(x27671,x27672)+~P45(x27671,x27673,x27674) % 19.23/19.06 [2768]P45(x27683,x27682,x27684)+~E(x27681,x27682)+~P45(x27683,x27681,x27684) % 19.23/19.06 [2769]P45(x27693,x27694,x27692)+~E(x27691,x27692)+~P45(x27693,x27694,x27691) % 19.23/19.06 [2770]~P128(x27701)+P128(x27702)+~E(x27701,x27702) % 19.23/19.06 [2771]P24(x27712,x27713,x27714,x27715,x27716,x27717)+~E(x27711,x27712)+~P24(x27711,x27713,x27714,x27715,x27716,x27717) % 19.23/19.06 [2772]P24(x27723,x27722,x27724,x27725,x27726,x27727)+~E(x27721,x27722)+~P24(x27723,x27721,x27724,x27725,x27726,x27727) % 19.23/19.06 [2773]P24(x27733,x27734,x27732,x27735,x27736,x27737)+~E(x27731,x27732)+~P24(x27733,x27734,x27731,x27735,x27736,x27737) % 19.23/19.06 [2774]P24(x27743,x27744,x27745,x27742,x27746,x27747)+~E(x27741,x27742)+~P24(x27743,x27744,x27745,x27741,x27746,x27747) % 19.23/19.06 [2775]P24(x27753,x27754,x27755,x27756,x27752,x27757)+~E(x27751,x27752)+~P24(x27753,x27754,x27755,x27756,x27751,x27757) % 19.23/19.06 [2776]P24(x27763,x27764,x27765,x27766,x27767,x27762)+~E(x27761,x27762)+~P24(x27763,x27764,x27765,x27766,x27767,x27761) % 19.23/19.06 [2777]~P42(x27771)+P42(x27772)+~E(x27771,x27772) % 19.23/19.06 [2778]P23(x27782,x27783,x27784,x27785,x27786,x27787)+~E(x27781,x27782)+~P23(x27781,x27783,x27784,x27785,x27786,x27787) % 19.23/19.06 [2779]P23(x27793,x27792,x27794,x27795,x27796,x27797)+~E(x27791,x27792)+~P23(x27793,x27791,x27794,x27795,x27796,x27797) % 19.23/19.06 [2780]P23(x27803,x27804,x27802,x27805,x27806,x27807)+~E(x27801,x27802)+~P23(x27803,x27804,x27801,x27805,x27806,x27807) % 19.23/19.06 [2781]P23(x27813,x27814,x27815,x27812,x27816,x27817)+~E(x27811,x27812)+~P23(x27813,x27814,x27815,x27811,x27816,x27817) % 19.23/19.06 [2782]P23(x27823,x27824,x27825,x27826,x27822,x27827)+~E(x27821,x27822)+~P23(x27823,x27824,x27825,x27826,x27821,x27827) % 19.23/19.06 [2783]P23(x27833,x27834,x27835,x27836,x27837,x27832)+~E(x27831,x27832)+~P23(x27833,x27834,x27835,x27836,x27837,x27831) % 19.23/19.06 [2784]~P107(x27841)+P107(x27842)+~E(x27841,x27842) % 19.23/19.06 [2785]~P141(x27851)+P141(x27852)+~E(x27851,x27852) % 19.23/19.06 [2786]~P84(x27861)+P84(x27862)+~E(x27861,x27862) % 19.23/19.06 [2787]~P34(x27871)+P34(x27872)+~E(x27871,x27872) % 19.23/19.06 [2788]~P102(x27881)+P102(x27882)+~E(x27881,x27882) % 19.23/19.06 [2789]~P73(x27891)+P73(x27892)+~E(x27891,x27892) % 19.23/19.06 [2790]~P97(x27901)+P97(x27902)+~E(x27901,x27902) % 19.23/19.06 [2791]P53(x27912,x27913,x27914)+~E(x27911,x27912)+~P53(x27911,x27913,x27914) % 19.23/19.06 [2792]P53(x27923,x27922,x27924)+~E(x27921,x27922)+~P53(x27923,x27921,x27924) % 19.23/19.06 [2793]P53(x27933,x27934,x27932)+~E(x27931,x27932)+~P53(x27933,x27934,x27931) % 19.23/19.06 [2794]P51(x27942,x27943,x27944,x27945)+~E(x27941,x27942)+~P51(x27941,x27943,x27944,x27945) % 19.23/19.06 [2795]P51(x27953,x27952,x27954,x27955)+~E(x27951,x27952)+~P51(x27953,x27951,x27954,x27955) % 19.23/19.06 [2796]P51(x27963,x27964,x27962,x27965)+~E(x27961,x27962)+~P51(x27963,x27964,x27961,x27965) % 19.23/19.06 [2797]P51(x27973,x27974,x27975,x27972)+~E(x27971,x27972)+~P51(x27973,x27974,x27975,x27971) % 19.23/19.06 [2798]P36(x27982,x27983)+~E(x27981,x27982)+~P36(x27981,x27983) % 19.23/19.06 [2799]P36(x27993,x27992)+~E(x27991,x27992)+~P36(x27993,x27991) % 19.23/19.06 [2800]P39(x28002,x28003,x28004,x28005)+~E(x28001,x28002)+~P39(x28001,x28003,x28004,x28005) % 19.23/19.06 [2801]P39(x28013,x28012,x28014,x28015)+~E(x28011,x28012)+~P39(x28013,x28011,x28014,x28015) % 19.23/19.06 [2802]P39(x28023,x28024,x28022,x28025)+~E(x28021,x28022)+~P39(x28023,x28024,x28021,x28025) % 19.23/19.06 [2803]P39(x28033,x28034,x28035,x28032)+~E(x28031,x28032)+~P39(x28033,x28034,x28035,x28031) % 19.23/19.06 [2804]P22(x28042,x28043,x28044,x28045,x28046)+~E(x28041,x28042)+~P22(x28041,x28043,x28044,x28045,x28046) % 19.23/19.06 [2805]P22(x28053,x28052,x28054,x28055,x28056)+~E(x28051,x28052)+~P22(x28053,x28051,x28054,x28055,x28056) % 19.23/19.06 [2806]P22(x28063,x28064,x28062,x28065,x28066)+~E(x28061,x28062)+~P22(x28063,x28064,x28061,x28065,x28066) % 19.23/19.06 [2807]P22(x28073,x28074,x28075,x28072,x28076)+~E(x28071,x28072)+~P22(x28073,x28074,x28075,x28071,x28076) % 19.23/19.06 [2808]P22(x28083,x28084,x28085,x28086,x28082)+~E(x28081,x28082)+~P22(x28083,x28084,x28085,x28086,x28081) % 19.23/19.06 [2809]~P94(x28091)+P94(x28092)+~E(x28091,x28092) % 19.23/19.06 [2810]~P83(x28101)+P83(x28102)+~E(x28101,x28102) % 19.23/19.06 [2811]~P66(x28111)+P66(x28112)+~E(x28111,x28112) % 19.23/19.06 [2812]~P108(x28121)+P108(x28122)+~E(x28121,x28122) % 19.23/19.06 [2813]P11(x28132,x28133,x28134)+~E(x28131,x28132)+~P11(x28131,x28133,x28134) % 19.23/19.06 [2814]P11(x28143,x28142,x28144)+~E(x28141,x28142)+~P11(x28143,x28141,x28144) % 19.23/19.06 [2815]P11(x28153,x28154,x28152)+~E(x28151,x28152)+~P11(x28153,x28154,x28151) % 19.23/19.06 % 19.23/19.06 %------------------------------------------- % 19.23/19.07 cnf(10050,plain, % 19.23/19.07 (E(f39(x100501,x100502,x100503,x100504,x100505,x100506,x100507,x100508,x100509,a25),x100502)), % 19.23/19.07 inference(rename_variables,[],[4350])). % 19.23/19.07 cnf(10053,plain, % 19.23/19.07 (E(f39(x100531,x100532,x100533,x100534,x100535,x100536,x100537,x100538,x100539,a25),x100532)), % 19.23/19.07 inference(rename_variables,[],[4350])). % 19.23/19.07 cnf(10056,plain, % 19.23/19.07 (~E(f341(a121,x100561),x100561)), % 19.23/19.07 inference(rename_variables,[],[4378])). % 19.23/19.07 cnf(10059,plain, % 19.23/19.07 (E(f39(x100591,x100592,x100593,x100594,x100595,x100596,x100597,x100598,x100599,a25),x100592)), % 19.23/19.07 inference(rename_variables,[],[4350])). % 19.23/19.07 cnf(10066,plain, % 19.23/19.07 (~E(f341(a121,x100661),x100661)), % 19.23/19.07 inference(rename_variables,[],[4378])). % 19.23/19.07 cnf(10077,plain, % 19.23/19.07 (~E(f341(a121,x100771),x100771)), % 19.23/19.07 inference(rename_variables,[],[4378])). % 19.23/19.07 cnf(10080,plain, % 19.23/19.07 (~P85(f341(f72(x100801,x100802,f185(f864(x100801,a850))),x100803))), % 19.23/19.07 inference(rename_variables,[],[4490])). % 19.23/19.07 cnf(10083,plain, % 19.23/19.07 (~P85(f341(f72(x100831,x100832,f185(f864(x100831,a850))),x100833))), % 19.23/19.07 inference(rename_variables,[],[4490])). % 19.23/19.07 cnf(10086,plain, % 19.23/19.07 (~E(f341(a121,x100861),x100861)), % 19.23/19.07 inference(rename_variables,[],[4378])). % 19.23/19.07 cnf(10089,plain, % 19.23/19.07 (~P85(f341(f341(f242(a857),x100891),f2(a857)))), % 19.23/19.07 inference(rename_variables,[],[4466])). % 19.23/19.07 cnf(10092,plain, % 19.23/19.07 (~P85(f341(f341(f242(a857),x100921),f2(a857)))), % 19.23/19.07 inference(rename_variables,[],[4466])). % 19.23/19.07 cnf(10109,plain, % 19.23/19.07 (~P85(f341(f341(f241(a857),f341(a121,x101091)),x101091))), % 19.23/19.07 inference(rename_variables,[],[4475])). % 19.23/19.07 cnf(10112,plain, % 19.23/19.07 (~E(f341(f341(f146(x101121),x101122),x101123),x101123)), % 19.23/19.07 inference(rename_variables,[],[4412])). % 19.23/19.07 cnf(10115,plain, % 19.23/19.07 (~E(f341(f341(f341(f81(x101151,f861(x101152)),x101153),x101154),f341(f235(x101152),x101155)),f341(f18(f861(x101152),x101151),f188(x101152)))), % 19.23/19.07 inference(rename_variables,[],[4487])). % 19.23/19.07 cnf(10121,plain, % 19.23/19.07 (~P85(f341(f341(f242(a857),x101211),f2(a857)))), % 19.23/19.07 inference(rename_variables,[],[4466])). % 19.23/19.07 cnf(10124,plain, % 19.23/19.07 (E(f39(x101241,x101242,x101243,x101244,x101245,x101246,x101247,x101248,x101249,a25),x101242)), % 19.23/19.07 inference(rename_variables,[],[4350])). % 19.23/19.07 cnf(10127,plain, % 19.23/19.07 (E(f39(x101271,x101272,x101273,x101274,x101275,x101276,x101277,x101278,x101279,a25),x101272)), % 19.23/19.07 inference(rename_variables,[],[4350])). % 19.23/19.07 cnf(10134,plain, % 19.23/19.07 (~P85(f341(f341(f242(a857),f341(f341(f89(a857),x101341),x101342)),x101342))), % 19.23/19.07 inference(rename_variables,[],[4491])). % 19.23/19.07 cnf(10137,plain, % 19.23/19.07 (~P85(f341(f341(f242(a857),f341(f341(f89(a857),x101371),x101372)),x101372))), % 19.23/19.07 inference(rename_variables,[],[4491])). % 19.23/19.07 cnf(10158,plain, % 19.23/19.07 (~P85(f341(f341(f242(a857),x101581),x101581))), % 19.23/19.07 inference(rename_variables,[],[4462])). % 19.23/19.07 cnf(10161,plain, % 19.23/19.07 (P85(f341(f341(f241(a857),f60(a857,x101611,x101612)),x101611))), % 19.23/19.07 inference(rename_variables,[],[3651])). % 19.23/19.07 cnf(10180,plain, % 19.23/19.07 (E(f341(f50(a857),f341(f266(a857),x101801)),x101801)), % 19.23/19.07 inference(rename_variables,[],[3096])). % 19.23/19.07 cnf(10188,plain, % 19.23/19.07 (~E(f341(a121,x101881),x101881)), % 19.23/19.07 inference(rename_variables,[],[4378])). % 19.23/19.07 cnf(10191,plain, % 19.23/19.07 (~E(f341(a121,x101911),x101911)), % 19.23/19.07 inference(rename_variables,[],[4378])). % 19.23/19.07 cnf(10194,plain, % 19.23/19.07 (~E(f341(a121,x101941),x101941)), % 19.23/19.07 inference(rename_variables,[],[4378])). % 19.23/19.07 cnf(10199,plain, % 19.23/19.07 (P85(f341(f341(f242(a857),x101991),f341(a121,x101991)))), % 19.23/19.07 inference(rename_variables,[],[3265])). % 19.23/19.07 cnf(10202,plain, % 19.23/19.07 (P85(f341(f341(f242(a857),x102021),f341(a121,x102021)))), % 19.23/19.07 inference(rename_variables,[],[3265])). % 19.23/19.07 cnf(10211,plain, % 19.23/19.07 (P85(f341(f341(f192(a25),x102111),x102111))), % 19.23/19.07 inference(rename_variables,[],[3195])). % 19.23/19.07 cnf(10218,plain, % 19.23/19.07 (E(f39(x102181,x102182,x102183,x102184,x102185,x102186,x102187,x102188,x102189,a25),x102182)), % 19.23/19.07 inference(rename_variables,[],[4350])). % 19.23/19.07 cnf(10221,plain, % 19.23/19.07 (E(f39(x102211,x102212,x102213,x102214,x102215,x102216,x102217,x102218,x102219,a25),x102212)), % 19.23/19.07 inference(rename_variables,[],[4350])). % 19.23/19.07 cnf(10246,plain, % 19.23/19.07 (~P85(f341(f341(f242(a857),x102461),x102461))), % 19.23/19.07 inference(rename_variables,[],[4462])). % 19.23/19.07 cnf(10283,plain, % 19.23/19.07 (~E(f341(a29,x102831),f30(x102832,x102833))), % 19.28/19.07 inference(rename_variables,[],[4396])). % 19.28/19.07 cnf(10296,plain, % 19.28/19.07 (P85(f341(f341(f241(a1),x102961),x102961))), % 19.28/19.07 inference(rename_variables,[],[3197])). % 19.28/19.07 cnf(10299,plain, % 19.28/19.07 (~E(f341(a121,x102991),x102991)), % 19.28/19.07 inference(rename_variables,[],[4378])). % 19.28/19.07 cnf(10306,plain, % 19.28/19.07 (P85(f341(f341(f192(a25),x103061),x103061))), % 19.28/19.07 inference(rename_variables,[],[3195])). % 19.28/19.07 cnf(10315,plain, % 19.28/19.07 (P85(f341(f341(f242(a857),x103151),f341(a121,x103151)))), % 19.28/19.07 inference(rename_variables,[],[3265])). % 19.28/19.07 cnf(10320,plain, % 19.28/19.07 (E(f341(f341(f132(x103201),f122(x103201)),x103202),x103202)), % 19.28/19.07 inference(rename_variables,[],[3151])). % 19.28/19.07 cnf(10357,plain, % 19.28/19.07 (~P85(f341(f341(f242(a857),x103571),x103571))), % 19.28/19.07 inference(rename_variables,[],[4462])). % 19.28/19.07 cnf(10387,plain, % 19.28/19.07 (~P85(f341(f341(f242(a857),x103871),x103871))), % 19.28/19.07 inference(rename_variables,[],[4462])). % 19.28/19.07 cnf(10392,plain, % 19.28/19.07 (P85(f341(f341(f242(a857),x103921),f341(a121,x103921)))), % 19.28/19.07 inference(rename_variables,[],[3265])). % 19.28/19.07 cnf(10405,plain, % 19.28/19.07 (~E(f341(a121,x104051),x104051)), % 19.28/19.07 inference(rename_variables,[],[4378])). % 19.28/19.07 cnf(10410,plain, % 19.28/19.07 (E(f341(f341(f341(f100(x104101),f605(x104101,x104102)),f804(x104101,x104102)),f815(x104101,x104102)),x104102)), % 19.28/19.07 inference(rename_variables,[],[3499])). % 19.28/19.07 cnf(10413,plain, % 19.28/19.07 (E(f341(f341(f341(f100(x104131),f605(x104131,x104132)),f804(x104131,x104132)),f815(x104131,x104132)),x104132)), % 19.28/19.07 inference(rename_variables,[],[3499])). % 19.28/19.07 cnf(10439,plain, % 19.28/19.07 (P85(f341(f341(f192(a25),x104391),x104391))), % 19.28/19.07 inference(rename_variables,[],[3195])). % 19.28/19.07 cnf(10442,plain, % 19.28/19.07 (P85(f341(f341(f242(a857),x104421),f341(a121,f341(f341(f89(a857),x104422),x104421))))), % 19.28/19.07 inference(rename_variables,[],[3644])). % 19.28/19.07 cnf(10445,plain, % 19.28/19.07 (P85(f341(f341(f241(a857),x104451),f341(f341(f90(a857),x104451),x104451)))), % 19.28/19.07 inference(rename_variables,[],[3468])). % 19.28/19.07 cnf(10448,plain, % 19.28/19.07 (P85(f341(f341(f241(a857),x104481),f341(f341(f90(a857),x104481),x104481)))), % 19.28/19.07 inference(rename_variables,[],[3468])). % 19.28/19.07 cnf(10453,plain, % 19.28/19.07 (P85(f341(f341(f242(a857),x104531),f341(a121,x104531)))), % 19.28/19.07 inference(rename_variables,[],[3265])). % 19.28/19.07 cnf(10456,plain, % 19.28/19.07 (P85(f341(f341(f242(a857),x104561),f341(a121,x104561)))), % 19.28/19.07 inference(rename_variables,[],[3265])). % 19.28/19.07 cnf(10459,plain, % 19.28/19.07 (P85(f341(f341(f343(x104591),x104592),f248(f864(x104591,a850))))), % 19.28/19.07 inference(rename_variables,[],[3352])). % 19.28/19.07 cnf(10472,plain, % 19.28/19.07 (~P85(f341(f341(f242(a857),f341(f341(f89(a857),x104721),x104722)),x104722))), % 19.28/19.07 inference(rename_variables,[],[4491])). % 19.28/19.07 cnf(10478,plain, % 19.28/19.07 (~P85(f341(f341(f241(a857),f341(a121,x104781)),x104781))), % 19.28/19.07 inference(rename_variables,[],[4475])). % 19.28/19.07 cnf(10481,plain, % 19.28/19.07 (~P85(f341(f341(f241(a857),f341(a121,x104811)),x104811))), % 19.28/19.07 inference(rename_variables,[],[4475])). % 19.28/19.07 cnf(10484,plain, % 19.28/19.07 (P85(f341(f248(f864(x104841,a850)),x104842))), % 19.28/19.07 inference(rename_variables,[],[3259])). % 19.28/19.07 cnf(10490,plain, % 19.28/19.07 (P85(f341(f341(f242(a857),x104901),f341(a121,x104901)))), % 19.28/19.07 inference(rename_variables,[],[3265])). % 19.28/19.07 cnf(10502,plain, % 19.28/19.07 (P85(f341(f341(f241(a1),x105021),x105021))), % 19.28/19.07 inference(rename_variables,[],[3197])). % 19.28/19.07 cnf(10511,plain, % 19.28/19.07 (E(f39(x105111,x105112,x105113,x105114,x105115,x105116,x105117,x105118,x105119,a25),x105112)), % 19.28/19.07 inference(rename_variables,[],[4350])). % 19.28/19.07 cnf(10517,plain, % 19.28/19.07 (P85(f341(f341(f241(a857),x105171),f341(f341(f90(a857),x105171),x105171)))), % 19.28/19.07 inference(rename_variables,[],[3468])). % 19.28/19.07 cnf(10557,plain, % 19.28/19.07 (P85(f341(f341(f241(a857),x105571),x105571))), % 19.28/19.07 inference(rename_variables,[],[3196])). % 19.28/19.07 cnf(10579,plain, % 19.28/19.07 (P85(f341(f341(f242(a857),x105791),f341(a121,x105791)))), % 19.28/19.07 inference(rename_variables,[],[3265])). % 19.28/19.07 cnf(10582,plain, % 19.28/19.07 (~E(f341(a121,x105821),x105821)), % 19.28/19.07 inference(rename_variables,[],[4378])). % 19.28/19.07 cnf(10585,plain, % 19.28/19.07 (P85(f341(f341(f241(a1),x105851),x105851))), % 19.28/19.07 inference(rename_variables,[],[3197])). % 19.28/19.07 cnf(10590,plain, % 19.28/19.07 (~P85(f341(f341(f242(a857),x105901),f2(a857)))), % 19.28/19.07 inference(rename_variables,[],[4466])). % 19.28/19.07 cnf(10605,plain, % 19.28/19.07 (~P85(f341(f341(f242(a857),x106051),f2(a857)))), % 19.28/19.07 inference(rename_variables,[],[4466])). % 19.28/19.07 cnf(10611,plain, % 19.28/19.07 (P85(f341(f341(f241(a857),x106111),x106111))), % 19.28/19.07 inference(rename_variables,[],[3196])). % 19.28/19.07 cnf(10614,plain, % 19.28/19.07 (P85(f341(f341(f241(a857),x106141),x106141))), % 19.28/19.07 inference(rename_variables,[],[3196])). % 19.28/19.07 cnf(10629,plain, % 19.28/19.07 (~P85(f341(f341(f242(a857),x106291),x106291))), % 19.28/19.07 inference(rename_variables,[],[4462])). % 19.28/19.07 cnf(10638,plain, % 19.28/19.07 (~P85(f341(f341(f343(x106381),x106382),f185(f864(x106381,a850))))), % 19.28/19.07 inference(rename_variables,[],[4478])). % 19.28/19.07 cnf(10647,plain, % 19.28/19.07 (P85(f341(f341(f241(a857),x106471),x106471))), % 19.28/19.07 inference(rename_variables,[],[3196])). % 19.28/19.07 cnf(10650,plain, % 19.28/19.07 (~P85(f341(f341(f343(x106501),x106502),f185(f864(x106501,a850))))), % 19.28/19.07 inference(rename_variables,[],[4478])). % 19.28/19.07 cnf(10653,plain, % 19.28/19.07 (P85(f341(f341(f288(a857),x106531),x106531))), % 19.28/19.07 inference(rename_variables,[],[3198])). % 19.28/19.07 cnf(10663,plain, % 19.28/19.07 (P85(f341(f341(f241(f864(x106631,a850)),f341(f163(x106631),f341(f133(x106631,x106632),x106633))),f341(f163(x106631),x106633)))), % 19.28/19.07 inference(rename_variables,[],[3839])). % 19.28/19.07 cnf(10671,plain, % 19.28/19.07 (P85(f341(f341(f241(a857),f2(a857)),x106711))), % 19.28/19.07 inference(rename_variables,[],[3218])). % 19.28/19.07 cnf(10674,plain, % 19.28/19.07 (P85(f341(f341(f241(a857),x106741),x106741))), % 19.28/19.07 inference(rename_variables,[],[3196])). % 19.28/19.07 cnf(10677,plain, % 19.28/19.07 (~P85(f341(f341(f242(a857),x106771),x106771))), % 19.28/19.07 inference(rename_variables,[],[4462])). % 19.28/19.07 cnf(10698,plain, % 19.28/19.07 (P85(f341(f341(f241(a857),x106981),f341(f341(f90(a857),x106981),x106981)))), % 19.28/19.07 inference(rename_variables,[],[3468])). % 19.28/19.07 cnf(10708,plain, % 19.28/19.07 (P85(f341(f341(f241(a857),x107081),x107081))), % 19.28/19.07 inference(rename_variables,[],[3196])). % 19.28/19.07 cnf(10722,plain, % 19.28/19.07 (P85(f341(f341(f343(x107221),x107222),f248(f864(x107221,a850))))), % 19.28/19.07 inference(rename_variables,[],[3352])). % 19.28/19.07 cnf(10752,plain, % 19.28/19.07 (P85(f341(f341(f241(a857),x107521),x107521))), % 19.28/19.07 inference(rename_variables,[],[3196])). % 19.28/19.07 cnf(10759,plain, % 19.28/19.07 (~P85(f341(f341(f343(x107591),x107592),f185(f864(x107591,a850))))), % 19.28/19.07 inference(rename_variables,[],[4478])). % 19.28/19.07 cnf(10767,plain, % 19.28/19.07 (P85(f341(f341(f343(x107671),x107672),f248(f864(x107671,a850))))), % 19.28/19.07 inference(rename_variables,[],[3352])). % 19.28/19.07 cnf(10777,plain, % 19.28/19.07 (~P85(f341(f341(f343(x107771),x107772),f185(f864(x107771,a850))))), % 19.28/19.07 inference(rename_variables,[],[4478])). % 19.28/19.07 cnf(10783,plain, % 19.28/19.07 (P85(f341(f341(f241(f864(x107831,a850)),x107832),f341(f341(f311(x107831),x107833),x107832)))), % 19.28/19.07 inference(rename_variables,[],[3639])). % 19.28/19.07 cnf(10789,plain, % 19.28/19.07 (P85(f341(f341(f241(f864(x107891,a850)),x107892),f341(f341(f311(x107891),x107893),x107892)))), % 19.28/19.07 inference(rename_variables,[],[3639])). % 19.28/19.07 cnf(10804,plain, % 19.28/19.07 ($false), % 19.28/19.07 inference(scs_inference,[],[4486,4350,10050,10053,10059,10124,10127,10218,10221,10511,4378,10056,10066,10077,10086,10188,10191,10194,10299,10405,10582,4396,10283,4390,3499,10410,10413,3039,3099,3064,3046,3255,3132,3151,10320,4487,10115,4412,10112,3096,10180,3975,3829,4495,3115,3394,3558,3504,3709,3265,10199,10202,10315,10392,10453,10456,10490,10579,3646,4466,10089,10092,10121,10590,10605,4482,3631,3404,3783,3224,3226,3199,4463,4406,3936,3839,10663,3559,3925,4488,3195,10211,10306,10439,3196,10557,10611,10614,10647,10674,10708,10752,3197,10296,10502,10585,3198,10653,4462,10158,10246,10357,10387,10629,10677,3352,10459,10722,10767,4478,10638,10650,10759,10777,3259,10484,3291,3715,3651,10161,4475,10109,10478,10481,3218,10671,4020,4473,3723,4454,4455,4457,3174,3175,4456,4458,4490,10080,10083,3800,3639,10783,10789,3468,10445,10448,10517,10698,4493,4494,4079,3674,4491,10134,10137,10472,3644,10442,3910,4506,4511,4517,4579,4581,4609,4627,4634,4635,4671,4700,4706,4810,4811,4848,4871,4872,4895,4897,4910,4914,4934,4940,4957,4961,4962,4963,4968,4973,4974,4996,5020,5021,5031,5036,5042,5086,5087,5095,5104,5106,5107,5116,5118,5125,5130,5143,5149,5152,5153,5157,5189,5199,5206,5208,5209,5212,5213,5214,5222,5223,5226,5230,5231,5232,5238,5242,5243,5244,5252,5255,5257,5263,5274,5281,5294,5296,5304,5305,5309,5312,5338,5344,5354,5355,5356,5371,5383,5405,5411,5429,5430,5433,5452,5460,5461,5463,5464,5473,5474,5487,5491,5500,5501,5503,5518,5522,5533,5544,5551,5564,5570,5576,5577,5578,5581,5586,5623,5625,5628,5630,5633,5634,5635,5637,5639,5641,5644,5651,5665,5679,5685,5686,5705,5706,5711,5712,5714,5717,5720,5721,5726,5770,5784,5792,5796,5808,5818,5836,5854,5857,5867,5894,5909,5931,5932,5933,5935,5955,5956,5959,5972,5974,5975,5977,5990,5991,5994,5996,5999,6000,6014,6020,6021,6022,6025,6027,6069,6079,6088,6123,6125,6127,6129,6139,6141,6144,6150,6152,6156,6159,6167,6174,6175,6176,6182,6208,6215,6222,6257,6258,6262,6263,6264,6265,6266,6267,6268,6275,6312,6313,6322,6342,6343,6368,6372,6383,6384,6392,6423,6424,6439,6461,6462,6481,6483,6484,6530,6538,6563,6603,6619,6628,6637,6638,6639,6640,6661,6662,6668,6680,6683,6686,6688,6689,6690,6692,6706,6719,6721,6722,6733,6736,6792,6805,6807,6813,6827,6830,6831,6868,6883,6911,6943,6993,7024,7081,7108,7111,7169,7181,7248,7250,7265,7275,7278,7279,7297,7303,7305,7358,7368,7374,7377,7390,7434,7437,7441,7488,7489,7507,7570,7577,7596,7620,7642,7656,7672,7681,7689,7718,7720,7722,7730,7774,7784,7809,7867,7899,7933,7978,7993,8080,8127,8145,8169,8188,8210,8292]), % 19.28/19.07 ['proof']). % 19.28/19.07 % SZS output end Proof % 19.28/19.07 % Total time :1.690000s %------------------------------------------------------------------------------